Michael Ruderman

• Kopfova, Jana & Ruderman, Michael (2026). On Cauchy problem and stability of inversion-free feedforward control of piecewise monotonic Krasnoselskii-Pokrovskii hysteresis. Physica. B, Condensed matter. ISSN 0921-4526. 742. doi: 10.1016/j.physb.2026.419252. Fulltekst i vitenarkiv Vis sammendrag

  We consider the non-homogeneous first-order differential equation with hysteresis described by the Krasnoselskii-Pokrovskii (KP) rate-independent hysteresis operator. Existence and uniqueness of solutions as well as the boundedness of solutions in response to a bounded input are proved. The global stability of the non-homogeneous equation is also investigated. Periodic solutions and their stability are also studied. The differential equation under analysis constitutes the so-called inversion-free feedforward control, which was proposed for mitigating arbitrary rate-independent hysteresis effects in the actuated systems. The experimentally identified non-smooth and non-strictly monotonic hysteresis of a magnetic shape memory alloy (MSMA) actuator serves as a motivating case study. The performed analysis is settled in a series of theorems which are then illustrated by numerical examples.

• Ruderman, Michael; Brescia, Elia; Massenio, Paolo; Cascella, Giuseppe Leonardo & Naso, David (2026). Robust Synchronous Reference Frame Phase-Locked Loop (PLL) with Feed-Forward Frequency Estimation. IEEE Transactions on Control Systems Technology. ISSN 1063-6536. 34, s. 1–8. doi: https:/ieeexplore.ieee.org/document/11558572. Fulltekst i vitenarkiv Vis sammendrag

  Synchronous reference frame phase-locked loop (SRF-PLL) techniques are widely used for interfacing and control applications in the power systems and energy conversion at large. Since a PLL system synchronizes its output with an exogenous harmonic signal, often 3-phases voltage or current, the locking of both the frequency and phase angle depends on the performance of the feedback loop with at least two integrator terms, and on the distortions of the measured input quantities as well. For the conventional SRF-PLL with a proportional-integral (PI) control in feedback, we are providing a robust design which maximizes the phase margin and uses the normalization scheme for yielding the loop insensitive to the input amplitude variations. The main improvement in the transient behavior and also in tracking of frequency ramps is achieved by using the robust feed-forward frequency estimator, which is model-free and suitable for the noisy and time-varying harmonic signals. The proposed feed-forward-feedback SRF-PLL scheme is experimentally evaluated on the 3-phases harmonic currents from a standard PMSM drive with the varying angular speeds and loads. Both, the tracked angular frequency and locked phase angle are assessed as performance indicators of the presented SRF-PLL with and without feedforwarding.

• Pavlov, Alexey & Ruderman, Michael (2026). Adaptive differentiating filter: case study of PID feedback control. IEEE 34th Mediterranean Conference on Control and Automation (MED2026). s. 1–6. doi: https:/ieeexplore.ieee.org/document/11598013. Fulltekst i vitenarkiv Vis sammendrag

  This paper introduces an adaptive causal discrete‑time filter for derivative estimation, exemplified by its use in estimating the relative velocity in a mechatronic application. The filter is based on a constrained least-squares estimator with window adaptation. It demonstrates low sensitivity to low-amplitude measurement noise, while preserving a broad bandwidth for large-amplitude changes in the process signal. Favorable performance properties of the filter are discussed and demonstrated in a practical case study of PID feedback controller and compared experimentally to a standard linear low-pass filter-based differentiator and a robust sliding-mode based homogeneous differentiator.

• Ruderman, Michael (2026). Analysis and extensions of control-oriented hydraulic actuator model. IEEE 34th Mediterranean Conference on Control and Automation (MED2026). s. 1–6. doi: https:/ieeexplore.ieee.org/document/11598553. Fulltekst i vitenarkiv Vis sammendrag

  In this paper, some structure- and physics-based limitations of a standard control-oriented modeling of hydraulic cylinder-driven actuators are analyzed and discussed, and possible extensions to bypass them are provided. While using a lumped-parameter signals-oriented modeling approach, we describe the transfer elements and subsystems, both in linear and nonlinear way, while a valve-controlled hydraulic servo system with the output displacement of the loaded cylinder rod can be seen in an input-output modeling paradigm. In particular, we provide the extensions for: sign-dependent pressure gradients in the orifice equations, smoothing dead-zone nonlinearity in the controlled servo valve, incorporating presliding into the force-velocity friction map, and capturing the mechanical motion boundaries at both end-caps of the cylinder stroke. Moreover, several important linearized transfer characteristic properties are complementary addressed, being essential for any feedback control design for such hydraulic actuators. Specifically measured and monitored experimental features from a hydraulic laboratory test bench are also demonstrated and highlighted along with the explanatory characteristic maps and graphs.

• Diepeveen, Jullian; Pavlov, Alexey; Steur, Erik & Ruderman, Michael (2026). Study of advanced motion controllers adapted for a safety-critical drilling process. 23rd IFAC World Congress. s. 1719–1724. Fulltekst i vitenarkiv Vis sammendrag

  The so-called gas kick scenario is a complex time-varying nonlinear and, most importantly, safety-critical dynamic process during drilling operations. It requires advanced pressure regulation on the top of the drilling system without whole sensing of the well-process variables. Adapted from the available advanced motion controllers, i.e. HIGS and nonlinear integral gain control, the nonlinear control architectures are proposed for standpipe pressure control in a well killing procedure. The proposed controllers use a nested structure with a feedback linearized inner PID-loop and extends the usual outer PI-loop for the standpipe pressure. The control performance is analyzed through the use of a high fidelity simulator (OpenLab), showing improvements of the overall control behavior for well killing procedures.

• Ruderman, Michael (2026). Model-free practical PI-Lead control design by ultimate sensitivity principle. 23rd IFAC World Congress. s. 5617–5622. doi: 10.48550/arXiv.2511.21641. Fulltekst i vitenarkiv Vis sammendrag

  Practical design and tuning of feedback controllers has to do often without any model of the given dynamic process. Only some general assumptions about the process, in this work type-one stable behavior, can be available for engineers, in particular in motion control systems. This paper proposes a practical and simple in realization procedure for designing a robust PI-Lead control without modeling. The developed method derives from the ultimate sensitivity principles, known in the empirical Ziegler-Nichols tuning of PID control, and makes use of some general characteristics of loop shaping. A three-steps procedure is proposed to determine the integration time constant, control gain, and Lead-element in a way to guarantee a sufficient phase margin, while all steps are served by only experimental observations of the output value. The proposed method is also evaluated with experiments on a noise-perturbed electro-mechanical actuator system with translational motion.

• Ruderman, Michael & Efimov, Denis (2026). Modified global finite-time quasi-continuous second-order robust feedback control. 23rd IFAC World Congress. s. 9324–9329. doi: 10.48550/arXiv.2512.05727. Fulltekst i vitenarkiv Vis sammendrag

  A non-overshooting quasi-continuous sliding mode control with sub-optimal damping was recently introduced in Ruderman and Efimov (2025) for perturbed second-order systems. The present work proposes an essential modification of the nonlinear control law which (i) allows for a parameterizable control amplitude limitation in a large subset of the initial values, (ii) admits an entire state-space R2 (that was not given in Ruderman and Efimov (2025)) for the finite-time control, and finally (iii) enables for the found analytic solution of the state trajectories in the unperturbed case. The latter allows also for an exact estimation of the finite convergence time, and open an avenue for other potentially interesting analysis of the control properties in the future. For a perturbed case, the solution-based and Lyapunov function-based approaches are developed to show the uniform global asymptotic stability. The proposed robustness and convergence analysis are accompanied by several illustrative numerical examples.

• Ruderman, Michael; Rehan, Ahmed & Boiko, Igor (2026). On chattering in conventional and terminal sliding-mode control. IEEE 18th International Workshop on Variable Structure Systems (VSS2026). s. 1–6. Fulltekst i vitenarkiv Vis sammendrag

  We consider the well-known phenomenon in non-ideal sliding-modes, called chattering, which always appears in (physical) systems due to some unaccounted dynamics, for instance when having inherent sensor and actuator elements in the loop. Moreover, any signal’s transport or/and sampling provide an additional phase lag which can render the relative degree to be higher than two, thus allowing for a harmonic balance solution to exist, and so chattering. Two methods, the describing function (DF) and the locus of a perturbed relay system (LPRS), are used for examine chattering. Our focus is to compare, building up the analysis from previous works, to which extent the chattering is appearing in conventional (i.e. linear) versus the so-called terminal sliding surface design. For the purpose of the latter, we perform linearization at the origin and show how the corresponding loop transfer function varies in gain and affects the harmonic balance solution. The paper reports a detailed experimental case, showing which chattering level can appear and why, especially in light of a not measurable output’s derivative required for sliding surface, unaccounted delay and sensor noise. Here DF is used to qualitatively justify chattering, while LPRS delivers its prediction with sufficiently accuracy. For the sake of a better exposition of the transient and steady-state responses, the SMC control with both linear and terminal surfaces are also compared with a loop-optimized standard PID control.

• Rachinskii, Dmitrii; Ruderman, Michael & Zagvozdkin, Andrei (2026). Dynamics of a 3D leader-follower system coupled via friction interface. Mathematics in Engineering. 8(3), s. 340–367. doi: 10.3934/mine.2026011. Fulltekst i vitenarkiv Vis sammendrag

  We consider dynamics of an oscillatory mechanical system with 1.5 degrees of freedom. The system consists of two linear subsystems, a leader and a follower, which are coupled via a kinetic friction interface, and additionally driven by a proportional control term. The kinetic friction model accounts for the Coulomb friction and the Stribeck effect (as negative damping) at the passage from zero to nonzero relative velocity. The equations of motion are equivalent to a Lur’e system with a single sign nonlinearity. We show that at a critical value of the parameter the zero steady state blows up into an attracting continuum (segment) of equilibrium states. Moreover, two antipodal small-amplitude periodic orbits bifurcate from the end points of the segment of equilibrium states, creating stick-slip vibrations. We consider other possible attractors consisting of stick-slip solutions of the Lur’e system such as a Z2-symmetric stick-slip periodic orbit and an attractor composed of a continuum of heteroclinic loops representing stick-slip motions towards a steady state.

