Design of a Genetic Algorithm (GA) and Particle Swarm Optimization (PSO)-based Linear Quadratic Gaussian (LQG) regulator for a Series Double Inverted Pendulum on a Cart

Abstract

This thesis focuses on the design of a Genetic Algorithm (GA) and Particle Swarm Optimization (PSO)-based Linear Quadratic Gaussian (LQG) regulator for a Series Double Inverted Pendulum on a Cart (SDIPC). The primary issues motivating the design of this regulator are the unstable behavior of the SDIPC, the slow settling times, and the significant steady-state errors observed in previously designed regulators. For this plant model, the LQG is developed using a cascaded combination of a GA and PSO-tuned Linear Quadratic Regulator (LQR) and a full-state observer, based on the separation principle theory of control systems. This approach is optimal for fully stabilizing the SDIPC and can withstand process and measurement noise through a Kalman filter. The entire system is designed in MATLAB®/SIMULINK®. Simulation results demonstrate that the PSO-tuned LQG achieves faster settling times and smaller steady-state errors compared to the GA-tuned LQG. With the PSO-tuned LQG, the steady-state errors for the upper pendulum angle, lower pendulum angle, and cart position are reduced to 1.033 × 10⁻⁴ rad, 4.206 × 10⁻⁵ rad, and 2.920 × 10⁻⁴ m, respectively. Additionally, the settling times for the upper pendulum angle, lower pendulum angle, and cart position are 0.897 s, 0.711 s, and 0.780 s, respectively. Thus, the regulator design objectives are successfully achieved with the PSO-tuned LQG than with GAtuned LQG.