Nonlinear SPKF-Based Time-Varying LQG for Inverted Pendulum System

Abstract

This paper deals with the holing issue of nonlinear inverted pendulum (IP) system. Close to the equilibrium point, IP is considered as a linear system without disruption and linear control is sufficient. However, when the IP swings over a wide range, its nonlinear dynamics becomes significant and the stabilization of IP becomes challenging task due to the inconsistency between its nonlinear dynamics and the controllers designed based on linearized models. Hence, the need for sophisticated control becomes highly demanding. This paper proposes an optimal time-varying linear quadratic Gaussian controller (TV-LQG) that is able to overcome this inconsistency problem. The proposed TV-LQG utilizes a sigma-point Kalman filter (SPKF) and a linear quadratic regulator with a prescribed degree of stability. SPKF is a highly accurate nonlinear state estimator since it does not use any linearization for calculating the state prediction covariance and Kalman gains. This leads, instantaneously, to a more exact nonlinear state estimation. The estimated states are fed to the Jacobian method, which updates, at once, the system dynamics accordingly. Thus, the parameters of the proposed TV-LQG are optimized based on the updated system dynamics. The proposed controller is intensively tested using simulation experiments and compared to the traditional LQG, LQR self-adjusting control and LQR-fuzzy control. The results proved the robustness and competitiveness of the proposed scheme to enhance the performance of the nonlinear IP system.