ROBUST CONTROL OF CLASSICAL AND ROTARY DOUBLE INVERTED PENDULUM

Abstract

The inverted pendulum stabilization has always been considered as an important problem for control theory and its application. The stabilization of such a system is challenging due to the presence of complex nonlinear dynamics and various sources of disturbances and the involvement of uncertainties. Therefore a robust control scheme is desirable to tackle such problems. In this work, nonlinear dynamic models of the classical and rotary double inverted pendulum system is analyzed first. Model uncertainties, including parametric variation in the viscous friction coefficients and the moment of inertia of the considered physical systems, are also characterized. The nominal nonlinear dynamics is linearized for the purpose of controller design by exploiting linear robust control techniques. Based on the linearized mathematical model and considering the associated uncertainties, the design of an H∞ controller for the stabilization of the double inverted pendulum system is attempted. After ensuring the robust stability of the system by the obtained H∞ controller, this work also aims to accomplish better robust performance by designing a controller following the μ-synthesis framework. For the rotary double inverted pendulum, a robust controller technique, particularly a μ-synthesis controller, is designed to fulfill the performance requirements along with ensuring the stability of the perturbed system. Since the resulting controllers are of considerably higher-order, controller order reduction has been incorporated without compromising the control performance. The effectiveness of the designed robust controllers is shown in the simulation results presented in this report.