• Massenio, Paolo Roberto; Ruderman, Michael; Brescia, Elia; Savastio, Luigi Pio; Rizzello, Gianluca & Naso, David (2026). LMI-based Robust Design of Back-EMF Observer with PLL in the Loop. IEEE Conference on Advanced Motion Control. Proceedings. doi: https:/ieeexplore.ieee.org/document/11435821. Fulltekst i vitenarkiv Vis sammendrag

  This paper presents a gain-scheduled robust back-EMF observer integrated into a quadrature phase-locked loop (QPLL) framework for rotor speed and position estimation in permanent-magnet synchronous motors (PMSMs). While conventional QPLL schemes often employ fixed-gain Luenberger observers tuned at a nominal speed for the back-EMF estimation, their performance deteriorates under varying operating conditions due to speed-dependent observer dynamics. The proposed method overcomes this limitation by scheduling the observer gains as an affine function of the electrical speed and synthesizing them via a Linear Parameter–Varying (LPV) formulation solved through Linear Matrix Inequality (LMI) optimization. By constraining the closed-loop poles within a predefined LMI region, the design ensures guaranteed stability, consistent dynamic performance across the speed range, and enforces that the damping ratio of the observer poles remains above a specified minimum value. Experimental results on a surface-mounted PMSM drive under load conditions confirm the effectiveness of the proposed approach

• Calmbach, Benjamin; Ruderman, Michael & Reger, Johann (2026). Continuous homogeneous differentiators with optimal gains applied to noisy measurements of hydromechanic drives. Mechatronics (Oxford). ISSN 0957-4158. 116. doi: 10.1016/j.mechatronics.2026.103488. Fulltekst i vitenarkiv Vis sammendrag

  Whenever time-derivatives of measurements are necessary for observation, fault detection or control, these signals need to be estimated, e.g. using differentiators. In general, large differentiator gains increase the effect of measurement noise on the differentiation estimation error whereas small gains yield insufficient attenuation of higher-order derivatives (of the base signal to be differentiated). This work deals with the optimal gain design for the family of continuous weighted homogeneous differentiators. That is, we design, apply and evaluate homogeneous differentiators (with negative homogeneity degree) based on a theoretical framework developed recently. The design follows a high-gain setup, meaning that stabilizing differentiator parameters are fixed and the only variable tuning parameter is a gain-scaling. This is chosen to minimize the estimated effect of noise and higher-order derivative on the differentiation estimation error in terms of the homogeneous Lp-gain for p=3 and p=infinity. Due to their practical relevance, hydromechanic drives are considered where the differentiator is applied to the noisy position measurements in order to estimate the cylinder piston’s acceleration. The experimental setup includes an accelerometer rendering the differentiation estimation error available for evaluation. Several harmonic excitation signals are considered (sinusoidal, chirp, multi-sine) and the performance is evaluated via standard metrics (root-mean-squared error), the transient response and frequency-domain characteristics. The differentiators are compared to a high-gain differentiator with optimal gains and a straight-forward approach. The evaluation underlines the promising theoretical results that it is based on.

• Ruderman, Michael; Reger, Johann; Calmbach, Benjamin & Fridman, Leonid (2026). Sensitivity Analysis and Experimental Evaluation of PID-Like Continuous Sliding Mode Control. International Journal of Robust and Nonlinear Control. ISSN 1049-8923. 36(8), s. 4591–4601. doi: 10.1002/rnc.70439. Fulltekst i vitenarkiv Vis sammendrag

  Continuous higher order sliding mode (CHOSM) controllers represent an efficient tool for disturbance rejection. For the systems with relative degree 𝑟, CHOSM approaches provide theoretically exact compensation of the matched Lipschitz perturbation, ensuring the finite-time convergence to the (𝑟 + 1)-th sliding-mode set, by using only information on the sliding output and its derivatives up to the order (𝑟−1). In this paper, we investigate the disturbance rejection properties of a PID-like CHOSM controller, as the simplest and intuitively clear example which incorporates nonlinear actions on the output error, its derivative, and integration of its sign. We use the harmonic balance approach and develop an analysis of propagation of the matched Lipschitz perturbation through the control loop in frequency domain. The resulted solution appears in form of the Bode-like loci which depend also on the amplitude of harmonic disturbances. Such amplitude-frequency characteristics allow certain comparability with standard disturbance sensitivity functions of a linear PID-controlled system in frequency domain. Also a simple and straightforward design procedure for the robust linear PID controller targeting the second-order system plants under investigation is provided for benchmarking. Additional (parasitic) actuator dynamics, which can lead to self-induced steady oscillations, i.e. chattering, is also respected. A detailed experimental case study, accomplished on an electro-mechanical actuator in laboratory setting, highlight and make the pros and cons of both PID and CHOSM controllers comparable for a broadband disturbance rejection.

• Ruderman, Michael; Brescia, Elia; Savastio, Luigi P.; Massenio, Paolo R.; Naso, David & Cascella, Giuseppe L. (2026). Comparison of linear observation techniques for robust load torque estimation in actuators. IEEE Conference on Advanced Motion Control. doi: https:/ieeexplore.ieee.org/document/11435824. Fulltekst i vitenarkiv Vis sammendrag

  The paper addresses the problem of estimating robustly the external load torque in rotary actuator systems, when only the generated motor drive torque and angular displacement are the available input and output. We compare, theoretically and experimentally, two sufficiently established linear observation techniques (i) reduced-order Luenberger observer and (ii) disturbance observer, both using the same identified model of a permanent magnet synchronous motor (PMSM)-based actuator. Our goal is to highlight several aspects related to the implementation, relative degree of the input-torque to estimated-load-torque transfer characteristics, observer open-loop transfer function, and the associated sensitivity (respectively stability margins) with respect to inherently uncertain system plants. Apart from the developed analysis, a detailed experimental case study is demonstrated where the load torque sensor provides reference measurements and allows for evaluation of both observers.

• Ruderman, Michael (2026). Reduced-order asymptotic observer of nonlinear friction for precise motion control. Control Engineering Practice. ISSN 0967-0661. 168. doi: 10.1016/j.conengprac.2025.106733. Fulltekst i vitenarkiv Vis sammendrag

  Nonlinear friction has long been, and continues to be, one of the major challenges for precision motion control systems. A linear asymptotic observer of the motion state variables with nonlinear friction uses a dedicated state-space representation of the dynamic friction force (including pre-sliding) [25], which is robust to the noisy input signals. The observer implements the reduced-order Luenberger observation law, while assuming the output displacement is the only available measurement. The latter is relevant for multiple motion control applications with use of encoder-type sensors. The uniform asymptotic stability and convergence analysis of the proposed observer are elaborated in the present work by using the Lyapunov function-based stability criterion by Ignatyev and imposing parametric constraints on the time-dependent eigenvalues of the system matrix to be always negative real. A design procedure for assigning a dominant, and thus slowest, real pole of the observer is proposed. Explanative numerical examples accompany the developed analysis. In addition, a thorough experimental evaluation is given for the proposed observer-based friction compensation which is performed for positioning and tracking tasks. The observer-based compensation, which can serve as a plug-in to a standard feedback controller, extends a PID feedback control that is optimally tuned for disturbance suppression. The experimental results are compared with and without the plugged-in observer-based compensator.

• Massenio, Paolo; Soleti, Giovanni; Ruderman, Michael; Naso, David & Rizzello, Gianluca (2026). Closed-Loop Energy Optimized Control of a Dielectric Elastomer Soft Robot via Policy Iteration. I Hadjicostis, Christoforos (Red.), Proceeding of IEEE CDC2025. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798350316339. s. 7789–7794. doi: 10.1109/CDC57313.2025.11312261. Fulltekst i vitenarkiv Vis sammendrag

  This paper presents an energy optimized closed loop control strategy for a soft robot based on dielectric elastomer actuators (DEAs). While soft robotics offer advantages in flexibility, compliance, and safety compared to conventional solutions, the development of energy-efficient actuation strategies remains a key challenge. Existing methods primarily focus on trajectory optimization or structural design, with limited attention to control strategies. This work addresses this issue by combining an energy-based inner stabilizing controller with an outer optimal control loop to optimize transient performance and energy consumption. The controller incorporates a nonlinear cost functional that balances electro-mechanical energy dissipation and dynamic performance. By embedding the DEAs’ electrical dynamics and using a Policy Iteration based approach, the method designs an additional control input with time-varying bounds, constrained by the voltage used by the stabilizing loop. Simulation results show significant improvements in dynamic performance, energy efficiency, and tuning flexibility.

• Ruderman, Michael & Efimov, Denis (2026). Regularization of non-overshooting quasi-continuous sliding mode control for chattering suppression at equilibrium. I Hadjicostis, Christoforos (Red.), Proceeding of IEEE CDC2025. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798350316339. s. 6037–6042. doi: 10.1109/CDC57313.2025.11312465. Fulltekst i vitenarkiv Vis sammendrag

  Robust finite-time feedback controller introduced for the second-order systems in [1] can be seen as a non-overshooting quasi-continuous sliding mode control. The paper proposes a regularization scheme to suppress inherent chattering due to discontinuity of the control [1] in the origin, in favor of practical applications. A detailed analysis with ISS and iISS proofs are provided along with supporting numerical results.

• Ruderman, Michael (2025). On convergence analysis of feedback control with integral action and discontinuous relay perturbation. Communications in nonlinear science & numerical simulation. ISSN 1007-5704. 145. doi: 10.1016/j.cnsns.2025.108698. Fulltekst i vitenarkiv Vis sammendrag

  We consider third-order dynamic systems which have an integral feedback action and discontinuous relay disturbance. More specifically for the applications, the focus is on the integral plus state-feedback control of the motion systems with discontinuous Coulomb-type friction. We recall the stiction region is globally attractive where the resulting hybrid system has also solutions in Filippov sense, while the motion trajectories remain in that idle state (called in tribology as stiction) until the formulated sliding-mode condition is violated by the growing integral feedback quantity. We analyze the conditions for occurrence of the slowly converging stick-slip cycles. We also show that the hybrid system is globally but only asymptotically stable, and almost always not exponentially. A particular case of the exponential convergence can appear for some initial values, assuming the characteristic equation of the linear subsystem has dominant real roots. Illustrative numerical examples are provided alongside with the developed analysis. In addition, a laboratory example is shown with experimental evidence to support the convergence analysis provided.

• Ruderman, Michael & Efimov, Denis (2025). Power-based control of output oscillations with online estimation of biased harmonics. IFAC-PapersOnLine. ISSN 2405-8971. 59(14), s. 98–103. doi: 10.1016/j.ifacol.2025.12.132. Fulltekst i vitenarkiv Vis sammendrag

  The recently introduced discrete power-based control (Ruderman (2024b)) reduces largely the communication efforts in the control loop when compensating for the marginally damped or even slowly diverging output oscillations. The control commutates twice per oscillations period (at the amplitude peaks) and uses the measured harmonic output only. The power-based control scheme requires the knowledge of the instantaneous frequency, amplitude, and bias parameters of the harmonic signal. This paper extends the power-based control by the finite-time estimation of the biased harmonics (Ahmed et al. (2022)). Also an improved analytic calculation of the impulse weighting factor is provided. The power-based oscillations control with online estimation of the harmonic parameters is evaluated experimentally on the fifth-order actuator system with a free hanging load under gravity and measurement noise.

• Ruderman, Michael; Giostra, Gianluca & Sette, Matteo (2025). Inversion-Free Feed-Forward and Feedback Control of MSM Based Actuator with Large Non-Smooth Input Hysteresis. IFAC-PapersOnLine. ISSN 2405-8971. 59(14), s. 161–166. doi: 10.1016/j.ifacol.2025.12.143. Fulltekst i vitenarkiv Vis sammendrag

  Dynamic systems with a large and non-smooth hysteresis in the feedforward channel challenge the design of feedback control since the instantaneous input gain is varying during the operation, in the worst case between zero and infinity. Magnetic shape memory (MSM) actuators with multi-stable transitions represent such untypical system plant with only the output displacement being measured. This paper provides a case study of designing the feedforward and feedback control system for an MSM-based actuator setup with a fairly high level of the output sensing noise. First, the recently introduced inversion-free feedforward hysteresis compensator is adapted for the Krasnoselskii-Pokrovskii operator model. Then, a robust feedback proportional-integral (PI) loop shaping is performed, while taking into account the lagging behavior of the low-pass filtering and system uncertainties. Experimental results show that the parallel action of feedforward and feedback parts improves the overall performance of position control.

