Experiments for Analysis and Design of Robust Controllers: The Inverted Pendulum Case

Abstract This paper introduces some experiments based on an inverted pendulum and MATLAB package which can be used to study the advantages and drawbacks of two of the well recognized methods to design robust controllers; the linear quadratic regulator and its extension with robust observer if the state is not measurable (LQR/LQE-LTR) and the optimal controller based on the H∞ theory. In particular, the lack of appropriated friction nonlinear model for the pendulum makes interesting the task of design a robust controller. Therefore the inverted pendulum is considered a suitable test-case for controller design methods and demands good preparation of graduate students to achieve satisfactory control system designs. Moreover to illustrate the difference between theory and practice the students can compare and investigate both design methods (LQG/LTR and H∞) by simulation and with the inverted pendulum. The main objectives of each experiment are described here and the experiments will be presented in the IFAC'96 Congress together with a video in which versatility and simplicity of the set are shown.