Research On Nonlinear Control Of Linear Double Inverted Pendulum

Inverted pendulum is a typical nonlinear time-varying system with high order,strong coupling,and open-loop instability,which can effectively reflect key issues such as stability and robustness in the control process.Therefore,as an experimental platform,the inverted pendulum system can test the effectiveness and timeliness of various complex algorithms.In practical engineering applications,the inverted pendulum can also be abstractly represented as a basic model of the controlled object in various control fields,so most control theories are developed based on the study of the inverted pendulum.This article mainly studies the stability control problem of a linear two-stage inverted pendulum system and designs a controller for the system.Firstly,ignoring the friction between the cart and the track in the linear two-stage inverted pendulum system,the mathematical model of the system is established through the EulerLagrange equation based on the physical model of the system and the relationship between the motion equation of the servo motor and the gear backlash.Linearization processing is performed using Taylor series expansion at the system’s operating point to obtain the state space model of the linear two-stage inverted pendulum system.The controllability and stability analysis of the system show that the linear two-stage inverted pendulum system is completely controllable at the operating point,but the system is open-loop unstable.Secondly,based on the underactuated and nonlinear characteristics of the inverted pendulum system,a control scheme based on the three-step method is designed,and the control law of the three-step method is derived.The three-step method control includes quasi-static control,reference dynamic feedforward control,and error feedback control,and the entire control law of the linear two-stage inverted pendulum system is calculated through these three steps.In order to verify its robustness,disturbance experiments are added,and simulation results show that the three-step method controller can achieve stable control of the inverted pendulum system and has certain robustness.Considering the problem of control input constraints in a linear two-stage inverted pendulum,an RBF neural network is proposed to compensate for control input saturation.The Sliding mode control law is designed according to the system error equation,and then the equivalent control law is introduced into the linear double inverted pendulum system,the switching function is replaced by the saturation function,and the parameters of the Gaussian basis function are designed according to the actual input range of the neural network combined with the RBF neural network.The simulation results show that the system can still achieve stable control of the two-stage inverted pendulum system even with limited control input.In order to further improve the response speed and anti-interference ability of the linear two-stage inverted pendulum system,a global fast terminal sliding mode control scheme based on the extended state observer is designed.In the design of the extended state observer,the system is divided into three subsystems according to the characteristics of the linear two-stage inverted pendulum system.The expanded system state is compensated into the controller to enhance the system’s anti-interference ability.Simulation results show that the extended state observer can perform disturbance observation and quickly track the system state.Combined with the global fast terminal sliding mode controller,the system response speed is accelerated.Regarding the stability control problem of the inverted pendulum system,this article proposes three control methods to address the issues of fast control,constrained control input,and anti-interference.Based on sliding mode control,different sliding mode controllers are designed to achieve stable control of the linear two-stage inverted pendulum system.Experimental results show that the designed controllers have good control performance.