SEMINAR:Sensitivity of Controllers for the Inverted Pendulum

Guest: John Chiasson, Boise State University, Idaho, USA

Title: Sensitivity of Controllers for the Inverted Pendulum 

Date/Time: October 23, 2024, 13:40

Location: FENS G035

Abstract: This talk looks at the feedback control of open-loop systems which have poles in the open right-half plane. Specifically, the inverted pendulum (cart-pole) system is considered. This system can be stabilized using feedback of just the cart position requiring an unstable controller to do so. However, the resulting (stable) closed loop system is too sensitive to be of any practical value. By sensitive is meant that a small reference input to the system will cause its output to vary far and wide before finally converging to the desired operating point. In fact, the output varies so far away that the linear model the controller design was based upon is no longer valid. This then results in a failed operation when applied to the actual inverted pendulum whose model is nonlinear. Further, the practical impossibility of using a feedback controller based on just the cart position is identified by the inverted pendulum’s right half-plane pole. Finally, it is shown why a linear state feedback controller does not have this sensitivity problem and does work to keep the pendulum rod upright. The generalization of Bode’s theorem by Freudenberg & Looze is the key to understanding these claims.

Bio: John N. Chiasson is in the Faculty of Electrical and Computer Engineering at Boise State University. He received his B.S. in Mathematics from the University of Arizona, his M.S. in Electrical Engineering from Washington State University, and his Ph.D. in Control Sciences from the University of Minnesota. He is the author of the books Modeling and High-Performance Control of Electric Machines, John Wiley & Sons, 2005, An Introduction to  Probability and Stochastic Processes, John Wiley & Sons, 2013, An Introduction to System Modeling and Control, John Wiley & Sons, 2022, and The Differential-Geometric Approach to Nonlinear Control, 2022. He is a Fellow of the IEEE for his contributions to the Control of Electric Machines and Power Converters.