Sliding Mode Based On Active Disturbance Rejection Control For Piezoceramic Micro-positioning Platform

In the field of modern high-precision instrument manufacturing and ultra-precision machining,piezoelectric micropositioning technology occupies a core position.Piezoelectric ceramics has many advantages that traditional smart materials does not have,such as high positioning resolution,large thrust,fast response-time,and less disturbed by magnetic field.However,the inherent rate-dependent hysteresis nonlinearity of piezoelectric ceramics severely restricts the positioning accuracy of piezoelectric micro-positioning platforms,which in turn limits the further promotion of piezoelectric micro-positioning platform.In this paper,the piezoelectric micro-positioning platform is taken as the research object.The trajectory tracking control of the piezoelectric micro-positioning platform is realized by establishing a high-precision hysteresis nonlinear model and designing a controller based on the hysteresis model.In order to achieve better control results and achieve high-precision positioning and tracking,the traditional Prandtl-Ishlinskii(PI)model and its principles has been introduced.Then,an improvement scheme has been proposed for the shortcomings of the PI model that can only express symmetric hysteresis characteristics and rate-dependent characteristics.The PI model based on the series dead zone operator which can express the asymmetric hysteresis characteristic is obtained by improving the series dead zone operator.In order to achieve higher accuracy,the operator form is need to be improved.The DZ-MPI(Dead-Zero Modified PI)model that can more accurately describe the hysteresis characteristics of the platform has been proposed.By using particle swarm algorithm and ant colony algorithm,the DZ-MPI model parameters to describe the static hysteresis portion of the platform has been cross-identified.Based on the improved model,the ARX function is used on the basis of the improved model.The frequency sweep signal is used as the input.The expected output is used as the model output.The ant colony algorithm is used to identify the ARX model parameters.And the model accuracy is verified through experiments.Aiming at the influence of inherent hysteresis nonlinearity on the positioning accuracy of the micro-displacement platform,a feedforward controller based on the DZ-MPI model has been established firstly to compensate the hysteresis characteristics of the piezoelectric platform.Compensation control is realized by connecting inverse model and platform in series secondly.The experiment results show that the feedforward control is effective and can reduce the imprecise problem caused by the hysteresis of the micro positioning platform.Usually the accuracy of feedforward control depends largely on the accuracy of the established model,so the fuzzy sliding mode control based on inverse model is designed on the basis of feedforward control to form a closed-loop system.And it is proved that the composite control can achieve higher control accuracy,and can achieve good results under various frequencies through the experiment.In order to achieve more accurate tracking and positioning effects,and suppress the influence of external disturbances on the system,an adaptive sliding mode active disturbance rejection controller that does not require inverse model has been proposed.In this method,the hysteresis characteristic and external disturbances are combined as system disturbances.And the non-singular terminal sliding mode switching surface is introduced into the active disturbance rejection control framework.In order to achieve a more accurate tracking and positioning effect,and to suppress the impact of external disturbances on the system.In this paper,an adaptive sliding mode ADRC without inverse model is proposed.The hysteresis and external disturbances are combined as system disturbances,and the nonsingular terminal sliding mode switching surface is introduced into the ADRC framework.The system not only has the anti-interference ability of ADRC,but also has the rapidity and stability of sliding mode control,which can effectively eliminate the influence of the inherent hysteresis of the platform on the system.