H ∞ tracking control for an inverted pendulum

Abstract

The objective of this paper is to design an $H_{\infty }$ controller for an inverted pendulum system, synthesized using the $H_{\infty }$ loop shaping technique. In the $H_{\infty }$ loop shaping technique, a linear plant model is augmented with certain weight functions, such as the sensitivity weight function and complementary sensitivity weight function, so that the closed loop transfer function of the plant will have the desired performance. In this work, the $H_{\infty }$ controller is synthesized and the analysis on robustness and performance of the system is done by taking the singular value response and robustness indicator plots.