Modeling And Iterative Sliding Mode Composite Control Method For Walking Piezoelectric Linear Motor

The walking piezoelectric platform,with the walking piezoelectric linear motor as the core component,overcomes the disadvantages of the ordinary stacked piezoelectric platform,so it is favored by the high-precision manufacturing field.In this paper,the walking piezoelectric linear motor is taken as the research object,and the mechanism characteristic analysis,model identification and tracking control of the whole walking piezoelectric platform are completed.The main content of the article is as follows:According to the actual demand,the walking piezoelectric experimental platform is built.Firstly,the operating theory and experimental conditions of the walking piezoelectric linear motor are introduced.Then,three signals are designed to test the characteristics of the motor.According to the actual input-output relationship of the open-loop test,it is known that the platform is in an unstable state under the open-loop condition and has the characteristics of hysteretic nonlinear and multi-valued mapping.Therefore,closed-loop data should be collected under the closed-loop condition for identification.Finally,the piezoelectric leg is equivalent to the cantilever beam model of two stacked piezoelectric ceramics.By introducing the piezoelectric equation and Euler-Bernoulli bending moment equation,the mechanism model of the whole walking piezoelectric platform is obtained through theoretical derivation and data fitting.In order to improve the accuracy of the model,subspace identification algorithm is used to identify the walking piezoelectric platform.Considering the noise and the open-loop instability of the platform,an auxiliary variable recursive space identification algorithm based on Error-in-variables was proposed.After the mean filter is used to preprocess the collected data and reduce the pollution of noise to the data,the known data set is used to design auxiliary variables to suppress the noise,and the system matrix is obtained by the least square method combining the orthogonal triangular decomposition(RQ decomposition)and the singular value decomposition(SVD).In the algorithm,the recursive calculation of auxiliary variables is realized by online RQ decomposition,and the forgetting factor is introduced in the recursive process to strengthen the influence of the current data on the identification results.Two sets of simulation experiments are designed.Compared with other subspace algorithms,the identification accuracy of the time invariant system is better,and the identification ability of the time invariant system is better.Finally,the platform identification experiment is carried out,and the accuracy advantage of the proposed algorithm is proved by comparing with the least square algorithm and other subspace algorithms.Moreover,the universality of the model is verified under three simulated conditions.In order to realize the trajectory tracking control of the walking piezoelectric platform,three kinds of trajectory including point-to-point continuous step,sine and third-order S-curve are planned according to the requirements and conditions.Then,considering the poor control effect of classical PID control and discrete sliding mode control,the iterative adaptive sliding mode composite control scheme is designed.In the controller design,the chattering phenomenon is improved by introducing filter,saturation function and adaptive terms based on sliding mode surface,and the openclosed-loop iterative learning control is added to improve the trajectory tracking ability.Finally,three kinds of trajectory tracking experiments were carried out on the platform,and the control effect was evaluated by experimental data and designed numerical indexes.The results show that the proposed iterative adaptive sliding mode composite controller is better than PID and discrete sliding mode in terms of speed and stability,which proves that the proposed controller has a good control effect on the walking piezoelectric platform with the walking linear motor as the core.