• Ruderman, Michael (2025). Nonlinear Integral Extension of PID Control With Improved Convergence of Perturbed Second-Order Dynamic Systems. Advanced Control for Applications. 7(2). doi: 10.1002/adc2.70017. Fulltekst i vitenarkiv Vis sammendrag

  Nonlinear extension of the integral part of a standard proportional-integral-derivative (PID) feedback control is proposed for perturbed second-order systems. The approach is model-free and requires solely the Lipschitz boundedness of the unknown matched perturbations. For constant disturbances, the global asymptotic stability is shown based on the circle criterion. For Lipschitz perturbations, an ultimately bounded output error is provided based on the steady-state behavior in frequency domain. Also the transient response to the stepwise disturbances is analyzed for the control tuning. Based on the developed analysis, the design recommendations are formulated as a step-by-step procedure. It is also discussed how the proposed control is applicable to second-order systems extended by additional (parasitic) actuator dynamics with low-pass characteristics. The proposed nonlinear control is proven to outperform its linear PID counterpart during the settling phase, that is, at convergence of the residual output error. An experimental case study of the second-order system with an additional actuator dynamics and considerable perturbations is demonstrated to confirm and benchmark the control performance.

• Ruderman, Michael & Rito, Francesco De (2025). Study of Frictional and Impact Transients in Active-Passive Mechanical Pair, Proceeding IEEE International Conference on Mechatronics ICM2025. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798331533892. doi: 10.1109/ICM62621.2025.10934848. Fulltekst i vitenarkiv Vis sammendrag

  We consider an active-passive mechanical pair in which the relative motion of the latter is constrained by the mechanical impact. The system dynamics is described by the previously introduced modeling frameworks of force transition and dissipation through the nonlinear Coulomb friction and structural damping, the later in accord with Hertzian contact theory. The focus of the recent study is on combining both interaction mechanisms, and the detailed experimental evaluation which discloses validity of the modeling assumptions. Such mechanical pair interactions can be found in various mechatronic systems and mechanisms, like for example clutches, backlash elements, sliding items on the shaking and inclining surfaces, conveyor belts and others. This practical study demonstrates and discusses the transients of a vibro-impact dynamics and shows theoretical developments in line with experimental evaluation.

• Ruderman, Michael (2025). Loop Shaping of Hybrid Motion Control with Contact Transition. I Hadjicostis, Christoforos (Red.), Proceedings of IEEE ECC2025 conference. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665497336. s. 2921–2926. Fulltekst i vitenarkiv Vis sammendrag

  A standard motion control with feedback of the output displacement cannot handle unforeseen contact with environment without penetrating into the soft, i.e. viscoelastic, materials or even damaging the fragile materials. Robotics and mechatronics with tactile and haptic capabilities, and in particular medical robotics for example, place special demands on the advanced motion control systems that should enable the safe and harmless contact transitions. This paper shows how the basic principles of loop shaping can be easily used to handle sufficiently stiff motion control in such a way that it is extended by sensor-free dynamic reconfiguration upon contact with the environment. A thereupon based hybrid control scheme is proposed. A remarkable feature of the developed approach is that no measurement of the contact force is required and the input signal and the measured output displacement are the only quantities used for design and operation. Experiments on 1-DOF actuator are shown, where the moving tool comes into contact with grapes that are soft and simultaneously penetrable.

• Estrada, Manuel; Ruderman, Michael; Loaiza, Oscar & Fridman, Leonid M. (2025). Hydraulic actuator control based on continuous higher order sliding modes. Control Engineering Practice. ISSN 0967-0661. 156. doi: 10.1016/j.conengprac.2024.106218. Fulltekst i vitenarkiv Vis sammendrag

  This paper presents the robust trajectory tracking of a hydraulic cylinder using an output feedback sliding mode technique. The proposed control scheme relies only on measuring the position of the cylinder rod. A robust, exact, finite-time observer of the output’s derivatives is provided to attain the control goal. Then, a continuous third-order sliding mode controller for the system with relative degree three is designed using the estimated derivatives. It is shown that the separation principle can be used for the closed-loop system, which includes the higher-order sliding mode observer and the controller. The paper includes experimental results on a hydraulic setup in which a second energized cylinder is also connected in an antagonistic way to produce external dynamic disturbances and demonstrate the control method’s feasibility and robustness.

• Ruderman, Michael & Efimov, Denis (2025). Non-overshooting quasi-continuous sliding mode control for second-order systems. European Journal of Control. ISSN 0947-3580. 85. doi: 10.1016/j.ejcon.2025.101355. Fulltekst i vitenarkiv Vis sammendrag

  This paper proposes a nonlinear sliding mode state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output of interest and its time derivative. The control has only one free design parameter, and the closed-loop system is shown to possess uniform boundedness and finite-time convergence of trajectories in the presence of matched disturbances. We derive a strict Lyapunov function for the closed-loop control system with a bounded exogenous perturbation, and use it for both, the control parameter tuning and analysis of the finite-time convergence. The essential features of the proposed control law is non-overshooting despite the unknown dynamic disturbances and the continuous control action during the convergence to zero equilibrium. Apart from the numerical results, a revealing experimental example is also shown in favor of the proposed control and in comparison with PD and sub-optimal nonlinear damping regulators.

• Estrada, Manuel; Ruderman, Michael & Fridman, Leonid M. (2024). Super-twisting based sliding mode control of hydraulic actuator without velocity state. Control Engineering Practice. ISSN 0967-0661. 142. doi: 10.1016/j.conengprac.2023.105739. Fulltekst i vitenarkiv Vis sammendrag

  This paper provides a novel surface design and experimental evaluation of a super-twisting algorithm (STA) based control for hydraulic cylinder actuators. The proposed integral sliding surface allows to track a sufficiently smooth reference without using the velocity state which is hardly accessible in the noisy hydraulic systems. A design methodology based on LMI’s is given, and the STA gains are designed to be adjusted by only one free parameter. The feasibility and effectiveness of the proposed control method are shown on a standard hydraulic test bench with one linear degree of freedom and passive load, where a typical motion profile is tracked with a bounded average error below 1% from the total drive effective output.

• Ruderman, Michael (2024). Experimental Benchmarking of Energy-Saving Sub-Optimal Sliding Mode Control. I Ferrara, Antonella (Red.), Proceeding of IEEE VSS2024. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781479955664. s. 208–213. doi: 10.1109/VSS61690.2024.10753417. Fulltekst i vitenarkiv Vis sammendrag

  The recently introduced energy-saving extension of the sub-optimal sliding mode control allows for control-off phase during the convergence to second-order equilibrium. This way, it enables for a lower energy consumption compared to the original sub-optimal sliding mode (SM) algorithm, both commutating a discontinuous control signal. In this paper, the energy-saving sub-optimal SM control is experimentally benchmarked against a standard second-order SM controller which also has a discontinuous control action. Here the so-called terminal second-order SM algorithm is used. The controlled plant is affected by the matched bounded disturbances which are unknown, and the output is additionally subject to the sensor noise. Moreover, a first-order actuator dynamics can lead to chattering, which is parasitic for SM applications. For a fair comparison, the same quadratic terminal surface is designed when benchmarking both SM controllers. Both experimentally compared SM algorithms have the same (bounded) control magnitude and states initial conditions.

• Ruderman, Michael (2024). Power Based Adaptive Compensator of Output Oscillations. I Liberzon, Daniel & Astolfi, Daniele (Red.), Proceeding of 4th IFAC Conference of Modelling, Identification and Control of Nonlinear Systems. IFAC Papers Online. s. 120–125. doi: 10.1016/j.ifacol.2024.10.157. Fulltekst i vitenarkiv Vis sammendrag

  Power-based output feedback compensator for oscillatory systems is proposed. The average input-output power of an oscillatory signal serves as an equivalent control effort, while the unknown amplitude and frequency of oscillations are detected at each half-period. This makes the compensator adaptive and discrete, while the measured oscillatory output is the single available signal in use. The resulting discrete control scheme enables a drastic reduction of communication efforts in the control loop. The compensator is designed for 2nd order systems, while an extension to higher-order dynamics, like e.g. in case of two-inertia systems, is also provided. Illustrative experimental case study of the 5th order oscillatory system is provided.

• Ruderman, Michael (2024). Adaptive time delay based control of non-collocated oscillatory systems. I Valavanis, Kimon P. (Red.), IEEE 32nd Mediterranean Conference on Control and Automation (MED2024). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798350395440. s. 125–130. doi: 10.1109/MED61351.2024.10566272. Fulltekst i vitenarkiv Vis sammendrag

  Time delay based control, recently proposed for non-collocated fourth-order systems, has several advantages over an observer-based state-feedback compensation of the low-damped oscillations in output. In this paper, we discuss a practical infeasibility of such observer-based approach and bring forward application of the time delay based controller, which is simple in both the structure and design. Moreover, robust estimation of the output oscillation frequency is used and extended by a bias canceling. The latter is required for positioning the oscillatory passive loads. This way, an adaptive version of time delay-based control is realized that does not require prior knowledge of the mass and stiffness parameters. The results are demonstrated on the oscillatory experimental setup with constraints in the operation range and control value.

• Voss, Benjamin; Ruderman, Michael & Reger, Johann (2024). Experimental Evaluation of Homogeneous Differentiators Applied to Hydraulic Stroke with Measurement Noise and Acceleration Disturbance, IEEE AMC2024 conference proceeding. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798350342819. doi: 10.1109/AMC58169.2024.10505713. Fulltekst i vitenarkiv Vis sammendrag

  The design and experimental evaluation of continuous homogeneous differentiators are considered. The differentiator gains follow the high-gain setup with variable gain-scaling parameter L. This parameter results from a minimization of the effect of measurement noise and disturbance on the differentiation estimation error in terms of the homogeneous L2 -gain. We consider and compare various homogeneity degrees including the linear (high-gain) case. It turns out that an optimum exists not only w.r.t. L but also w.r.t. homogeneity degree d. For experimental evaluation, a hydraulic cylinder controlled by a servo-valve is excited over a frequency range and the noisy cylinder stroke measurements are differentiated. Via classical metrics (root-mean-square and maximum absolute error) and a precise full-order simulation model, we evaluate the velocity estimation accuracy. Applying a second differentiation to the stroke measurements, an acceleration disturbance can be detected from a comparison of its measurement and estimate.

• Efimov, Denis & Ruderman, Michael (2024). Stability analysis and integral extension of sub-optimal nonlinear damping control. International Journal of Robust and Nonlinear Control. ISSN 1049-8923. 34(13), s. 9055–9066. doi: 10.1002/rnc.7447. Fulltekst i vitenarkiv Vis sammendrag

  The problems of robustness with respect to external inputs and of convergence rate estimation are considered for the so called sub-optimal nonlinear damping control [1]. To this end, existence of solutions is justified, a strict Lyapunov function is found and its properties are investigated. The hyperexponential convergence of the unperturbed sub-optimal nonlinear damping control is demonstrated. Moreover, an integral extension is proposed to complement the controller with capability of compensation for static errors. The results are illustrated by numeric simulations and the control experiments.

• Ruderman, Michael (2023). Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction. Applications of Mathematics. ISSN 0862-7940. 68(6), s. 845–860. doi: 10.21136/AM.2023.0283-22. Fulltekst i vitenarkiv Vis sammendrag

  The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In this paper, we discuss the energy dissipation and convergence during the pre-sliding cycles and show how a piecewise smooth force-displacement hysteresis map enters into the energy balance of an unforced system of the second order. An existing friction modeling approach with a low number of the free parameters, the Dahl model, is then exemplified alongside the developed analysis.

