Research On Motion Control Of Cart-Ball System By Sliding Mode Variable Structure Control

With the coming of the two wheeled self-balancing electrical vehicle, the research on the inverted pendulum system, cart-ball system has aroused the attention of people increasingly. The cart-ball system is a complicated, self-unstable, nonlinear system. The cart-ball system problem is a classical problem of balance control of nonlinear system, and the research on it reflects nonlinear problem, robustness problem, stabilization problem, follow-up problem and tracking problem in control theory effectively. The control of the cart-ball system can also test if the new control method has strong ability to deal with the nonlinear problem and unstable problem and so on.Based on the Lagrange equation and Newton mechanics, this paper established the mathematical model of the cart-ball system and compared the mathematical model and system structure with the rectilinear inverted pendulum system, and came to a conclusion that both of them are all nonlinear and self-unstable system. By necessary condition method, this paper had tested the correctness of the mathematical model and proved it. Based on modern control theory, the controllability and observability of the system had been tested.In order to realize the stable control of the cart-ball system, this paper designed the double closed loop PID controller and tested the control effect and robustness by simulation. The result is very ideal. However, the rapidness of the double closed loop PID control is not perfect. Based on the characteristic and advantage of the sliding mode variable structure control, this paper designed the sliding mode-PD control of the cart-ball system. The simulation result shows that the rapidness of the sliding mode-PD control of the cart-ball system is much better than the double closed loop PID control, at the same time the robustness is so perfect.To verify the conclusions above, the cart-ball system hardware experiment platform is established. The experimental bench is completed by machining operation after designing the cart-ball system structure by Visio. And then this paper build the visual inspection system using industrial camera to inspect the angle of the ball and send the angle to the control center through serial port communication; By using laser range finder the cart position is measured and send tot the control center after conversion by switching circuit. Based on DSP the system realized the stable control of the self-unstable cart-ball system.