Stabilization of a Pan-Tilt System Using a Polytopic Quasi-LPV Model and LQR Control

Linear parameter varying (LPV) models are widely used in control applications of the nonlinear MIMO dynamic systems. LPV models depend on the time varying parameters. This paper develops a polytopic quasi-LPV model for a nonlinear pan-tilt robotic system. A Linear Quadratic Regulator (LQR) that utilizes Linear Matrix Inequalities (LMIs) with well tuned weighting matrices is synthesized based on the developed LPV model. The number of time varying parameters in the developed polytopic LPV model is 4 so the number of vertices becomes 16. The desired controller is generated by the interpolation of LMIs at each vertex. The performance of the optimal LQR controller is evaluated by using the designed feedback gain matrix to stabilize the nonlinear pan-tilt system. Simulations performed on the nonlinear model of the pan-tilt system demonstrate success of the proposed LPV control approach.