Improvement Of Particle Swarm Optimization And Its Application In Linear Double Inverted Pendulum System

The inverted pendulum system is a classic problem in the control of nonlinear dynamic systems.It is a typical multivariable,strongly coupled and unstable nonlinear system.The inverted pendulum problem in the control process can effectively reflect the key issues such as stability and robustness in the control.Another reason for the comprehensive study of the inverted pendulum is that in many important engineering systems,the inverted pendulum can ly represent the basic model of control objects in a variety of application fields,and can be used as an ideal multiintelligent control algorithm verification control application platform.Its control methods and ideas have high theoretical guiding significance in aerospace technology,military industry,intelligent robots and other fields.In this paper,through the analysis of the physical model of the linear double inverted pendulum,the Lagrange formula is used to obtain the equation of motion of the system.These equations are linearized by Taylor series expansion,and the state space model of the system is obtained.In order to achieve the stable control of the position of the trolley and the second-level link in the linear inverted pendulum system,a linear quadratic regulator(LQR)based on the classic trial and error method is designed in this paper.In the optimal control,the selection of the weight matrix Q and R parameters often requires the designer to continuously adjust the parameters of the weight matrix according to the output response of the system,so that it can obtain a more excellent output response.This kind of parameter selection strategy directly exposes the shortcomings.Because it relies too much on expert experience,the process of trial and error is not only time-consuming,but also cannot guarantee that every trial and error can obtain effective parameters.Therefore,even if we can achieve the stability of the second-level pendulum through the traditional trial and error method,we cannot guarantee that the weight matrix we obtained is optimal,and then the optimal feedback coefficient we obtained will not guarantee the optimal control effect of the system.In order to design the optimal state feedback control matrix K,to overcome the shortcomings of the weight matrix Q and R in the general LQR control design relying on experience selection and trial and error,in order to obtain the best controller parameters and high performance for the purpose,this paper proposes to Many scholars have studied the idea of swarm intelligence algorithm combined with optimal control theory,trying to apply particle swarm algorithm(PSO)to the optimization of LQR controller parameters.In addition,in view of the shortcomings of the classic PSO optimization algorithm,such as insufficient local search ability and easy premature convergence,this paper proposes a new improved particle swarm optimization strategy.The improved particle swarm optimization algorithm(SFPSO)is applied to the optimization of the Q parameter and R parameter of the LQR weighted matrix of the linear quadratic optimal controller.The simulation study is conducted in the simulink environment of the MATLAB software toolbox,and the LQR optimized by the SFPSO algorithm is tested.The effectiveness of the controller.Compared with the manual trial and error method,the SFPSO algorithm is very effective and robust.The simulation example verifies that the SFPSO optimization algorithm realizes the optimization of the control system of the LQR linear double inverted pendulum,and has extremely important theoretical significance for improving the stability of the linear double inverted pendulum control system,laying the foundation for the practical application of the inverted pendulum system.The foundation has certain application value.