Optimization of Mechatronic Systems

Description

The course gives insight into the mathematical formulation of optimization problems and deals with advanced methods and algorithms to solve these problems. The knowledge of the possibilities and shortcomings of these algorithms should lead to a beter understanding of their applicability in solving concrete engineering problems. An emphasis will be placed on mechatronic systems: the student learns to select the appropriate solving methods and software for a wide range of optimization problems from the field of mechatronics, and learns to correctly interpret the results. The following knowledge and skills will be acquired during this course: The student will be able to formulate a mathematical optimization problem starting from a concrete engineering problem. The student will be able to classify optimization problems into appropriate categories (e.g., convex vs. non-convex problems). The student will be familiar with different optimization strategies and their properties, and will hence be able to decide which strategy to use for a given optimization problem. The student will be able to formulate the optimality conditions for a given optimization problem. The student will have a profound understanding of a wide variety of optimization algorithms and their properties, and will be able to apply the appropriate algorithms for a given optimization problem. The student will be familiar with state-of-the-art optimization software packages, and will be able to use these in an efficient manner. The student is able to independently define and solve practical optimization problems for mechatronic systems (e.g. trajectory optimization, motion control, vibration reduction). To this end he is able to formulate a mathematical model of the mechatronic system, the objective function and the constraints (e.g. in terms of position/velocity/acceleration, actuation limits, technological limits). While doing this he is able to make simplifying assumptions, and to make these assumptions explicit. Based on the mathematical formulation the student is able to recognize the nature of the optimization problem, select an appropriate numerical solution technique and apply this solution technique using existing software packages. The student is able to verify the validity of the obtained results, and is able to critically evaluate and interpret the results (e.g. obtained accuracy, required calculation time) based on physical insight in light of the assumptions made.