Introducing the use of Matlab / Simulink. Short repetition of linear differential equations and Laplace transformation. The physical laws. The deduction of some simple mathematical models and mathematical solution of these models for mechanical vibrations, electrical fluctuations and distribution of heat from a heat source. Solution of optimization problems using linear, quadratic and mixed-integer programming.
Mechanical systems who are modeled by systems of linear (and non-linear) differential equations. Stability analysis of stationary and periodic solutions.
Special mechatronical problem´s who are modelled by the heat equation (1 and 2 dimensions, 1D and 2D), the wave equation (1D and 2D) and the Laplace equation (2D). Some simple models solved by separation of the independent variable. Solutions using the differences.
On successful completion of the course, the student should be able to
formulate, and in some cases derive, mathematical models in Mechatronics, based on the physical laws of mechanics, heat and electricity learn
solve the mathematical models using analytical and numerical methods
apply theory and computer tools for solving optimization problems
Teaching methods and workload
Lectures, calculation exercises, project in groups of two students (optimization theory and practical problem solving)
The course evaluation is completed as a midterm evaluation in accordance with the provisions listed in the Quality Assurance System Chapter 2.1.1. A final evaluation may be completed as required.
Assessment methods and criteria
Written exam, 4 hours (70 %). Portifolio consisting of 1 project work (30 %). Graded assessment.