• Checchin, Riccardo; Ruderman, Michael & Oboe, Roberto (2023). Robust two-degrees-of-freedom control of hydraulic drive with remote wireless operation. I Ruderman, Michael & Chen, Wen-Hua (Red.), Proceeding IEEE International Conference on Mechatronics (ICM2023). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665466615. doi: 10.1109/ICM54990.2023.10101993. Fulltekst i vitenarkiv Vis sammendrag

  In this paper, we present a controller design targeting a remotely operated hydraulic drive system. We use a two-degrees-of-freedom PID position controller, which is designed so that to maximize the integral action under robust constraint. A linearized model of the system plant, affected by the parameters uncertainties such as variable communication time-delay and overall system gain, is formulated and serves for the control design and analysis. The performed control synthesis and evaluation target a remote operation where the wireless communication channel cannot secure a deterministic real-time of the feedback loop. The provided analysis of uncertainties makes it possible to ensure system stability under proper conditions. We demonstrate the theoretically expected results through laboratory experiments on the standard industrial hydraulic components.

• Ruderman, Michael (2023). Inversion-free feedforward hysteresis control using Preisach model, Proceedings of 2023 European Control Conference (ECC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9783907144084. doi: 10.23919/ECC57647.2023.10178206. Fulltekst i vitenarkiv Vis sammendrag

  We introduce a new inversion-free feedforward hysteresis control using the Preisach model. The feedforward scheme has a high-gain integral loop structure with Preisach hysteresis operator in negative feedback. This allows obtaining a dynamic quantity which corresponds to the inverse hysteresis output, as the loop error tends towards zero for a sufficiently high feedback gain. By analyzing the loop sensitivity function with hysteresis that acts as a state-varying phase lag, we demonstrate the achievable bandwidth and accuracy of the proposed control method. Remarkable fact is that the control bandwidth is theoretically infinite, provided the Preisach operator in feedback can be implemented in a way to ensure the C 0 continuous hysteresis output. Numerical control examples with the Preisach hysteresis model in differential form are presented.

• Ruderman, Michael (2023). Robust asymptotic observer of motion states with nonlinear friction, 22nd IFAC World Congress. Elsevier. ISSN 9781510850712. s. 5931–5936. doi: 10.1016/j.ifacol.2023.10.1909. Fulltekst i vitenarkiv Vis sammendrag

  This paper revisits the previously proposed linear asymptotic observer of the motion state variables with nonlinear friction and provides a robust design suitable for both, transient presliding and steady-state sliding phases of the relative motion. The class of motion systems with the only measurable output displacement is considered. The reduced-order Luenberger-type observer is designed based on the obtained simplified state-space representation with a time-varying system matrix. The resulted observation error dynamics proves to be robust and appropriate for all variations of the system matrix, which are due to the nonlinear spatially-varying friction. A specially designed tribological setup to accurately monitor the relative motion between two contacting friction surfaces is used to collect the experimental data of the deceleration trajectories when excited by a series of impulses. The performance of the state estimation using the proposed observer is shown based on the collected experimental data.

• Ruderman, Michael (2023). Time-delay based output feedback control of fourth-order oscillatory systems. Mechatronics (Oxford). ISSN 0957-4158. 94. doi: 10.1016/j.mechatronics.2023.103015. Fulltekst i vitenarkiv Vis sammendrag

  We consider stabilization of the fourth-order oscillatory systems with non-collocated output sensing. Worth recalling is that the fourth-order systems are relatively common in mechatronics as soon as there are two-mass or more generally two-inertia dynamics with significant elasticities in the link. A novel yet simple control method is introduced based on the time-delayed output feedback. The delayed output feedback requires only the oscillation frequency to be known and allows for a robust control design that leads to cancelation of the resonance peak. We use the stability margins to justify the transfer characteristics and robustness of the time-delay control in frequency domain. The main advantage of the proposed method over the other possible lead-based loop-shaping strategies is that neither time derivatives of the noisy output nor the implementation of transfer functions with a numerator degree greater than zero are required to deploy the controller. This comes in favor of practical applications. An otherwise inherently unstable proportional-integral (PI) feedback of the non-collocated output is shown to be stabilized by the proposed method. The control developed and associated analysis are also confirmed by the experimental results shown for the low damped two-mass oscillator system with uncertainties.

• Ruderman, Michael; Zagvozdkin, Andrei & Rachinskii, Dmitrii (2022). Dynamics of inertial pair coupled via frictional interface. I Aghdam, Amir & IEEE, . (Red.), IEEE 61st Conference on Decision and Control (CDC 2022). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665467612. s. 1324–1328. doi: 10.1109/CDC51059.2022.9993163. Fulltekst i vitenarkiv Vis sammendrag

  Understanding the dynamics of two inertial bodies coupled via a friction interface is essential for a wide range of systems and motion control applications. Coupling terms within the dynamics of an inertial pair connected via a passive frictional contact are non-trivial and have long remained understudied in system communities. This problem is particularly challenging from a point of view of modeling the interaction forces and motion state variables. This paper deals with a generalized motion problem in systems with a free (of additional constraints) friction interface, assuming the classical Coulomb friction with discontinuity at the velocity zero crossing. We formulate the dynamics of motion as the closed-form ordinary differential equations containing the sign operator for mapping both, the Coulomb friction and the switching conditions, and discuss the validity of the model in the generalized force and motion coordinates. The system has one active degree of freedom (the driving body) and one passive degree of freedom (the driven body). We demonstrate the global convergence of trajectories for a free system with no external excitation forces. Then, an illustrative case study is presented for a harmonic oscillator with a frictionally coupled second mass that is not grounded or connected to a fixed frame. This simplified example illustrates a realization and main features of the proposed (general) modeling framework. Some future development and related challenges are discussed at the end of the paper.

• Ruderman, Michael & Fridman, Leonid M. (2022). Analysis of relay-based feedback compensation of Coulomb friction. I Oliveira, Tiago (Red.), Proceeding of IEEE 16th International Workshop on Variable Structure Systems. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781479955664. s. 95–100. doi: 10.1109/VSS57184.2022.9902091. Fulltekst i vitenarkiv Vis sammendrag

  Standard problem of one-degree-of-freedom mechanical systems with Coulomb friction is revised for a relay-based feedback stabilization. It is recalled that a system with Coulomb friction is asymptotically stabilizable via a relay-based output feedback, as formerly demonstrated in [1]. Assuming an upper bounded Coulomb friction disturbance, a time-optimal gain of the relay-based feedback control is found by minimizing the derivative of the Lyapunov function proposed in [2] for the twisting algorithm. Furthermore, changing from the discontinuous Coulomb friction to a more physical discontinuity-free one, which implies a transient presliding phase at motion reversals, we analyze the residual steady-state oscillations, in the sense of stable limit cycles, in addition to chattering caused the by the actuator dynamics. The numerical examples and an experimental case study accompany the provided analysis.

• Voss, Benjamin; Ruderman, Michael; Weise, Christoph & Reger, Johann (2022). Comparison of Fractional-Order and Integer-Order H-infinity Control of a Non-Collocated Two-Mass Oscillator. I Peaucelle, Dimitri (Red.), Proceeding of 10th IFAC Symposium on Robust Control Design (ROCOND 2022). IFAC Papers Online. ISSN 9783902823373. s. 145–150. doi: 10.1016/j.ifacol.2022.09.338. Fulltekst i vitenarkiv Vis sammendrag

  We consider the robust control of a two-mass oscillator with a dominant input delay. Our aim is to compare a fractional-order tuning approach including the partial compensation of non-minimum phase zeros with a classical H∞ loop-shaping design, since both these designs lead to a relatively high controller order. First of all a detailed physical model is derived and validated using measurement data. Based on the line arized model both controllers are designed to be comparable, i.e. they show a similar crossover frequency in the open loop and the final controller order is reduced to the same range for both designs. The major differences between both are the different methods how the feed-forward action is included. The loop-shaping approach with fractional-order elements relies on the plant inverse using a fat output, whereas the H∞ design incorporates a two-degree of freedom control, i.e. the reference signal is included into the known inputs of the generalized plant. Each controller is tested in simulation and experiment. As both open-loops are nearly identical in the frequency range of interest, the results from an input disturbance experiment show no major difference. The different design approaches of the feed forward path are clearly visible in the tracking experiment.

• Voss, Benjamin; Weise, Christoph; Ruderman, Michael & Reger, Johann (2022). Fractional-Order Partial Cancellation of Integer-Order Poles and Zeros. I Peaucelle, Dimitri (Red.), Proceeding of 10th IFAC Symposium on Robust Control Design (ROCOND 2022). IFAC Papers Online. ISSN 9783902823373. s. 259–264. doi: 10.1016/j.ifacol.2022.09.356. Fulltekst i vitenarkiv Vis sammendrag

  The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase response of these fractional-order terms is derived to include these compensators into the loop-shaping design. Such compensators can be generalized to conjugate complex zeros/poles, and also implicit fractional-order terms can be applied. In the case of the non-minimum phase zero, its compensation leads to a higher phase margin and a steeper open-loop amplitude response around the crossover frequency resulting in a reduced undershooting in the step-response, as illustrated in the numerical example.

• Oboe, Roberto & Ruderman, Michael (2022). The 17th IEEE International Conference on Advanced Motion Control [Society News]. IEEE Industrial Electronics Magazine. ISSN 1932-4529. 16(3). doi: 10.1109/MIE.2022.3190982. Fulltekst i vitenarkiv
• Ruderman, Michael (2022). Motion control with optimal nonlinear damping: From theory to experiment. Control Engineering Practice. ISSN 0967-0661. 127, s. 105310–105310. doi: 10.1016/j.conengprac.2022.105310. Fulltekst i vitenarkiv Vis sammendrag

  Optimal nonlinear damping control was recently introduced for the second-order SISO systems, showing some advantages over a classical PD feedback controller. This paper summarizes the main theoretical developments and properties of the optimal nonlinear damping controller and demonstrates, for the first time, its practical experimental evaluation. An extended analysis and application to more realistic (than solely the double-integrator) motion systems are also given in the theoretical part of the paper. As comparative linear feedback controller, a PD one is taken, with the single tunable gain and direct compensation of the plant time constant. The second, namely experimental, part of the paper includes the voice-coil drive system with relatively high level of the process and measurement noise, for which the standard linear model is first identified in frequency domain. The linear approximation by two-parameters model forms the basis for designing the PD reference controller, which fixed feedback gain is the same as for the optimal nonlinear damping control. A robust sliding-mode based differentiator is used in both controllers for a reliable velocity estimation required for the feedback. The reference PD and the proposed optimal nonlinear damping controller, both with the same single design parameter, are compared experimentally with respect to trajectory tracking and disturbance rejection.

• Ruderman, Michael (2021). Optimal nonlinear damping control of second-order systems. Journal of the Franklin Institute. ISSN 0016-0032. 358(8), s. 4292–4302. doi: 10.1016/j.jfranklin.2021.03.022. Fulltekst i vitenarkiv Vis sammendrag

  Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global asymptotic stability, passivity property, and convergence time and accuracy are demonstrated. Also the control saturation case is explicitly analyzed. The suggested nonlinear damping is denoted as optimal since requiring no additional design parameters and ensuring a fast convergence, without transient overshoots for a non-saturated and one transient overshoot for a saturated control configuration.

• Ruderman, Michael (2021). Robust output feedback control of non-collocated low-damped oscillating load, Proceeding of IEEE 2021 29th Mediterranean Conference on Control and Automation (MED). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665422581. s. 639–644. doi: 10.1109/MED51440.2021.9480239. Fulltekst i vitenarkiv Vis sammendrag

  For systems with order of dynamics higher than two and oscillating loads with low damping, a non-collocation of the sensing and control can deteriorate robustness of the feedback and, in worst case, even bring it to instability. Furthermore, for a contactless sensing of the oscillating mechanical load, like in the system under investigation, the control structure is often restricted to the single proportional feedback only. This paper proposes a novel robust feedback control scheme for a low-damped fourth-order system using solely the measured load displacement. For reference tracking, the loop shaping design relies on a band reject filter, while the plant uncertainties are used as robustness measure for determining the feedback gain. Since prime uncertainties are due to the stiffness of elastic link, correspondingly connecting spring, and due to the gain of actuator transducer, the loop sensitivity function with additive plant variation is used for robustness measure. In order to deal with unknown disturbances, which are inherently exciting the load oscillations independently of the loop shaping performance, an output delay-based compensator is proposed as a second control-degree-of-freedom. That one requires an estimate of the load oscillation frequency only and does not affect the shaped open-loop behavior, correspondingly sensitivity function. An extensive numerical setup of the modeled system, a two-mass oscillator with contactless sensing of the load under gravity and low damping of the connecting spring, is used for the control evaluation and assessment of its robustness.

