Design of LQR fuzzy PID controller for double inverted pendulum based on PSO optimization

Abstract

In this design, through the analysis of the physical model of the linear double inverted pendulum, the motion equation of the system is obtained by using the classical Newtonian mechanical formula, and the obtained equation is linearized at the stable point, and the state space model of the system is obtained. In order to realize the stable control of the trolley position and the secondary linkage in the linear inverted pendulum system, the linear quadratic optimal controller is used in this design to obtain an excellent output response. In order to design the optimal state feedback control matrix K, the shortcomings of weight matrices Q and R in general LQR control design that depend on experience selection and trial and error are overcome. This design attempts to apply PSO algorithm to LQR controller parameter optimization. PSO algorithm is applied to optimize Q parameters and R parameters of LQR weighting matrix of linear quadratic optimal controller, and K matrix is obtained. The matrix is applied to a fuzzy PID controller designed by the fusion algorithm to overcome the disadvantage that a single PSO cannot adapt itself. Finally, a comparative simulation study is carried out in the Simulink environment of Matlab software toolbox, which verifies the effectiveness of the fuzzy PID controller based on particle swarm optimization algorithm, laying a theoretical foundation for the practical application of the inverted pendulum system, and has certain application value.