Adaptive Control Of Pure-feedback Nonlinear Systems With Hysteresis Input

Piezoelectric actuators are widely used in precise positioning and measurement due to their advantages such as large output force,high bandwidth and fast response time.However,the inherent hysteresis nonlinearity in piezoelectric materials can damage the system performance and even cause instability.Therefore,the control and modeling of hysteresis is a research hotspot in the field of precision machinery.Pure-feedback nonlinear system is a class of complex nonlinear system which is more universal than strict-feedback nonlinear system and can represent the real system more accurately.The design of virtual control law and actual control law is difficult to realize because the pure-feedback nonlinear systems usually appear non-affine characteristics.Considering the above situations,the research on adaptive control of pure-feedback nonlinear systems with hysteresis input has important theoretical significance and application meaning.Focusing on this topic,according to the hysteresis characteristics of piezoelectric actuators,hysteresis modeling and adaptive control of pure-feedback systems with hysteresis input are studied.Specific research contents are as follows:(1)A modified Bouc-Wen model for asymmetric hysteresis of piezoelectric actuators is proposed.Considering the asymmetry of hysteresis nonlinearity in the piezoelectric actuator,the problem that the traditional Bouc-Wen model cannot describe the asymmetric hysteresis is solved by introducing an asymmetric term into the traditional model.The introduced asymmetric term in this model can guarantee the intermediate variable is bounded and provide an important theoretical premise for the subsequent controller design.Compared with other modified Bouc-Wen models,it can be seen that the model has the advantages of fewer parameters and easier control design.Based on the experimental data of piezoelectric actuator platform and the modified particle swarm optimization algorithm,the effectiveness of the modified Bouc-Wen model is proved via simulation.(2)A rate-dependent hysteresis model of piezoelectric actuator based on elliptic curve is established.Compared with other mathematical modeling methods,elliptic equations can be determined through a set of parameters,which simplifies the modeling process.The implementation of this method is divided into two parts:major loop and minor loop.The major loop is described by constrained conic form elliptical curve,and ellipse-specific direct least square fitting method is used to identify the elliptic curve and experimental data.Through the transformation of major loop,the relation between the parameters of minor loop and the parameters of major loop is constructed.The above relation can be used to adjust the angle and shape of the minor loop,so as to realize the modeling of minor loop based on the knowledge of major loop.Through experiments,the modeling method based on elliptic curve has high identification accuracy for both major loop and minor loop,which proves the effectiveness of this method.(3)An adaptive controller for pure-feedback nonlinear systems with hysteresis input is designed.The asymmetric hysteresis nonlinearity is described by the modified Bouc-Wen model proposed in the first point above.The non-affine function in the pure-feedback nonlinear system is directly used to replace the state variable in the coordinate transformation in back-stepping design.Taking advantage of the above replacement,the transformation from pure-feedback systems to strict-feedback form could be avoided.Thus,the proposed method may avoid additional uncertainty and the circular design problem,thus,controller design is simplified.Based on Lyapunov theory,the stability of the closed-loop system is analyzed.Through simulation example and experiment results,the effectiveness and superiority of the control scheme are demonstrated.In view of the above-mentioned hysteresis modeling method and pure-feedback nonlinear systems control scheme,this paper has carried out research and verified the effectiveness of the modeling method and the feasibility of the control design through Matlab/Simulink simulation example and dSPACE DS1103 platform experiment results.Modeling method and control scheme have certain reference value in practical applications.