STATE AND OUTPUT FEEDBACK CONTROL WITH TIME AND FREQUENCY REQUIREMENTS FOR THE INVERTED PENDULUM

Abstract

The inverted pendulum is widely used in numerous applications, one of which is the control of a rocket’s orientation during the launch phase. Control of an inverted pendulum presents a significant degree of complexity due to its unstable, nonlinear and under-actuated characteristics. This article presents design and comparative analyses of state and output feedback techniques based on time and frequency requirements. The design techniques are the linear quadratic controller (LQR) and the modified linear quadratic controller (LQRy). Nonlinear and linear models of the inverted pendulum are presented. In addition, synthesis and analysis models are presented, the gains tuning is detailed, and the respective linear analysis is performed including their time responses, stability margins, and the closed-loop poles. Finally, the designed control laws are subjected to nonlinear simulations for further comparisons, considering trajectory tracking, disturbance, noise and control efforts.