Control Of Inverted Pendulum System Considering Control Input Constraints

Inverted pendulum system main characteristics are high order,strong coupling,nonlinearity and open loop instability,etc.It contains almost all the characteristics of complex systems,so most control theories are research is carried out based on the stability control of the inverted pendulum.In the actual physical control system,it is very common for the control input of the actuator to reach saturation.The input of all control systems is limited.Once the control range is exceeded,the system will be unstable or even crash.Of course,the inverted pendulum system is no exception.These problems bring difficulties to the stability research of the inverted pendulum system.In the research on the motion control of the inverted pendulum system,this paper takes into account the input saturation of the actuator,and establishes the mathematical model of the servo system based on the voltage equation and motion equation of the DC motor of the inverted pendulum system.The integrated model of the inverted pendulum system of the servo system makes the control variable and its constraint range more accurate.Then linearization obtains the linear motion equation of the inverted pendulum,and analyzes the controllability of the inverted pendulum system,which provides feasible conditions for the realization of the control algorithm.In order to solve the actual input limitation problem of the control system,this paper uses the Wind-up variable structure PID,which integrates the control input saturation error,and then uses the adjustment of the coefficient to realize the adaptive adjustment of the integral term.The radial basis function neural network(RBF)is adopted to approximate the input saturation error to compensate the error.The two methods not only ensure that the inverted pendulum system is operating stably,the control quantity remains within the input constraint range,but also has strong stability and superiority,and realizes the accurate stable pendulum control of the inverted pendulum system.This paper adopts the global dynamic fast terminal sliding mode control based on ESO,uses the expanded state observer to treat the uncertainty of the system and the external disturbance as a whole,and finally generates a brand new expanded state,and the disturbance value is measured by the observer.The real-time observation will compensate the sliding mode control law according to the observation value.This method enhances the anti-interference ability of the entire system,reduces the influence of the nonlinear part and disturbance of the system on the switching gain of the sliding mode controller,and effectively The chattering of the system is reduced,and the stable pendulum control of the inverted pendulum system is finally realized.