Research On Control Algoritnm Of Linear Inverted Pendulum

Due to the typicality of the inverted pendulum system in the field of control,it has become a long-term research direction.In this paper,the linear inverted pendulum system is taken as the research object,and the algorithm research on the swing control of the linear first-level inverted pendulum system and the stability control of the linear two-level inverted pendulum system is completed.This paper first studies the structure and basic composition of the linear inverted pendulum system,and then through in-depth analysis of the system,the inverted pendulum system has strong coupling,underactuation,nonlinearity,uncertainty and open loop instability.Secondly,based on the nature of the inverted pendulum system,a more accurate mathematical model is established.Because the structure of the straight-line inverted pendulum system is relatively simple,the Newton Euler method is used to establish the mathematical model;while the structure of the straight-line inverted pendulum system is relatively complicated,the Lagrange equation method is used to establish the mathematical model model.After related derivation,the respective nonlinear differential equations are obtained,and then linearized at the equilibrium point,the linear differential equations are obtained and converted into the state space expression of the system.For the convenience of simulation experiments,the obtained state space expressions and nonlinear differential equations were modeled by using the State-Space module and S-function module in Simulink.Then,based on the established mathematical model of the system,the stability of the system and the controllability and observability are analyzed using the Lyapunov stability method and the controllability and observability criterion,and the vertical position of the straight inverted pendulum system is obtained.The vicinity is absolutely unstable,but controllable and observable.Then on the basis of the established mathematical model,the algorithm research is carried out around optimal control and sliding mode variable structure control.First,the LQR controller is designed according to the basic principles of the LQR control algorithm,and then the genetic algorithm is used to perform the LQR control method.Parameter optimization,so as to find the optimal parameters and achieve optimal control.And based on this method,the simulation experiment of the inverted pendulum system is completed.After observing the results,the system can be stabilized near the vertical upward equilibrium position,and it is found that the LQR optimized by genetic algorithm is better than the LQR designed by trial and error method in system overshoot.Be smaller.Secondly,the sliding mode variable structure controller is designed according to the basic principles of the sliding mode variable structure control algorithm,and the process of reaching law parameters is optimized by fuzzy control.Then use these two methods to carry out simulation experiments in Simulink respectively.After observing the results,the system can also be stabilized near the vertical upward equilibrium position.By analyzing the control of these two methods on the inverted pendulum system,it is found that each of them can better complete the system stability;but for the system robustness,the sliding mode variable structure control algorithm is more robust.Next,the swing control of the linear first-level inverted pendulum system was studied around the energy feedback control algorithm and the Bang-Bang control algorithm.First,different controllers were designed according to the basic principles of these two algorithms.Through simulation experiments,it was found that both The system implements swing control,but the energy feedback control algorithm is superior to the Bang-Bang control algorithm in swing time.Finally,based on different control algorithms,the pendulum pendulum system's swing and stability control were verified in kind,which fully confirmed the effectiveness and correctness of the algorithm.