Research On Modeling And Control For Hysteresis Nonlinearity In High Precision Positioning System

Accompanied by the rapid development of micro-nano technology,high-precision positioning system has also become a hot spot.Because of the advantages of fast response speed,high positioning accuracy and good stability,intelligent materials such as piezoelectric ceramics,shape memory alloys are widely used in the field of high precision positioning.However,these intelligent materials have inherent hysteresis characteristics.The hysteresis characteristics not only cause errors and oscillations,but also reduce the control accuracy of the system,and even cause system instability.In order to eliminate the adverse effects of hysteresis nonlinearity in the high-precision positioning system,it is necessary to establish hysteresis model for the intelligent material and to design the corresponding controller for precise control.Main contents and achievements are as follow:(1)The hysteresis model of extreme learning machine based on Duhem operator is established.First,the Duhem basic operator is introduced to transform the hysteresis relation from multi-valued mapping to one-to-one mapping.Then the extreme learning machine is used to approximate the hysteresis relation and train network.Finally,the effectiveness of the modeling method is verified by hysteresis modeling for the actual piezoelectric actuator,the simulation results show that the method can accurately establish the hysteresis model.(2)The prescribed performance adaptive sliding mode backstepping controller is designed for the hysteresis nonlinear system.For a class of nonlinear system with hysteresis characteristics,the Backlash-like model is introduced to describe the hysteresis in the system.First,the mathematical expression of the Backlash-like model is analyzed,and the RBF neural network is used to approximate the perturbation term in the hysteresis model.Then the prescribed performance function is introduced to accomplish error transformation.Combined with the sliding mode backstepping method and Lyapunov stability theory,an adaptive sliding mode backstepping controller is designed for the hysteresis nonlinear system.Finally,it is verified by simulation.(3)The adaptive sliding mode controller is designed for the hysteresis nonlinear system with input constraint.For a class of input-constrained nonlinear system with Backlash-like hysteresis.First,the RBF neural network is introduced to approximate the perturbation term in the hysteresis model.Then a stable adaptive system is proposed to realize the compensation of the control saturation with dynamically amplifing the input saturation error.Finally,the adaptive sliding mode controller is designed by Lyapunov function for the hysteresis system.This control method takes into account the input constraint present in the actual project,which not only effectively eliminate the adverse influence of the hysteresis nonlinearity in the system,but also improve the control precision and stability performance.The simulation results verify the effectiveness of the control method.