Control Part. Arenberg Doctoral School of Science, Engineering & Technology. Moritz Diehl, Gianluca Frison, Benjamin Stickan
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1 Arenberg Doctoral School of Science, Engineering & Technology Control Part Faculty of Engineering Science Department of Electrical Engineering of Power Electronic Devices and Circuits Moritz Diehl, Gianluca Frison, Benjamin Stickan Systems Control and Optimization Laboratory Department of Microsystems Engineering (IMTEK) and Department of Mathematics Albert Ludwig University of Freiburg some videos are from when MD was the PI of the Optimization in Engineering Center (OPTEC) at KU Leuven University Freiburg, June 1, 2017
2 Aims and Topics of Control Part Aims: - know about control concepts in state space - be able to design state space controllers on a computer Topics: - State Space Control for Linear Time Invariant (LTI) Systems - Linear Quadratic Regulator (LQR) - State Estimation and Kalman Filter (KF) - Model Predictive Control (MPC) - Exercises in MATLAB (incl. homework) M. Diehl 2
3 Introduction of Teachers Lecturers: - Moritz Diehl (Professor for Systems, Control and Optimisation at IMTEK) - Gianluca Frison (Postdoc, expert on embedded model predictive control) Tutor: - Benjamin Stickan (PhD student at ISE Fraunhofer and IMTEK) M. Diehl 3
4 Team Specialty: Embedded Optimization (optimization algorithm acting on a stream of incoming data) SENSORS GPS acceleration radar vision... State Estimation: fit model to data Model Predictive Control (MPC): make optimal plan, realize only first step ACTUATORS flight surfaces steering wheel motor speeds joint torques 4
5 Model Predictive Control (MPC) Always look a bit into the future Example: driver predicts and optimizes, and therefore slows down before a curve M. Diehl 5
6 Optimal Control Problem in MPC For given system state x, which controls u lead to the best objective value without violation of constraints? simulated state trajectory controls (unknowns / variables) prediction horizon (length also unknown for time optimal MPC) M. Diehl 6
7 Optimal Control Problem in MPC For given system state x, which controls u lead to the best objective value without violation of constraints? simulated state trajectory controls (unknowns / variables) prediction horizon (length also unknown for time optimal MPC) M. Diehl 7
8 Time Optimal Motion of a Crane Univ. Leuven [Vandenbrouck, Swevers, D. et al] 8
9 Optimal solutions varying in time (inequalities matter) Solver qpoases [PhD H.J. Ferreau, 2011], [Ferreau, Kirches, Potschka, Bock, D., A parametric active-set algorithm for quadratic programming, Mathematical Programming Computation, 2014] M. Diehl 9
10 Crane Writing Time Optimally Univ. Leuven 10
11 Predictive control example: time-optimal racing of model cars Freiburg/Leuven/ETH/Siemens-PLM. 100 Hz sampling time using MPC [Verschueren, De Bruyne, Zanon, Frasch, D. CDC 2014] (Nonlinear MPC video from in Freiburg) Robin Verschueren 11
12 Metamorphosis of a wind turbine
13 Predictive Control of Kite Carousel in Freiburg Jonas Schlangenhauf Thorbjörn Jörger 20Hz/50ms sampling time using ACADO (Nonlinear MPC video from in Freiburg) (video by Ben Schleusener) 13
14 Schedule (this week) Thu, June 1, 2017, Lecture Slot 1 - Introduction - Linear time invariant (LTI) systems in state space - Controllability Fri, June 2, 2017, Lecture Slot 2 - Linear Quadratic Regulator (LQR) - Explanation of Exercise 1 (homework) Seven weeks to rehearse background material and to work on Exercise 1 M. Diehl 14
15 Schedule (cont.) Thu, July 20, 2017, Lecture Slot 3 o Discussion and Solution of Exercise 1 o Observers, Kalman Filter and Output Feedback Fri, July 21, 2017, Lecture Slot 4 o Discrete Time Systems o Explanation of Exercise 2 (homework) Thu, July 27, 2017, Lecture Slot 5 o Model Predictive Control (MPC) Fri, July 28, 2017, Lecture Slot 6 o Discussion and Solution of Exercise 2 o Lecture Summary M. Diehl 15
16 Course Webpage All info can be found on > Teaching > Power Electronics Devices and Circuits - Control Part In particular, download and read the PDF of the Course Manuscript M. Diehl 16
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