Research On Hysteresis Nonlinearity Of Piezoelectric Actuator Based On T-S Fuzzy System

With the advancement of technology,industrial development puts higher demands on the accuracy of high-precision positioning systems.Piezoelectric actuators are preferred in the field of high-precision positioning due to their fast response speed,high positioning accuracy and good stability.However,hysteresis in the piezoelectric actuator is characterized by multi-mapping,rate-dependent,memory,and non-smooth characteristics,which not only reduces the positioning accuracy of the system,but also may cause system instability in severe cases.To suppress the adverse effects of hysteresis characteristics on high-precision positioning systems,modeling and designing the appropriate controller will be an effective method.The main research of this paper includes the following points:(1)A T-S fuzzy model based on dynamic hysteresis operator is proposed.Firstly,a dynamic hysteresis operator is proposed to extract the memory and rate correlation of hysteresis,and then the input space is extended based on the hysteresis operator,and the T-S fuzzy space is constructed together with the hysteresis input and output data.Then,the triangle membership function is selected to divide the fuzzy space evenly,and the fuzzy post-parameter parameters are identified by the recursive least squares method.Finally,the fuzzy rules are simplified by combining the nearest neighbor and the maximum membership method.The simulation is performed separately under the condition that input differs by frequency and amplitude.(2)A dynamic hysteresis model based on novel fuzzy C-regression clustering algorithm(NFCRM)for fuzzy space is proposed.First,the fuzzy C-means clustering algorithm(FCM)is used to initialize the fuzzy frontware,and the central parameter is initialized by the least squares method.Then,using the improved fuzzy C-regression clustering algorithm(FCRM)to determine the fuzzy antecedent,the hyperplane membership function corresponding to the fuzzy C-regression clustering algorithm is introduced.Finally,the fuzzy post-parameter parameters are identified by the recursive least squares method.Experiments have confirmed the effectiveness of the model at input frequencies from 10 Hz to 200 Hz.(3)A hysteresis inverse compensation controller based on T-S fuzzy system is proposed.First,a simple two-input-single-output T-S fuzzy model structure is selected.Then,the Gaussian function is used to evenly divide the fuzzy space,and the recursive least squares method is used to identify the post-component parameters.Finally,the inverse model is obtained by analytical method,and the inverse model is connected in series with the piezoelectric actuator for inverse compensation control.The simulation results show that the inverse compensation controller based on the model has a positive compensation effect.