• Aracil, Carmen; Sziebig, Gabor; Korondi, Peter; Oh, Sehoon; Tan, Zhichao & Ruderman, Michael [Vis alle 11 forfattere av denne artikkelen] (2021). Toward Smart Systems: Their Sensing and Control in Industrial Electronics and Applications. IEEE Industrial Electronics Magazine. ISSN 1932-4529. 15(1), s. 104–114. doi: 10.1109/MIE.2020.3042171. Fulltekst i vitenarkiv
• Ruderman, Michael; Kaltenbacher, Stefan & Horn, Martin (2021). Pressure-flow dynamics with semi-stable limit cycles in hydraulic cylinder circuits, Proceeding of IEEE International Conference on Mechatronics (ICM2021). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538669594. doi: 10.1109/ICM46511.2021.9385620. Fulltekst i vitenarkiv Vis sammendrag

  In hydraulic circuits of the standard fluid-power actuators and mechanisms, like the linear-stroke cylinders, some hydrodynamic effects are often neglected. It happens mainly due to their complexity and secondariness in comparison with the principal transient and steady-state behavior of the hydromechanical process variables, such as the differential pressure and relative displacement and its rate, in other words the piston stroke and velocity. However, a constrained motion of the cylinder piston can give rise to the back coupled excitation of the pressure-flow dynamics, especially upon mechanical impact at the cylinder limits. Following to that, semi-stable limit cycles can arise while the hydraulic cylinder remains under pressure without apparent displacement. This paper analyzes such back-coupled pressure-flow dynamics, derived from the partial differential momentum equation with involvement of Darcy-Weisbach hydraulic damping and continuity equation, out from which the closed-form system dynamics is formulated. In both, simulations and laboratory experiments, it is shown that if a constrained motion applies, the solution diverges from steady-state and can develop to the behavior similar to a semi-stable limit cycle.

• Tavares, Rafael Pinto & Ruderman, Michael (2021). Frequency-domain experimental setup for mechatronic and suspension system components, Proceeding of IEEE International Conference on Mechatronics (ICM2021). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538669594. doi: 10.1109/ICM46511.2021.9385640. Fulltekst i vitenarkiv Vis sammendrag

  This paper presents a frequency-domain experimental setup for modal analysis of mechatronic and suspension system components. Design, instrumentation and dynamic behavior of the one degree-of-freedom (DOF) system, capable of providing both, periodic and application-specific, excitation forces is described. The excitation is realized by an electromagnetic modal shaker with additional assembly and interface components designed and instrumented for frequency -domain analysis of vertical dynamics. Frequency response functions (FRFs) of the implemented system are experimentally measured and the associated basic model parameters are calculated, correspondingly identified. Accurate fit between the measured FRFs and modeled dynamics is shown for sufficiently large frequency range 0.1-30 Hz of the mechanical system response. Exemplary standard road profile excitations are also conducted to demonstrate the applicability of the designed system for frequency-domain testing of components in the vehicle suspension systems.

• Ano, Shuta; Seki, Kenta; Ruderman, Michael & Iwasaki, Makoto (2021). Estimating Sway Angle of Pendulum System Using Hybrid State Observer Incorporating Continuous and Discrete Sensing Signals. IEEJ Journal of Industry Applications. ISSN 2187-1094. 10(1), s. 69–75. doi: 10.1541/IEEJJIA.20004820. Fulltekst i vitenarkiv Vis sammendrag

  This paper presents the design of a hybrid state observer that estimates the sway angle in trolley systems with a pendulum, such as overhead cranes. In the system, sway angle signals detected by angular sensors are generally used for designing the anti-sway control of the pendulum or observing the pendulum state. By contrast, in this study, a linear state observer without sensors is applied to estimate the sway angle of the pendulum. The use of a standard asymptotic state observer leads to estimation error due to the system's nonlinearities and parametric errors. This paper proposes using a hybrid state observer design that combines discrete event sensing with a linear state observer. In the hybrid state observer, the estimation performance is improved by correcting the state of the system based on the discrete sway angle and angular velocity using discrete sensing. In addition, the parametric error of the pendulum length of the system is identified using the same hybrid setting. The effectiveness of the hybrid state observer and the parametric adaptation of the pendulum length are verified by conducting experiments using a downscaled prototype of a trolley system with a pendulum.

• Ruderman, Michael (2021). On stiffness and damping of vibro-impact dynamics of backlash, IEEE 30th International Symposium on Industrial Electronics (ISIE). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728156354. doi: 10.1109/ISIE45552.2021.9576274. Fulltekst i vitenarkiv Vis sammendrag

  We consider the stiffness and damping properties of the vibro-impact in a backlash pair. Opposed to the existing and mostly used models of the backlash, we address the problem of contact and separation, and the associated force propagation within a mechanical pair, from a viewpoint of vibro-impact dynamics. We discuss the impact forces with the coefficient of restitution as a principal factor which shapes the transient backlash response. We show that a common approach to modeling the backlash by means of a dead-zone in a restoring force is unsuitable for correctly capturing the mechanical impact. We exemplary demonstrate a qualitative accord between an experimental backlash response and the postulated modeling approach. Backlash related energy losses of the vibroimpact damping are also addressed in brief.

• Ruderman, Michael (2021). Extended fractional-order Jeffreys model of viscoelastic hydraulic cylinder. Journal of Dynamic Systems Measurement, and Control. ISSN 0022-0434. 143(7), s. 074502–074502. doi: 10.1115/1.4050253. Fulltekst i vitenarkiv Vis sammendrag

  A novel modeling approach for viscoelastic hydraulic cylinders, with negligible inertial forces, is proposed, based on the extended fractional-order Jeffreys model. Analysis and physical reasoning for the parameter constraints and order of the fractional derivatives are provided. Comparison between the measured and computed frequency response functions and time domain transient response argues in favor of the proposed four-parameter fractional-order model.

• Ruderman, Michael (2021). Stick-slip and convergence of feedback-controlled systems with Coulomb friction. Asian journal of control. ISSN 1561-8625. 24(6), s. 2877–2887. doi: 10.1002/asjc.2718. Fulltekst i vitenarkiv Vis sammendrag

  An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium set, is proved to be always reachable and globally attractive. It is shown that only asymptotic convergence can be achieved, with at least one but mostly an infinite number of consecutive stick-slip cycles, independent of the initial conditions. Theoretical developments are supported by a number of numerical results with dedicated convergence examples.

• Weise, Christoph; Pfeffer, Philipp; Reger, Johann & Ruderman, Michael (2021). Parameter Identification of Fractional-Order LTI Systems using Modulating Functions with Memory Reduction, Proceedings of IEEE CDC2021 conference. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665436595. doi: 10.1109/CDC45484.2021.9682920. Fulltekst i vitenarkiv Vis sammendrag

  The parameter estimation problem of a linear time-invariant fractional-order system is investigated by means of the modulating function method. Based on the assumption of known model structure and derivative orders, the modulating function method can be generalized to the fractional-order case in three different ways. We show that two approaches are identical for linear systems. This facilitates the computation of the fractional-order derivatives of modulating functions. The second part includes the initialization of the fractional-order system. We show that the spline type modulating function is capable of reducing the effect of the memory on the parameter estimation. However, it is not possible to compensate the initialization completely. In contrast to these tuning principles also the robustness against measurement noise must be considered. For this purpose we decouple the memory and noise compensation. The adjusted spline-type modulating functions reduce the initialization effect and the recursive least square estimation provides the possibility to increase the numbers of equations such that the effect of the noise is reduced.

• Ruderman, Michael (2021). Optimal terminal sliding mode control for second-order motion systems, Proceedings of IEEE CDC2021 conference. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665436595. s. 6421–6426. doi: 10.1109/CDC45484.2021.9683172. Fulltekst i vitenarkiv Vis sammendrag

  Terminal sliding mode (TSM) control algorithm and its non-singular refinement have been elaborated for two decades and belong, since then, to a broader class of the finite-time controllers, which are known to be robust against the matched perturbations. While TSM manifold allows for different forms of the sliding variable, which are satisfying the q/p power ratio of the measurable output state, we demonstrate that q/p=0.5 is the optimal one for the second-order Newton’s motion dynamics with a bounded control action. The paper analyzes the time-optimal sliding surface and, based thereupon, claims the optimal TSM control for the second-order motion systems. It is stressed that the optimal TSM control is fully inline with the Fuller’s problem of optimal switching which minimizes the settling time, i.e. with time-optimal control of an unperturbed double-integrator. Is is also shown that for the given plant characteristics, i.e. the overall inertia and control bound, there is no need for additional control parameters. The single surface design parameter might (but not necessarily need to) be used for driving system on the boundary layer of the twisting mode, or for forcing it to the robust terminal sliding mode. Additional insight is given into the finite-time convergence of TSM and robustness against the bounded perturbations. Numerical examples with different upper-bounded perturbations are demonstrated.

• Ruderman, Michael (2021). Convergent dynamics of optimal nonlinear damping control, 6th IFAC Conference on Analysis and Control of Chaotic Systems CHAOS 2021. IFAC Papers Online. s. 141–144. doi: 10.1016/j.ifacol.2021.11.039. Fulltekst i vitenarkiv Vis sammendrag

  Following the Demidovich’s concept and definition of convergent systems, we analyze the optimal nonlinear damping control which was recently proposed for the second-order systems. Targeting the problem of servo-regulation, and more specifically output tracking of the C1 reference trajectories, it is shown that all solutions of the proposed control system are globally uniformly asymptotically stable. The existence of the unique limit solution in the coordinates origin of the control error and its time derivative are shown in the sense Demidovich’s convergent dynamics. Explanatory numerical examples are provided to accompany the analysis.

• Ruderman, Michael (2021). One-parameter robust global frequency estimator for slow-varying amplitude and noisy oscillations. Mechanical systems and signal processing. ISSN 0888-3270. 170, s. 108756–108756. doi: 10.1016/j.ymssp.2021.108756. Fulltekst i vitenarkiv Vis sammendrag

  Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped vibrations. A novel robust frequency-estimation algorithm is proposed here, motivated by the existing globally convergent frequency estimator. The advantage of the proposed estimator is in requiring one design parameter only and being robust against measurement noise and initial conditions. The proven global convergence also allows for slowly varying amplitudes, which is useful for applications with damped oscillations or additionally shaped harmonic signals. The proposed analysis is simple and relies on an averaging theory of the periodic signals. Our results show an exponential convergence rate, which depends, analytically, on the sought frequency, adaptation gain and oscillation amplitude. Numerical and experimental examples demonstrate the robustness and efficiency of the proposed estimator for signals with slowly varying amplitude and noise.

