LPV techniques for control of an inverted pendulum

Abstract

The authors present a comprehensive application of linear fractional transformation and polytopic control techniques to the control of an arm-driven inverted pendulum, The particular interest of this application lies in the fact that all ingredients of the design problem have to be taken into account; from the specifications up to the constraints inherent to real-world implementations. In this context, it has been shown that currently available synthesis methodologies, such as μ and LPV techniques, may fail to provide acceptable answers, A major obstacle is undoubtedly the implementation constraint that puts hard limitations on the controller dynamics, These limitations are generally difficult to handle within the usual formulation of LPV control techniques. It has been shown that a suitable extension of these techniques including LMI region constraints on the closed-loop dynamics can overcome this difficulty. When implementable, it has been observed that LPV controllers outperform fixed μ controllers both in robustness and performance. These observations were confirmed by simulations but more importantly by a number of records on the physical experiment.