Research On Control Algorithm Of Ball&Plate System

Ball&Plate System is the 2-D expansion of ball-beam system. It is a typical multi-variable nonlinear under-actuated system. It is a typical experiment platform of the study of control algorithm. The object is to achieve the position control and trajectory tracking of the ball on the plate. It is mainly used to test the effectiveness of the control algorithm. The paper discusses the control performances of three control algorithms based on the object of Ball&Plate System. Because the structure of traditional variable domain adaptive fuzzy controller is complex, there is integration which is hard to choose in the output control quantity, and the calculation is large. So we improve the algorithm of variable domain adaptive fuzzy control according to control precision, stability and rapidity of the position of the ball. Weighted expansion factor is applied in the design of variable domain adaptive fuzzy controller, so the structure of the controller is simplified and the control results are improved.First, dynamics character of the Ball&Plate System is analyzed applying the Lagrange equation establishing the math model of Ball&Plate System with the control quantity of acceleration. Ball&Plate System is linearized at the balance position (horizontal position), and the controllability and observability are analyzed. The controllability and observability of Ball&Plate System are proved in the certain boundary of balance position.Second, the design principle and procedure of poles controller, fuzzy controller and variable domain adaptive fuzzy controller are showed. The three kinds of controllers are designed and simulation experiments are performed. The position tracking curve, the output curve of plate tilt angle and the output curve of control quantity are analyzed. The results show: the three controllers are effective to the Ball&Plate System; comparing the three controllers, it is stated fully that in the control of Ball&Plate System, the variable domain adaptive fuzzy controller with weighted expansion factor has good stability, control precision and respond speed, the control result is better than poles control and fuzzy control.