• Tranninger, Markus & Ruderman, Michael (2021). Stability Analysis of a Linear Parameter Varying Adaptive Output Feedback Control System, 4th IFAC Workshop on Linear Parameter-Varying Systems. IFAC Papers Online. ISSN 9781713807773. doi: 10.1016/j.ifacol.2021.08.582. Fulltekst i vitenarkiv Vis sammendrag

  Output feedback control systems often require an adaptive filter for properly shaping the loop transfer function, as certain system plant parameters may be uncertain or varying. This renders the overall closed loop to a linear parameter varying (LPV) system, for which the stability analysis is challenging due to non-trivial dynamics of the adaptation law. This paper develops a stability analysis technique of a feedback controlled oscillatory system. A polytopic overapproximation of the parameter set together with the feasibility of certain LMIs guarantees asymptotic stability of the closed loop. The varying parameter is only required to be lower and upper bounded, where the bounds can be obtained from the proposed strategy. Hence, any filter adaptation law is allowed for this parameter range. A meaningful numerical example based on a fifth-order plant and a second-order adaptive filter demonstrates the usefulness and appealing simplicity of the proposed approach.

• Tavares, Rafael Pinto & Ruderman, Michael (2020). Dissipation in suspension system augmented by piezoelectric stack: port-Hamiltonian approach, Proceeding IEEE 28th Mediterranean Conference on Control and Automation (MED'2020). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538678909. s. 168–173. doi: 10.1109/MED48518.2020.9183317. Fulltekst i vitenarkiv Vis sammendrag

  Analysis of damping in semi-active and active suspension systems is prerequisite for an advanced control and, eventually, energy harvesting functions. This paper addresses the damping in suspension system augmented by the piezoelectric (PE) stack. The Hamiltonian system approach with port-power modeling of single subsystems is used for describing and studying the dissipative properties of piezoelectric stack element, integrated in series with a standard quarter-car suspension. The slightly improved, compared to the underlying passive suspension system, frequency response of the sprung mass acceleration is demonstrated. Moreover, the overall power flow in the system, caused by the disturbing road profile, and the dissipated power due to PE-augmented suspension are analyzed and discussed in detail. The results of dissipation analysis provide helpful tools for further developments towards PE-based energy harvesting.

• Pasolli, Philipp Thomas & Ruderman, Michael (2020). Hybrid Position/Force Control for Hydraulic Actuators, Proceeding IEEE 28th Mediterranean Conference on Control and Automation (MED'2020). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538678909. s. 73–78. doi: 10.1109/MED48518.2020.9183305. Fulltekst i vitenarkiv Vis sammendrag

  In this paper a novel hybrid position/force control with autonomous switching between both control modes is introduced for hydraulic actuators. A hybrid position/force control structure with feed-forwarding, full-state feedback including integral control error, pre-compensator of the dead-zone nonlinearity and low-pass filtering of the control value is designed. Controller gains are obtained via local linearization and pole placement accomplished separately for the position and force control. A hysteresis-based autonomous switching is integrated into the closed control loop, while multiple Lyapunov function based approach is applied for stability analysis of the entire hybrid control system. Experimental evaluation is shown on the developed test setup with the standard industrial hydraulic cylinders, and that for different motion and load profiles.

• Oboe, Roberto; Ruderman, Michael & Fujimoto, Yasutaka (2020). Guest Editorial: Advanced Motion Control for Mechatronic Applications with Precision and Force Requirements. IEEE transactions on industrial electronics (1982. Print). ISSN 0278-0046. 68(1), s. 721–723. doi: 10.1109/TIE.2020.3023847. Fulltekst i vitenarkiv Vis sammendrag

  Motion Control (MC) is concerned with all the issues arising in the control of the movement of a physical device. This means that MC is not limited to the use of proper devices for sensing and actuation, in addition to suitable control algorithms, but it also deals with all the possible interactions of the controlled devices with the environment. This is the most remarkable aspect of MC, nowadays deployed in numerous mechatronic systems, especially those which are dynamically acting in heterogenous, time-varying, active, and human-accessible environments. With the progress of new technological solutions and design methods in the motion control systems, like virtual sensors, human-machine and environmental interfaces and, above all, novel control strategies including observation, adaption, and precision- and robustness-enhancing techniques, the level of motion control performance further raised in the last years. Especially the mechatronic systems which have comprehensive application-specific requirements on the precision of controlled motion and the complying interactive forces are benefiting from the advanced motion control techniques and related methods. Reduced energy consumption when inducing a controlled motion appears as an additional challenge.

• Ruderman, Michael (2020). Lead-Lag-Shaped Interactive Force Estimation by Equivalent Output Injection of Sliding-Mode, Proceeding of European Control Conference (ECC 2020). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9783907144015. s. 1619–1623. doi: 10.23919/ECC51009.2020.9143619. Fulltekst i vitenarkiv Vis sammendrag

  Estimation of interactive forces, which are mostly unavailable for a direct measurement on the interface between the system and its environment, is an essential task in various motion control applications. This paper proposes an interactive force estimation method, based on the well-known equivalent output injection of the second-order sliding mode. The equivalent output injection is used to obtain a dynamic quantity, which is first not appropriately shaped in the frequency domain, but appears as a matched external disturbance that encompasses interactive forces. Afterwards, a universal lead-lag shaper, which depends on the inherent dynamics of the motion control system coupled with environment, is used to extract an interactive force quantity. Once identified, the lead-lag shaper can be applied to the given system structure. An experimental case study with valve-controlled hydraulic cylinder and dynamic load is demonstrated. An accurate estimation of the interactive force, in comparison to the reference measurement, is shown.

• Tavares, Rafael Pinto & Ruderman, Michael (2020). Energy harvesting using piezoelectric transducers for suspension systems. Mechatronics (Oxford). ISSN 0957-4158. 65. doi: 10.1016/j.mechatronics.2019.102294. Fulltekst i vitenarkiv
• Ruderman, Michael; Iwasaki, Makoto & Chen, Wen-Hua (2020). Motion-Control Techniques of Today and Tomorrow: A Review and Discussion of the Challenges of Controlled Motion. IEEE Industrial Electronics Magazine. ISSN 1932-4529. 14(1), s. 41–55. doi: 10.1109/MIE.2019.2956683. Fulltekst i vitenarkiv Vis sammendrag

  The paper states that continued progress in integrated mechatronic design and novel actuator technologies has created new challenges for motion control technologies.

• Kapp, Daniela; Weise, Christoph; Ruderman, Michael & Reger, Johann (2020). Fractional-Order System Identification of Viscoelastic Behavior: A Frequency Domain Based Experimental Study. I Ruderman, Michael; Pavlov, Alexey & Iwasaki, Makoto (Red.), Proceeding of IEEE International Workshop on Advanced Motion Control (AMC2020). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728131894. s. 153–160. doi: 10.1109/AMC44022.2020.9244449. Fulltekst i vitenarkiv Vis sammendrag

  In this work, the fractional-order modeling of viscoelastic behavior is investigated based on measurement data in the frequency domain. For the results of two different test setups we apply existing parameter estimation algorithms designed for fractional-order transfer functions. These algorithms require a priori knowledge of the system structure including the commensurate order of differentiation. An iterative procedure is used to evaluate the influence of the unknown structure. The measured polymer samples show a viscoelastic stress response. We can show that integer-order models are not capable of capturing this behavior. For a set of predefined structures, the best obtained fractional-order models, however, show a significant variation of parameters. The chosen structure also depends on the used algorithm, therefore additional considerations have to be included in the identification process to generate reliable physical models.

• Weise, Christoph; Tavares, Rafael Pinto; Wulf, Kai; Ruderman, Michael & Reger, Johann (2020). A Fractional-Order Control Approach to Ramp Tracking with Memory-Efficient Implementation. I Ruderman, Michael; Pavlov, Alexey & Iwasaki, Makoto (Red.), Proceeding of IEEE International Workshop on Advanced Motion Control (AMC2020). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728131894. s. 15–22. doi: 10.1109/AMC44022.2020.9244309. Fulltekst i vitenarkiv Vis sammendrag

  We investigate the fractional-order (FO) control of arbitrary order LTI systems. We show that, for ramp tracking or input disturbance rejection, it is advantageous to include an FO integrator to the open-loop if we have to increase the order of integration further than one. With the lower phase-loss of the FO integrator it is easier to guarantee a desired phase margin. Furthermore the flat phase response around the crossover-frequency (iso-damping property) can be achieved for a wider frequency range such that the closed-loop is more robust wrt. amplitude and phase margins. The drawback of the FO approach is the increased implementation effort and the algebraic decay, which slows down the transient response for larger times. The algebraic decay can be reduced by placing the fractional closed-loop poles to the corresponding integer-order poles. The remaining FO transfer zeros are compensated by an additional filter. We acheieve a more efficient implementation by reducing the memory needed by a direct discretization of the Grünwald-Letnikov definition. As the controller design is done in the frequency domain, we investigate the effect of the different memory truncations. All strategies are demonstrated by simulation.

• Ruderman, Michael (2020). On stability of linear dynamic systems with hysteresis feedback. Mathematical Modelling of Natural Phenomena. ISSN 0973-5348. 15(52). doi: 10.1051/mmnp/2020014. Fulltekst i vitenarkiv Vis sammendrag

  The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure’s problem) can be proved by the well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set. The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis loop, an equivalent transformation of the closed-loop system is provided. This allows for the application of the circle criterion of absolute stability. Invariant sets as a consequence of hysteresis are discussed. Several numerical examples are demonstrated, including a feedback-controlled double-mass harmonic oscillator with hysteresis and one stable and one unstable poles configuration.

• Tavares, Rafael Pinto; Ruderman, Michael; Menjoie, Daan; Molina, Joan Vazquez & Dhaens, Miguel (2020). Modeling and field-experiments identification of vertical dynamics of vehicle with active anti-roll bar. I Ruderman, Michael; Pavlov, Alexey & Iwasaki, Makoto (Red.), Proceeding of IEEE International Workshop on Advanced Motion Control (AMC2020). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728131894. s. 161–167. doi: 10.1109/AMC44022.2020.9244454. Fulltekst i vitenarkiv Vis sammendrag

  This paper deals with modeling and identification of vertical dynamics of the ground vehicle equipped with two active anti-roll torsion bars. A series of field tests of a full-scale drive have been performed, from which multiple displacement and acceleration data of the unsprung and sprung masses have been collected for each vehicle corner. The standard full vertical vehicle model is extended by the developed model of an active anti-roll torsion bar and valve-controlled semi-active shock absorbing damper. Along with the three-dimensional damping map, the nonlinear progressive stiffness of the elastomer-based decoupling unit are identified from the available data. The multi-channel and multi-state linearized dynamic system model is also obtained. Several MIMO transfer characteristics are exemplary shown for comparing the measured frequency response functions and those estimated from the input-output behavior of the full model. The vehicle setup with the anti-roll bars and performed field tests are described along with the drive trajectories and road excitation conditions.

• Ruderman, Michael (2019). On Stability of Virtual Torsion Sensor for Control of Flexible Robotic Joints with Hysteresis. Robotica (Cambridge. Print). ISSN 0263-5747. doi: 10.1017/S0263574719001358. Fulltekst i vitenarkiv Vis sammendrag

  Aim of the virtual torsion sensor (VTS) is in observing the nonlinear deflection in the flexible joints of robotic manipulators and, by its use, improving positioning control of the joint load. This model-based approach utilizes the motor-side sensing only and, therefore, replaces the load-side encoders at nearly zero hardware costs. For being applied in the closed control loop, the stability and robustness of VTS are most crucial. This work extends the previous analysis by a general case of nonlinear joint stiffness with hysteresis and provides straightforward conditions with respect to the system dynamics. The dissipativity and passivity of the torsion-torque hysteresis map are analyzed and discussed in detail. The absolute stability of VTS inclusion into position control loop is shown based on the equivalent loop transformations and Popov criteria, including the sector conditions. Illustrative numerical examples of the control error dynamics and its convergence are provided.

