Research On Contour Control Of Direct-Drive H-Type Platform Based On Differential Geometry Decoupling

As a key functional component of high-end CNC equipment,H-type motion platform driven by linear motors is widely used in CNC machine tools precision machining,precision measurement,laser engraving and other occasions.The structural characteristics of double side drive and high rigid physical connection of direct drive H-type motion platform make it have the potential to obtain better performance.However,as a nonlinear strong coupling system,there are some disturbance factors such as dynamic mismatch between platform axes,motor parameter perturbation,and actuator load change,which improve the difficulty of contour control and reduce the accuracy of system contour control.Contour error estimation is the basis of contour error control.However,in the process of tracking large curvature trajectory,the geometric approximation method and coordinate transformation method are inaccurate in estimating contour error,which cannot meet the requirements of precision contour control of Htype platform.To solve these problems,this dissertation proposes a contour tracking control method based on differential geometry decoupling.This method has the advantages of strong anti-interference ability and high contour control accuracy,which improves the large curvature contour tracking accuracy of the strong coupling system,and provides a theoretical support for the precise contour control of the multi-dimensional system.This dissertation analyzes the basic structure and working principle of the H-type motion platform,fully considers the factors that affect the dynamic equation such as beam mass and moving load,and derives the system dynamic model using Lagrangian Euler equation.In addition,the causes of contour error are analyzed,the mechanism relationship between tracking error and contour error of H-type motion platform is described,and various disturbance factors affecting the dynamic characteristics of H-type motion platform are summarized.A decoupling control method based on differential geometry principle is proposed to solve the problem that the coupling term of the dynamic model of H-type motion platform affects the contour control accuracy.Based on the theory of nonlinear differential geometry,a suitable differential homeomorphism is constructed.By using the properties of Lie derivative operator and Lie bracket vector field,a decoupling matrix of the system dynamics model is built.The MIMO coupling system is decoupled into three single input single output(SISO)integral series systems,realizing the decoupling mapping of the system from the expected motion state input to the expected control law.In addition,in order to solve the problem that the decoupling algorithm based on the nominal model is vulnerable to the influence of uncertain factors such as parameter changes,external disturbances and friction,which will reduce the servo performance,a sliding mode controller with fast response speed and insensitivity to parameter changes and external disturbances is designed to realize the decoupling control of the H-type motion platform.In order to improve the convergence speed of the system,overcome the influence of disturbances such as parameter perturbation and actuator load change on the system,and overcome the chattering problem of traditional sliding mode control,a precise position tracking method based on adaptive fuzzy neural network time-varying sliding mode controller(Adaptive Fuzzy Neural Network Time-varying Sliding Mode controller,AFNNTSMC)is proposed.The AFNNTSMC controller introduces the time-varying sliding mode surface into the traditional sliding mode controller.By adjusting the slope of the time-varying sliding mode surface in real time,it effectively shortens the time for the system state to reach the sliding mode and improves the response speed of the system.Because the final slope of the rotation in the time-varying sliding mode control cannot be predicted,which affects the effect of the time-varying sliding mode control,the fuzzy neural network algorithm is used to estimate the slope value of the time-varying sliding mode surface in real time and adjust it online to ensure the optimal servo performance of the system.Aiming at the problems of inaccurate contour error estimation and low contour control accuracy when the direct drive H-type platform tracks complex contour with large curvature,a cross coupled iterative contour control method based on Laguerre iterative estimation is proposed.Laguerre iterative contour error estimation method uses the method of rational polynomial root to isolate each root in a complex plane rectangle,and calculates the number of roots in the complex rectangle based on parameter principle and Sturm sequence.After the calculated roots are fully isolated,the iterative method is used to determine the accuracy of each root.Laguerre method is used to up Fdate the roots,and the convergence root is taken as the initial value of Laguerre iteration to accurately calculate the profile error model in the process of high speed movement with large curvature.The Laguerre iterative estimation method is combined with the cross coupling controller to design a control scheme that comprehensively considers the multi axis cooperative motion to ensure the high performance contour tracking of such systems in practical applications.Finally,the contour control experiment system of H-type motion platform driven by linear motor was built by upper computer,motion control box and multi axis motion platform.The position tracking control based on decoupling model adaptive fuzzy neural network timevarying sliding mode controller and cross coupling control strategy based on Laguerre iterative contour error estimation method were studied experimentally,The feasibility and effectiveness of the contour control method of the H-type motion platform proposed in this dissertation are verified.