Research On Modeling And Control Of Ball And Plate System

The ball and plate system is a classic nonlinear control object basically,with such characteristics as multivariable,strong coupling,underdrive and so forth.It is usually used to verify the effectiveness of the control algorithm and to judge the performance of the algorithm.As a typical benchmark experimental research platform for control theory,the system has received extensive attention from scholars at home and abroad.Based on its research at home and abroad,it can be seen that the strong coupling,uncertainty,and non-linearity of the ball and plate system can be extended to a large number of similar industrial control equipments.This type of system itself is usually influenced by many elements,such as the ball and plate system,the ball rolling speed,the size of the friction coefficient,the interference factors of the equipment operating environment,the precision of the mechanical coupling of the equipment itself,etc.The impact of the system's operating status is directly reflected in its degree of fitting to the desired trajectory,the fitting time,and the tracking speed.Focused on this issue,the main research methods and results of this paper are as follows:(1)The introduction to the ball and plate system and its dynamic modeling: the stance and force of the ball and plate system are analyzed,and mechanism of the system is introduced.Based on the analysis of the control system,a dynamic model is established based on the motion of the ball on the plate.According to the established dynamics model,the corresponding dynamic differential equations and dynamic state equations are proposed,and some problems,such as the linearized solution of equations,are further discussed and deduced.(2)The fuzzy PID auto-tuning control of the ball and plate system: based on the verification of dynamic model,and due to the difficulty of the traditional PID control parameters trial and error method,in this paper the author combines the advantages of traditional PID control theory and fuzzy control algorithm,and designs a corresponding fuzzy adaptive PID controller for the system,with some characteristics,such as simple structure and small amount of calculation.At the same time,the realization of PID parameter self-tuning greatly improves the speed of parameter correction and the efficiency of the control system.(3)The sliding mode control of inversion dynamic surface for ball and plate system: in response to the factors,such as structural uncertainty,parametric uncertainties,and environmental disturbances of the system,in this paper it is correspondingly proposed an inversion adaptive dynamic sliding mode control scheme.Because the sliding mode control has nothing to do with the environment disturbance and the object parameters,and the response is quick and the noise immunity is excellent,the trajectory tracking performance of the ball and plate system under multi-disturbance factors can be effectively improved.At the same time,the dynamic surface sliding mode can effectively solve the problem of differential big explosion in the inversion method.(4)The sliding mode control of Non-singular terminal for ball and plate system based on disturbance observer: considering that the movement process of a ball on a flat plate is highly susceptible to interference,in the paper the author introduces a nonlinear observer to estimate and compensate the system disturbance.It can effectively reduce the impact of external disturbances on the trajectory tracking accuracy.Combined with the fact that the terminal sliding mode can achieve limited convergence with singularity,a non-singular terminal sliding mode controller based on a nonlinear observer is constructed.With grouping experiments conducted for different working conditions,the corresponding control performance of the system examined,the author analyzes the effectiveness of the tracking of the system under external disturbance.Through the discussion of the series of problems,such as the stability control of the ball and plate system,the trajectory tracking fit control,and the anti-jamming performance,the qualitative analysis and the controller design of the corresponding three types of control algorithms are conducted,and the effectiveness of the controller designed in this paper is verified through different methods.The simulation results show that the proposed control scheme achieves a certain degree of improvement in its accuracy,real-time performance,and immunity.