Variable Structure Control Of The Transverse Vibration Of Belt Drive Systems Via Neural Networks

Because of the advantage of simple structure, far transmitting power, little manufacturing cost and overload protection, etc., the belt drive system has been widely used in various mechanical devices. However, the vibration in the course of high-speed movement will affect the system performance and hinder its applications in some engineering fields. So it is necessary to study some control methods to restrain and eliminate the vibration of the belt system. The belts of the system do not sustain bending resistance and have small gravity and move along the direction of the axial tension, as a result, it can be modeled to be the axially moving string. Because of the simple structure of the axially moving string, active control methods are generally adopted to suppress its transverse vibration.Sliding mode variable structure control (SMVSC) has better robustness when it comes to the system perturbation and external disturbance, and it also has the advantage of rapid response, no online system identification and simple physically implementation, etc. Neural networks which can approximate any complex linear and nonlinear reiationships have strong online learning and adaptive ability. By combining the neural network with sliding mode control methods, it can make the system not only maintain strong perturbation and external interference robustness, but also try to eliminate chattering. The theory that the transverse vibration of belts is coupled to the movement of the tensioner is used to establish the linear dynamics equations of the actuator. In order to reduce chattering and improve the robustness and the dynamic quality of performance of the system, the discrete index reaching law of which parameters are adaptively revised by BP neural networks is employed to design the variable structure controller. The simulated results show that the angular displacement of the actuator can be effectively constrained by the variable structure controller that designed by BP neural networks and the discrete index reaching law, which thereby indirectly suppressed the transverse vibration of the belt drive system.Considering the defect of slow training speed and easily falling into the local minimum of the BP neural network, the RBF neural network is adopted to devise the variable structure control law. The variable structure control law of position tracking that approached by the RBF neural network is designed by utilizing the equivalent control method and location tracking method, which makes the movement of the system gradually approach the position command function and eventually achieve to control the motion of the actuator and reduce the transverse vibration of the string.As for the belt drive system that has an additional incentive, the theory of the dynamic coupling between the string and the tensioner is employed to create the new linear ordinary differential equation of the actuator and the transverse vibration function of belts. Use the BP neural network and the discrete index reaching law to design the variable structure controller. With the consideration of the deficiencies of the BP neural network, the ultimate attractor is introduced to improve the learning speed of neural networks and to prevent being trapped at local minima. The simulation conducted by Matlab show that the control law well restricts the transverse vibration of the controlled string.