• Ano, Shuta; Seki, Kenta; Ruderman, Michael & Iwasaki, Makoto (2019). Estimation of Sway-angle Based on Hybrid State Observer Using Continuous and Discrete Sensing, Proceeding 45th Annual Conference of the IEEE Industrial Electronics Society - IECON 2019. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728148786. s. 3123–3128. doi: 10.1109/IECON.2019.8927378. Fulltekst i vitenarkiv Vis sammendrag

  A hybrid state observer design is presented herein to estimate sway-angle and angular velocity in trolley systems with pendulum. In general, anti-sway control for trolley systems with pendulum such as overhead cranes are designed based on sway-angle signals detected by angular sensors. Opposed to that, a state observer without those sensors is proposed to estimate the sway-angle of the pendulum. A standard linear continuous feedback observer causes estimation error owing to the system nonlinearity and modeling error. This paper proposes a hybrid state observer incorporating discrete sensor signals. In the hybrid state observer, the estimation performance is improved by correcting the state of the system based on discrete signals. The effectiveness of the hybrid state observer is verified by conducting experiments using a downscaled testbed of a trolley system with pendulum.

• Tavares, Rafael Pinto; Molina, Joan Vazquez; Sakka, Monzer Al; Dhaens, Miguel & Ruderman, Michael (2019). Modeling of an active torsion bar automotive suspension for ride comfort and energy analysis in standard road profiles, Proceeding of 8th IFAC Symposium on Mechatronic Systems and 11th IFAC Symposium on Nonlinear Control Systems. IFAC Papers Online. s. 181–186. doi: 10.1016/j.ifacol.2019.11.671. Fulltekst i vitenarkiv
• Ruderman, Michael & Fridman, Leonid (2019). Model-free sliding-mode-based detection and estimation of backlash in drives with single encoder. IEEE Transactions on Control Systems Technology. ISSN 1063-6536. 29(2), s. 812–817. doi: 10.1109/TCST.2019.2956914. Fulltekst i vitenarkiv
• Seki, Kenta; Hirata, Jun-ya; Ruderman, Michael & Iwasaki, Makoto (2019). Creep Modeling with Time-dependent Damping Parameters in Piezoelectric Actuators, IEEE 2019 International Conference on Mechatronics. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538669594. s. 135–140. doi: 10.1109/ICMECH.2019.8722864. Fulltekst i vitenarkiv

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• Ruderman, Michael & Seki, Kenta (2024). IEEE AMC2024 conference proceeding. IEEE (Institute of Electrical and Electronics Engineers). ISBN 9798350342819. 660 s. Fulltekst i vitenarkiv
• Ruderman, Michael (2023). Analysis and Compensation of Kinetic Friction in Robotic and Mechatronic Control Systems. CRC Press. ISBN 9781032539454. 67 s. Fulltekst i vitenarkiv Vis sammendrag

  This book comprehensively covers kinetic friction in a robotics, mechatronics, and control engineering context. Providing the theory behind kinetic friction, as well as compensation methods and practical solutions, the book is a key companion to studying different control systems. Beginning with a clear introduction to the subject, the book goes on to include three main facets of kinetic friction, starting with phenomena of kinetic friction in drives. This chapter explains friction interfaces and friction effects. Following on from this, the next chapter looks at motion dynamics with friction, which introduces dynamic system equations and focuses on both energy balance and dissipation. Finally, the book looks at compensation of friction in motion control, which summarises key compensation methods in controlled mechanical systems. Introducing various basic feedback control methods, including observer-based methods to compensate for kinetic friction, the book provides practical information which can be used in a wide variety of contexts not specific to particular systems or applications. The book will be of interest to students and industry workers in the field of robotics, mechanical systems and control engineering.

• Ruderman, Michael & Chen, Wen-Hua (2023). Proceeding IEEE International Conference on Mechatronics (ICM2023). IEEE (Institute of Electrical and Electronics Engineers). ISBN 9781665466615. 450 s. Fulltekst i vitenarkiv
• Tsuji, Toshiaki; Ruderman, Michael; Fujimoto, Hiroshi & Ivanov, Valentin (2021). Proceeding of IEEE International Conference on Mechatronics (ICM2021). IEEE (Institute of Electrical and Electronics Engineers). ISBN 9781538669594. Fulltekst i vitenarkiv
• Ruderman, Michael & Tsuji, Toshiaki (2021). 2021 IEEE International Conference on Mechatronics (ICM). IEEE (Institute of Electrical and Electronics Engineers). ISBN 9781728144436. 650 s. Fulltekst i vitenarkiv
• Ruderman, Michael; Pavlov, Alexey & Iwasaki, Makoto (2020). Proceeding of IEEE International Workshop on Advanced Motion Control (AMC2020). IEEE (Institute of Electrical and Electronics Engineers). ISBN 9781728131894. Fulltekst i vitenarkiv

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• Ruderman, Michael (2026). Model-free tuning of feedback controller: derived from stability margins perspective. doi: https:/dii.univpm.it/2026/06/14/avviso-di-seminario-37/. Fulltekst i vitenarkiv Vis sammendrag

  Loop shaping and the corresponding amplitude and phase transfer characteristics play one of the most important roles when synthesizing automatic feedback controllers, while different stability margins can be formulated in frequency domain for both robustness and performance properties. For SISO systems of the type one, without explicit model structure and parameter values, the talk will show a novel model-free tuning method proposed for PI-Lead type feedback. We will recall and summarize some relevant properties of a loop transfer function to be shaped via linear feedback of generic type. Then, we will accentuate that the robustness and performance often result directly from the loop characteristics around the crossover frequency and different stability metrics derived based on that. The proposed method roots in the ultimate sensitivity principles and it makes use of some general characteristics of loop shaping. The three-steps tuning procedure, based on the output measurements only, will be explained. Along with general principles and ideas, some illustrative experimental examples will also be shown.

• Ruderman, Michael (2026). Robust frequency estimation in core of some feedforward and feedback control applications. Fulltekst i vitenarkiv Vis sammendrag

  Oscillatory signals and system states can occur in quite different processes, for instance mechanical vibrations, electric and power circuits, electromagnetic waves, bio-medical signals, and others. Often, the parameters of a harmonic signal must first be robustly estimated for feed-forward or feedback control purposes, while only a limited set of process quantities is available from sensing. A general problem with physical oscillatory signals is that they can be biased, have time-varying parameters, and are mostly subject to the noise. Although the amplitude and phase can also be essential in several cases, mostly it is the angular frequency which needs to be accurately known, for instance in non-stationary applications such as synchronous motors, inverters, or flexible structures with varying operation points and load. In this seminar talk, a robust frequency estimator proposed in 2021 will be first discussed and demonstrated on different (also experimental) data. Then, we will exemplify how and under which assumptions and constraints a real-time estimate of the main harmonic frequency can be used in feedback and feed-forward control. For feedback control scenario, the frequency estimation will serve the time-delay-based feedback control proposed in 2023 for fourth-order oscillatory systems. For feed-forward control scenario, the robust frequency estimation will be demonstrated to be used in a standard PLL architecture, this way improving its transient behavior and allowing for e.g. applications with frequency ramps and other time-varying frequency processes. While the talk will focus mostly on the recently published works, it also opens a discussion for further application scenarios and non-trivial cases where some additional dynamics and stronger pronounced nonlinearities can be in place.

• Ruderman, Michael (2026). Loop properties for feedback control tuning: novel model-free approach. Fulltekst i vitenarkiv Vis sammendrag

  When focusing on the synthesis tools for automatic feedback controllers, noteworthy is that apart from the established and advanced state-space methods, energy shaping and power port techniques, and Lyapunov-based design approaches, the signal processing view with the corresponding norms and transfer functions is still one of the most common feedback design techniques. Loop shaping and the corresponding amplitude and phase transfer characteristics play here the most important roles. For single-input-single-output (SISO) systems, the robustness and performance properties often result directly from the loop characteristics around the crossover frequency and different stability metrics derived based on that. At the beginning, we will recall and summarize the most relevant properties of a loop transfer function to be shaped via a linear feedback controller of generic type. We will also recall some loop shaping principles accommodated in advanced PID controllers [1], which continue to be a proven workhorse in countless industrial and generally commercializable scenarios and applications. Then, a novel model-free and, therefore, purely experimental practical tuning method of PI-Lead control introduced recently in [2] will be shown. The developed method derives from the ultimate sensitivity principles, well known in empirical Ziegler-Nichols tuning of PID controllers, and makes use of some general characteristics of the loop shaping. Along with the general principles and ideas, some illustrative experimental examples will also be shown.

• Ruderman, Michael (2026). Controlling flexible systems by output feedback only. doi: https:/sites.google.com/view/bayujayawardhanainaugural/home. Fulltekst i vitenarkiv Vis sammendrag

  Opto-mechatronics, which is particularly assuming and placing high demands on precision engineering, often involves the actuated flexible elements (or systems at large) like for example flexure hinges, cantilevers, and similar. Despite the often complex and not trivial structures and topologies, such systems exhibit usually some well pronounced oscillating behavior, that renders them similar to two-inertia dynamics problem, while the major harmonic is often uncertain and commonly dependent on operation time and/or state. The sensing point of a tool (or structural output) is often non-collocated with an actuating element and, moreover, there is mostly an only limited set of state variables available from the sensors to compensate for such oscillatory behavior. This workshop talk will deal with a newly proposed control [1] of flexible oscillatory systems, in which a time-delay based compensation is robustly achieved by using only the feedback output. Also, the robust global frequency estimator [2] will be brought in combination with time-delay based control, thus allowing for a model-free tuning of the oscillation harmonic, or even a real-time adaptive compensation or it [3]. We will also discuss the sensitivity of the proposed methods and derive their limits of applicability as well as the additional modeling knowledge required. Laboratory experimental examples will be shown in confirmation of the controlling methodology. While the talk focuses mostly on the mentioned recently published works, it opens a discussion for further application scenarios and non-trivial cases where some additional dynamics and stronger pronounced nonlinearities are in place.

• Ruderman, Michael (2025). A Way to Shape the Force and Impedance Control for Robotics. Fulltekst i vitenarkiv Vis sammendrag

  A standard motion control based on the feedback of output displacement cannot handle unforeseen contact with the environment without penetrating into soft (i.e. viscoelastic or plastic) materials or even damaging fragile materials. Robotics with tactile and haptic capabilities, and in particular medical robotics as a demanding example, place special demands on the advanced motion control systems that should enable safe and harmless contact transitions. When focusing on methodologies and tools for synthesizing the motion and force controllers, it is noteworthy that apart from the established and advanced state-space methods, energy shaping and power port approaches, and Lyapunov-based design, the signal processing view with the corresponding norms and transfer functions is still one of the most common feedback design techniques. Control loop shaping and the so-called sensitivity functions play here one of the most important roles for robustness and performance when designing feedback controllers for a given input-output system representation. This talk will be dedicated to the control loop shaping with aspects of varying structure due to the interaction of a system plant (i.e. manipulator tool) with its environment. In particular, it will be shown how the basic principles of loop shaping can easily be used to handle sufficiently stiff motion control with reconfiguration into sufficiently smooth impedance control upon the contact. A remarkable feature of such approach is that it can work without measurement of the contact forces, and the control signal and the measured output displacement are the only quantities used for design and operation. Along with the general principles and backgrounds of the stiff motion control and soft force control, some illustrative experiments will be shown where the moving mechanical tool comes into contact with grapes that are soft and simultaneously penetrable.

