Design Of Fixed Point And Trajectory Tracking Controller For Ball&Plate System

The ball&plate system is two-dimensionally extended from the ball&stick system,and it is used as a typical experimental platform for the control algorithm together with the inverted pendulum system and the ball&stick system.Ball&plate system is a complex,typical nonlinear system.Trajectory tracking control of the ball on the plate is a very important problem in the ball&plate system.It is an important sign to judge the performance of the control system whether it can accurately track the given curve.In recent years,more and more control algorithms are proposed,but the accuracy,fastness and robustness of tracking can not meet the requirements.In this paper,a new controller is designed to solve the problem of track control in ball&plate system.The main work of this paper is as follows:Firstly,the research background and significance of cricket system are summarized.The research results of experts and scholars at home and abroad are introduced,and the control algorithm is designed on cricket platform.Some basic concepts,important lemmas and solving tools used in the controller design are summarized and refined,which provides the theoretical basis for the subsequent controller design.Secondly,the lagrangian dynamics model of ball&plate system was established and the mathematical model is obtained.The model is simplified under a series of assumptions,and the model linearization method is used to get the cricket system linearization model.Verify that the linearization model is fully controllable and observable.Then,based on our tracking task,the internal model principle is introduced,and the form of the servo compensator is constructed according to the modes of the unstable external signal and the unsatisfactory control effect.The stabilization controller is designed to stabilize the controlled object composed of the servo compensator and the controlled object.Then the LQR method is used to optimize the control parameters,and the linear matrix inequality(LMI)is used to solve the control parameters.Finally,the controller parameters were loaded into the original controlled object,and the simulation experiment was carried out on MATLA software.The system simulation curve is obtained and the tracking effect is analyzed.The simulation results show that the system achieves asymptotic tracking for all kinds of curves,namely zero static error tracking.The controller combines the control theory of servo compensation,dynamic output feedback and quadratic adjustment,and achieves the system zero tracking,and has good dynamic quality and has certain robustness.