Modeling And Control Of Piezoelectric Actuators Based On T-S Fuzzy System

With the rapid development of technology,higher accuracy requirements are put forward in positioning systems.Piezoelectric actuators are widely used in the positioning of ultra-precise systems because of small size and high accuracy.However,the non-linear nature of hysteresis in piezoelectric actuators can lead to positioning errors,which affect the accuracy of positioning.So it is important to eliminate the negative effects of hysteresis characteristics.T-S fuzzy systems excel in the field of identification of nonlinear systems.Theoretically T-S fuzzy systems have been shown to have powerful approximation capabilities for nonlinear systems.Moreover,the application of interval type 2 fuzzy sets can effectively deal with the uncertainty of the system,so identifying the T-S fuzzy model of the hysteresis nonlinearity is a key step to eliminate its negative impact.Once an effective model has been established the selection of the control scheme is carried out.The generalised predictive control has a strong robustness and the obtained T-S fuzzy model is used as a predictive model to complete the construction of the controller,thus realising the control effect on the hysteresis characteristics.The main elements of the research in this paper are as follows.(1)A type 1 T-S fuzzy model based on the dynamic hysteresis operator is proposed.Firstly,in order to solve the multi-valued mapping problem in hysteresis non-linear input-output,a dynamic hysteresis operator is introduced to transform this problem into a one-to-one correspondence,thus simplifying the input-output relationship and at the same time better describing the rate-dependent properties of hysteresis.Secondly,a type 1 T-S fuzzy modelling scheme is proposed to effectively identify the hysteresis characteristics of piezoelectric actuators.Finally,the modelling is completed by using the dynamic hysteresis operator as one of the inputs to the type 1 T-S fuzzy model.The model solves the difficulties in modelling caused by multi-valued mapping in hysteresis,while combining the ability to describe the rate-dependent properties of dynamic hysteresis operators with the powerful approximation capability of a type 1 T-S fuzzy system for non-linear systems,which can effectively identify the non-linear correlation properties of hysteresis.(2)An interval type 2 T-S fuzzy model based on an modified fuzzy c-regression clustering algorithm is proposed.Firstly,compared to the previously described type 1 T-S fuzzy system,the interval type 2 T-S fuzzy system can better handle the uncertainty of the system by further fuzzifying the affiliation function to form a type 2 fuzzy set.Secondly,an improved interval type 2 fuzzy C-regression model(FCRM)clustering algorithm is proposed for fuzzy space partitioning by invoking the vertical distance formula to replace the traditional error calculation formula,so that the clustering algorithm is directly related to the identified hyperplane results and the interval partitioning accuracy is improved.Finally,hyperplane affiliation functions that match the structure of the fuzzy rules are introduced,due to the problem of mismatch between hyperspherical Gaussian affiliation functions and the structure of hyperplane-type clustering algorithms.This interval type 2 T-S fuzzy model can not only deal with the uncertainty and non-linearity of the system effectively,but also has high recognition accuracy.(3)A generalized predictive control strategy based on an interval type 2 T-S fuzzy model is proposed.Firstly,the model in Chapter 3 of this paper adopts a linear time-invariant subsystem weighted sum form and uses the interval type 2 T-S fuzzy model proposed in this paper as the parametric model.The model structure is simple and easy to optimise online,and the model accuracy is high enough to accurately predict the future output of the system for effective control.Secondly,this paper adopts a local sub-model control scheme and implements a generalised predictive control algorithm for each sub-model to obtain the control increment,which is weighted according to the activation strength of each sub-model to obtain the total control amount of the model to realise the control of the hysteresis characteristics of the piezoelectric actuators.Finally,experimental simulations demonstrate that the generalised predictive control method proposed in this chapter can effectively compensate for the negative effects of hysteresis.