Research On Friction Characteristic Analysis And Friction Compensation Algorithm Of Ball And Plate System

Friction is complicated, nonlinear and uncertain phenomena of nature, it almost exists between contact surface of two objects when they are in motion or trending to move. In the modernization industry and people's daily life, the friction may expend some effective power and cause energy loss. It's estimated that one third of world energy was consumed by friction. The directly results caused by friction is abrasion and performance decrease. Therefore, damage due to the friction is huge. On the other hand, sometimes we will use the friction, such as vehicles and people move on the road, self-locking machine of mechanism and so on. In a word, the friction is an important part in the construction of human civilization. It is a new challenge at present that how to utilize the friction and minimize the damage and loss caused by friction as possible as we can.Ball and plate system is multi-variable, strong coupling, parameters uncertainty and nonlinear system, which through adjusting the rotary angels of the plate to control the positions or moving states of a ball on the plate. Ball and plate system is used as a standard experimental platform to research diverse control schemes.Ball and plate system is an exemplification of nonlinear dynamics system, it has been received more and more attentions. Many scholars have designedcontrol algorithm only based on simplification model of ball and plate system, but they thought little of nonlinear, coupling and uncertainty. However, the friction is one of the most important factors affecting control precision and dynamic performance of the system. Ball and plate system has two control loops exist friction nonlinear, inner loop controls step motor and the friction is in servo system such as gearing, reducer. Outer loop controls the moving states of the ball and the friction is between ball and plate. Therefore, this paper is emphasis on friction in the ball and plate system based on studying the mechanism of friction nonlinear, analyzes some influencing factors of friction, and then a local friction compensation controller of ball and plate system is designed to offset the real friction acting on the system.The task of research on fiction characteristic analysis and friction compensation algorithm of ball and plate system is based on the theory of nonlinear observation and system discrimination. It is on the ball and plate experimental platform BPVS-JLUâ… which is built by our laboratory to achieve the following goals.Firstly, through analyzing friction when the ball in motion to rebuild the mathematics model of ball and plate system which considering the factor of the friction. Secondly, Least square method is adopted to estimate the uncertain parameters of friction model based on the theory of system discrimination. Finally, a local friction compensation algorithm is studied to improve the velocity of the ball, the precision of the trajectory and dynamic characteristic of the system.The mathematic model of ball and plate system is the basic for analyzing its kinematics and control characteristic. However, the mathematic model of system is built in condition of neglecting the friction in ball and plate system, which may lead a large difference between real system and mathematic model. Due to difficulty of the friction math model, an extended Kalman filter is designed to observe the value of the friction between ball and plate system. Through analyzing the fiction, some factors affection the friction are obtained,such as the angel of the plate, the surface medium and the velocity of the ball. Then, according to the relation of friction coefficient and velocity, the mathematic of friction is built. Using Least square method estimates to discriminate unknown parameters.The ball on a plate is able to move freely and has no ability to recognize the environment. So the unconstrained object can not control its behavior by itself. Due to the surface materials of the plate are asymmetry and the states change of the plate, the friction shows strong time-variability. Some control schemes are required more and more exigent to minimize the effects of equanimity and moving trajectory of the ball and the phenomenon of stopping moving of the ball near the steady point which caused by the friction. So, in this paper, the relations of friction and the angels of the plate is studied firstly, and then a local friction compensation scheme is implemented to offset the real friction of the ball and plate system.In a word, this paper do a lot of academic and experimental research on the friction nonlinear of ball and plate system, and basically achieves its given goals. Because of the exemplification of ball and plate system in its dynamics and kinematics analysis and control issues, the work of this paper will be contributive to the following research on similar dynamic systems.