Control Of Ball And Plate System Based On Interactive ESO Backstepping Algorithm

The ball and plate system has high-order,uncertain,non-linear dynamic characteristics,and it is a typical verification object for the control theory algorithm research.In this paper,we develop Backstepping algorithm control research based on online estimation for the ball and plate system.For the special structure and dynamic characteristics of the target system,ESO is used to estimate the model,which is combined with the Backstepping to carry out interactive control design.At the same time,on the basis of this method,further improved way was carried out.The main work as following:1.For the Backstepping algorithm applicable to the under-actuated ball and plate system,an interactive ESO Backstepping control method is proposed,which combines the model estimation with all levels of inversion control subsystems interactively.On the one hand,this way can provide model estimation for all levels of subsystems;on the other hand,the control design based on Lyapunov theory guarantees the stability of the overall system.To achieve the above purpose,the system is first constructed as a standard form of cscade strict feedback to solve the problem that the ESO Backstepping algorithm is restricted to the strict feedback structure of the model.This paper discusses the tracking speed of the virtual controller and proposes a sampling interval that satisfies the system's stability.Then,in the Backstepping control design subsystem,the reduced order LESO is used to estimate the sum of the nonlinear terms,uncertain terms,and state variables in the subsystem.Finally,based on the Lyapunov function,a hierarchical control design is carried out with the help of a virtual controller to obtain an actual controller that guarantees the overall stability of the system.2.In order to further improve the control performance of the ball and plate system,a new type of differential tracker is constructed based on the optimal output theory;under the premise of interactive design,pseudo-control gain coefficients are introduced to avoid the use of actuator gain coefficients,making the ESO Backstepping algorithm In the controller design process,it is no longer limited by the model parameters,and the related equivalence is proved for ?;the design energy function optimizes the observer parameters,and finally the stability of the system is verified based on the theory.3.The ball and plate system of Quanser was used as the experimental object for method verification.The experiment mainly includes two parts:?This platform is used to verify the effectiveness of the interactive ESO Backstepping algorithm.The cascade PID algorithm is designed as a comparison.The experimental results show that the interactive ESO Backstepping has higher tracking accuracy than the cascade PID;?This platform is used to verify the superiority of the improved interactive ESO Backstepping algorithm.The controller before and after the improvement is used in the tracking experiment of the ball and plate system.The experimental results show that the optimized algorithm improves the tracking accuracy by about 10%and the controller energy consumption by about 48%.Finally,the superiority of the proposed strategy is verified.