Research On Sliding Mode Variable Structure Control Algorithm Of Ball-beam System Based On Feedback Linearization

Ball-beam system is one of the most enduring and popular equipments in the control labs at present. Not only is its structure simple and safe, but also it covers many characteristics of classical and modern controlled objects, such as nonlinear characteristic, open-loop instability and so on which is the general nature of complex controlled objects. Nevertheless, the advantages and disadvantages of control methods can be reflected on the system very well. Therefore, as an ideal test tool for studying control theory, ball-beam system can be successfully used to test the effect of a variety of advanced control strategies.This thesis is based on the GBB1004ball-beam system which is provided by Googol technology Co., Ltd. The feedback linearization theory and the sliding mode variable structure theory are in-depth studied in this thesis. The main work is as follows:First of all, the feature, composition and working principle of ball-beam system are introduced briefly in the thesis. On this basis, we establish the nonlinear math model of ball-beam system by way of the Lagrange equation and make it simplified. Then, the simulation diagram is set up. According to the open loop response curves of the system, we can analyze its nonlinear characteristic and open-loop instability more intuitively.Secondly, we realize the stability of the system using the feedback linearization algorithm. Nonlinear feedback linearization method is such kind of algorithm which requires exact mathematic model, and through the input-state and input-output feedback, realize the global linearization of the system, then, the ball-beam system is linearized in the small range of equilibrium point and design the controllers upon them respectively by using the LQR optimal control. In this way, the merits and demerits of the two linear control methods are analyzed.Then, combined with the modern control theory, sliding mode control method, a sliding mode controller is designed based on the feedback linearization. In order to enhance the ability of the system to suppress the chattering, the quasi-sliding mode controller is designed to improve it; What’s more, we put forward a method of designing the dynamic sliding mode control for the system. At the same time, a comparative study of simulation is done among the control methods, including the beam’s largest controllable inclination range, the anti-jamming capabilities and the ability to inhibit the chattering. The simulation results can not only show the strong robust performance of the variable structure control, but also indicate that the dynamic sliding mode controller has the apparent advantage on the control range and inhibiting chattering, however, its capacity of resisting the external interference will diminish accordingly.Finally, we summarize the work done, and put forward the prospect of further research directions and problems.