Design And Control Implementation Of Ball-Beam System

The Ball-beam system has the characteristics of simple mechanical structure,little space occupation and easy observation.It is often used as the basic platform for the control theory laboratory.Because the Ball-beam system itself has non-linearity and open loop instability,it is a typical system studied by control theory and a typical device for verifying control theory or control methods.The devices of Ball-beam system are various.In this paper,GBB2004 Ball-beam system of GOOGOLTECH Company is selected.The mathematical model of mechanical part and servo motor is established.By means of linear treatment of some certain procedures,a simplified model is obtained.Because of the characteristic of servo motor,it can be simplified approximately as a gain part in the process of modeling.Therefore,the key of modeling is to establish a mathematical model of mechanical drive parts.The mathematical model of the Ball-beam system is analyzed,and the model reference adaptive control is constructed.In order to ensure the stability of the closed-loop system,the Lyapunov stability theory is chosen to design the appropriate control law to stabilize the ball in the desired position.Based on the characteristics of the transfer function of the Ball-beam system,the case of mn(28)-2 is selected to establish the Narendra self-adaption control algorithm.Make Z-transform to the continuous model of system's mechanical part and servo motor to obtain the discrete mathematical model of the controlled object.So it is suitable for self-correction controller design.Since the stability of the controlled system can be affected by the zero-pole of the closed-loop system,the pole configuration control algorithm is used during the design of self-correction control to arrange the closed-loop poles of the Ball-beam system in the desired position.In this paper,the closed-loop identification of the Ball-beam system is analyzed,and the parameters of the mechanical part and the DC servo motor are estimated by the least squares recursive estimation.There are many control algorithms for the Ball-beam system,including root trajectory control,PID control,neural network control,fuzzy control method and so on.Two kinds of self-adaption controllers are designed.In the environment of Matlab 2012b/Simulink,makereal-time control to the designed Narendra controller and the pole controller on the Ball-beam and compare with the traditional PID control results.The result shows that,the designed Narendra self-adaption controller and the pole configuration controller in this study can have a good effect on the control of Ball-beam system.