Simulation And Control Of Input Limited Ball And Plate System

The ball and plate system is a typical underactuated system,which has the characteristics of high order,nonlinear,strong coupling,open loop instability and so on.Actuator saturation is common in the actual control system,so the input control amount of all control systems is limited,and the ball and plate system is no exception.These problems make it difficult to control the ball and plate system.In this paper,in the study of the motion control of ball and plate system,considering the actuator dynamics,according to the equation of motion of dc motor and the gear transmission of knowledge,servo system mathematical model is established,combined with the Lagrange equation established servo system + "plate-ball" system integration model,has been clear about the scope of control variables and constraints.In order to solve the immeasurable problem of velocity variables of small balls in the system,a dimensionless state observer is designed on the basis of simplified integrated model.In order to study the fixed-point control and trajectory tracking control of the ball and plate system,a sliding mode controller was designed for the nonlinear integration model by using chain derivative method,and the stable control of the ball and plate system was realized.In order to improve the steady-state performance of the trajectory tracking control system,the feedforward control quantity of the control target is calculated by using the differential flat technique,and the trajectory tracking deviation system is established.The stabilization control quantity of the deviation system is calculated by the rolling LQR control algorithm,and the accurate control of the trajectory tracking is realized.For the problem of input constraint in ball and plate system,this paper used two methods: RBF neural network approximation compensation input saturation error,LMI in the input constraint range and variable elliptic domain optimization solution controller,to realize the control quantity of ball and plate system in the input constraint range under stable operation.The two control algorithms used in this paper have strong track tracking performance and robust performance,among which the rolling LQR control algorithm based on differential flat has higher control accuracy and better steady-state performance.