Fuzzy LQG with high-gain observer for robust control of a double inverted pendulum on a cart

Abstract

This paper addresses the stabilization problem of the double inverted pendulum on a cart (DIPC), a benchmark system that exhibits strong nonlinearity and instability. To enhance control performance under realistic operating conditions, two hybrid control schemes are proposed: the Fuzzy Linear Quadratic Regulator (FLQR) and the Fuzzy Linear Quadratic Gaussian (FLQG) controller. The FLQR is constructed by integrating fuzzy logic with the classical LQR framework to improve adaptability and dynamic response, while the FLQG extends this approach by incorporating a Kalman Filter for robust state estimation in noisy environments. Furthermore, a High-Gain Observer (HGO) is developed to estimate unmeasurable velocity states using only position and angular measurements, thereby reducing the dependency on full-state sensing. Simulation studies are conducted for both the ideal case, with complete and noise-free measurements, and the realistic case, involving measurement noise and external disturbances. The results demonstrate that the FLQG controller with observer consistently outperforms FLQR and achieves superior robustness.