Critically damped stabilization of inverted-pendulum systems using continuous-time cascade linear model predictive control

In this paper, a cascade continuous-time linear MPC controller with 7 well defined parameters is proposed to stabilize the inverted pendulum system around the desired equilibrium points. The proposed controller scheme is composed of two MPC controllers in cascade. These controllers are tuned so as to obtain a doubly critically damped behavior for the inner and outer loops. Explicit generalized expressions of the MPC controller parameters in relation to the inverted pendulum characteristics and the chosen horizon time parameter with the robustness analysis of the controlled system are given to facilitate the controller design for a wide class of inverted pendulum systems. Simulation results show that the MPC controller is compared favorably to the well known parallel two-PID control scheme.