• Ruderman, Michael & Kopfova, Jana (2025). On Cauchy problem and stability of inversion-free feedforward control of piecewise monotonic Krasnoselskii-Pokrovskii hysteresis (extended abstract). Fulltekst i vitenarkiv
• Ruderman, Michael (2024). Seminar: Robustly estimating and compensating uncertain oscillatory output. Fulltekst i vitenarkiv
• Ruderman, Michael (2024). Understanding kinetic friction and its control related challenges. Fulltekst i vitenarkiv Vis sammendrag

  Kinetic friction occurs wherever two mechanical parts are in physical contact and there is relative motion between the two. Our engineering understanding of the Coulomb and viscous friction go back to the classical one- (or maximal two-) lumped parameter models, while the overall resulting dynamics of actuated bodies with friction is always non-trivial for analysis, identification and, especially, control. Despite more sophisticated heuristic dynamic friction models (with more parameters and internal unmeasurable states) are also available, they are not always helpful in mastering the kinetic friction. This talk will provide a brief introduction to the main context and assumptions related to kinetic friction, focusing on the linear viscous and nonlinear Coulomb friction in a one-dimensional setting of the generalized coordinates and forces. In addition to a well-understood frictional behavior at steady-state, we will pay attention especially to pre-sliding transients at the beginning and stop and reversals of relative motion. Kinetic friction will equally be considered from the perspective of energy dissipation and incorporated into the standard Lagrangian framework of dynamic system modeling. The problems associated with using the standard feedback regulators (like PD or PID) for motion with friction will be highlighted and discussed in context of convergence of an output value under control. The talk will also demonstrate several motivating numerical examples and experimental observations, picked out from the own and also from other independently published works.

• Ruderman, Michael (2024). On structural hysteresis damping of vibro-impact dynamics: case study. Fulltekst i vitenarkiv Vis sammendrag

  It is understood that a homogeneous solution for free motion with frictional damping is well defined for all positive dry and viscous coefficients of friction and initial conditions. Mechanical systems in engineering are often subject also to a vibro-impact, thus giving rise to a constrained motion and additional structural damping which is in accord with Hertzian contact theory. The present case study demonstrates how the vibro-impact dynamics evolves and damp the kinetic energy at the impact, with the corresponding hysteresis losses. A series of accurate mechanical experiments with Coulomb friction and stiff impact argue in favor of the assumed modeling. The study confirms the interpretation of restitution coefficient and impact force proposed by Hunt and Crossley in 1975, and provides additional aspects related to the structural hysteresis losses assessed both in time and frequency domain.

• Ruderman, Michael (2024). Shaping robustly control loop: look into stability margins and uncertainties. Fulltekst i vitenarkiv
• Ruderman, Michael (2024). Robustly estimating and compensating uncertain oscillatory output. Fulltekst i vitenarkiv Vis sammendrag

  Oscillatory quantities occur in almost all types of the processes, for instance mechanical vibrations, electric and power circuits, electromagnetic waves, bio-medical signals, and others. Often, an oscillatory output state must first be estimated, in particular regarding the unknown and/or time varying frequency, and then compensated for in a robust manner. A general problem with physical oscillatory signals is that they can be biased, have time-varying parameters, and can also be influenced by noise. Moreover, there is often only a limited set of the state variables available from the sensors to compensate for oscillatory behavior. In the worst case, only an output feedback value can be used for control in the applications, while the internal dynamic states cannot be measured or accurately observed. This talk will illustrate how a robust estimation of the unknown and even varying frequency, proposed in [1], can be combined with the time-delay based output feedback control of the low-damped oscillations, provided in [2]. Since both the robust frequency estimator [1] and output oscillations compensator [2] are independent from each other in analysis and design, the former can be used as a plug-in, thus making the whole compensation scheme truly adaptive [3]. We will first present and examine both approaches and then evaluate their interaction on a real experimental system with noisy measurements and additional process noise. Some additional aspects of parameter tuning and constraints limiting applicability will also be demonstrated, theoretically and based on experimental observations, and brought into a concluding discussion.

• Ruderman, Michael (2023). Interplay between linear integral and discontinuous relay feedback: challenging issue for standard PI/PID controllers in presence of Coulomb friction. Fulltekst i vitenarkiv Vis sammendrag

  We consider linear time invariant system plants with an unbounded integral control action and discontinuous relay in feedback. Examples for that are the standard PI/PID controllers, widely used in various types of robotic and mechatronic systems. Inherent challenge of a discontinuous relay feedback can be directly associated with presence of the Coulomb friction and mechanical setups, that downgrades the convergence performance of motion control systems for set-point stabilization tasks. Other application examples in which a relay non-linearity in the loop represents part of the plant dynamics are also conceivable. As a matter of fact, a slowly converging stick-slip behavior with continuously growing periods appears in such systems, owing to an interplay between the integral feedback and relay nonlinearity. In this talk, we will look into analysis of the convergence behavior and highlight the appearance of sticking phases and set of possible trajectories in vicinity to the globally stable equilibrium and associated region of attraction. A novel solution to convergence analysis of such systems, based on the classical sliding mode principles, will be presented. Some aspects of estimating upper bound of the convergence time will also be treated at the edge. The talk will also include several motivating numerical examples and experimental observations known from the other published works.

• Ruderman, Michael (2023). Motion control with optimal nonlinear damping. Fulltekst i vitenarkiv Vis sammendrag

  In second-order feedback control systems, a linear damping enables shaping the transient response and obtaining sub-optimality in the output trajectory without transient overshoot. However, linear damping has certain limitations in performance given by the locus of double real poles. Considering a second-order feedback system from the point of view of energy balance through the control, it becomes clear what role the feedback of the output and its time derivative play. The first one is creating a potential field and supplies the system with potential energy unless the output control error becomes zero. The second one is shaping the system energy via the corresponding damping and, this way, ensures convergence to zero equilibrium. In systems with linear damping, the asymptotic convergence slows down near zero equilibrium, according to the exponential behavior. For improving transient and convergence performance of the feedback controlled second-order systems, the nonlinear damping control was proposed in [1,2]. This talk will summarize that so-called optimal nonlinear damping control, discuss its principal properties, and show some further developments and experimental evaluation results [3]. Several open questions of interest for future research will also be discussed along with practical challenges of the motion control. References: [1] Optimal nonlinear damping control of second-order systems. M. Ruderman. Journal of The Franklin Institute, Vol 358, pp 4292-4302, 2021, https://doi.org/10.1016/j.jfranklin.2021.03.022 [2] Convergent dynamics of optimal nonlinear damping control. M. Ruderman. IFAC 6th Hybrid Conference on Analysis and Control of Chaotic Systems, IFAC-PapersOnLine, Vol 54(17), pp 141-144, 2021, https://doi.org/10.1016/j.ifacol.2021.11.039 [3] Motion control with optimal nonlinear damping: from theory to experiment. M. Ruderman. Control Engineering Practice, Vol 127, pp 105310, 2022, https://doi.org/10.1016/j.conengprac.2022.105310

• Nguyen, Anh-Tuan; Dinh, Truong Quang; Chong, Junjie; Iwasaki, Makoto; Precup, Radu-Emil & Ruderman, Michael (2023). Guest editorial introduction to the special issue on “Emerging control and automation technologies for advanced mechatronic systems”. Control Engineering Practice. ISSN 0967-0661. 136, s. 105532–105532. doi: 10.1016/j.conengprac.2023.105532. Fulltekst i vitenarkiv
• Lucia, Oscar; Ruderman, Michael & Chen, Wen-Hua (2023). 2023 IEEE International Conference on Mechatronics [Society News]. IEEE Industrial Electronics Magazine. ISSN 1932-4529. 17(3), s. 68–69. doi: 10.1109/MIE.2023.3300089. Fulltekst i vitenarkiv
• Ruderman, Michael (2023). Motion control with optimal nonlinear damping and convergent dynamics. Fulltekst i vitenarkiv Vis sammendrag

  In second-order feedback control systems, a linear damping enables shaping the transient response and obtaining sub-optimality in the output trajectory without transient overshoot. However, linear damping has certain limitations in performance given by the locus of double real poles. This talk will summarize the recently developed optimal nonlinear damping control, discuss its principal properties, and show some theoretical and experimental results.

• Ruderman, Michael (2022). Constrained input modulation for impulse-based motion control. Fulltekst i vitenarkiv
• Ruderman, Michael (2022). Application of motion control with optimal nonlinear damping and convergent dynamics. Fulltekst i vitenarkiv
• Ruderman, Michael (2022). Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction. Fulltekst i vitenarkiv
• Ruderman, Michael (2021). Modeling and control of kinetic friction for robotics. Fulltekst i vitenarkiv
• Ruderman, Michael (2020). Nonlinear damping in system dynamics and control. Fulltekst i vitenarkiv Vis sammendrag

  Damping is a natural way to extract energy from an autonomous, to say isolated, dynamic system. Physically it means an irreversible dissipation process, mostly through heat transfer, while in the control systems it is inherently associated with stabilization of the state solutions, correspondingly convergence to a stable equilibrium. Nonlinear damping is relevant but, at the same time, not trivial for both – analysis and modeling of the dynamic systems and controller synthesis for their efficient regulation. This talk, devoted to nonlinear damping, will consist of two parts. In the first one, we will analyze some nonlinear damping phenomena, while focusing on rate-independent (sometimes called structural or hysteresis) damping and discussing dissipation power, local stabilizing properties, and invariant sets of equilibria. The second part of the talk will discuss nonlinear damping in the feedback control, with focus on the phase-plane analysis of solution trajectories. A novel nonlinear damping control with optimal convergence without transient overshoot will also be illustrated in detail.

• Ruderman, Michael; Kaltenbacher, Stefan & Horn, Martin (2020). Pressure-flow dynamics with semi-stable limit cycles in hydraulic cylinder circuits. Fulltekst i vitenarkiv
• Molina, Juan; Tavares, Rafael Pinto; Sakka, Monzer Al; Ruderman, Michael & Dhaens, Miguel (2019). Industrial Mathematics at DRiV TM. Fulltekst i vitenarkiv
• Pasolli, Philipp Thomas & Ruderman, Michael (2020). Hybrid modeling and control of mechatronic systems using a piecewise affine dynamics approach. Universitetet i Agder. ISSN 9788271179748. Fulltekst i vitenarkiv Vis sammendrag

  This thesis investigates the topic of modeling and control of PWA systems based on two experimental cases of an electrical and hydraulic nature with varying complexity that were also built, instrumented and evaluated. A full-order model has been created for both systems, including all dominant system dynamics and non-linearities. The unknown parameters and characteristics have been identi ed via an extensive parameter identi cation. In the following, the non-linear characteristics are linearized at several points, resulting in PWA models for each respective setup. Regarding the closed loop control of the generated models and corresponding experimental setups, a linear control structure comprised of integral error, feed-forward and state-feedback control has been used. Additionally, the hydraulic setup has been controlled in an autonomous hybrid position/force control mode, resulting in a switched system with each mode's dynamics being de ned by the previously derived PWA-based model in combination with the control structure and respective mode-dependent controller gains. The autonomous switch between control modes has been de ned by a switching event capable of consistently switching between modes in a deterministic manner despite the noise-a icted measurements. Several methods were used to obtain suitable controller gains, including optimization routines and pole placement. Validation of the system's fast and accurate response was obtained through simulations and experimental evaluation. The controlled system's local stability was proven for regions in state-space associated with operational points by using pole-zero analysis. The stability of the hybrid control approach was proven by using multiple Lyapunov functions for the investigated test scenarios.

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