Stabilization of pan-tilt systems using acceleration based LMI-LQR controller

Abstract

This paper extends the previous work on LPV modeling of a pan-tilt system [1] and tackles the robust stabilization problem by employing angular acceleration feedback in an LMI based optimal LQR controller. The state vector of the LPV model is augmented to include the integral of the position errors in addition to joint angles and velocities. Therefore, an extended polytopic quasi-LPV model of the pan-tilt system is derived. The LMI based optimal LQR controller that utilizes acceleration feedback is synthesized based on the extended LPV model. Since the time varying parameter vector is 4 dimensional, the proposed controller is synthesized by interpolating LMIs at 16 vertices of the polytope. A cascaded nonlinear high gain observer is also designed to estimate reliable positions, velocities and accelerations from noisy encoder measurements. Simulation results show that the proposed LMI based optimal LQR controller outperforms the classical LMI based LQR controller.