Discrete-time Adaptive Dynamic Surface Control Stategy Ang Its Application

In the process of the manufacturing industry fast development,smart material actuator plays a more and more important role in precision manufacturing,which makes micro/nano level manufacture comes to the door.However,problems brought by smart materials must be solved when they are put into use.Hysteresis,the inherent characteristic smart material has,strengthen the system nonlinearity deeply.To take the most advantage of smart material,strenuous efforts must be made to handle hysteresis.Dynamic surface control method shows a satisfactory outcomes in control problems of nonlinear,especially high order nonlinear systems.Moreover,the introducing of low-pass filters overcomes the difficulty of "explosion of complexity",and the structure of controller is immensely simplified,which attracts numbers of researchers.Sampling or digital signals used in discrete-time domain perform well in noise inhibition,and control elements with high sensitive level can be used to promote the control precision.For systems with large time-delays,disturbances resulted from time-delays can be mitigated by sampling,moreover,digital control systems possess better performance in reproducibility,profits and cost,which are regarded better than continuous time methods in stability and feasibility.This thesis focuses on discrete-time nonlinear systems with hysteresis,designing controllers through using adaptive dynamic technology to meet the requirements in system errors and stabilities,and the effectiveness of the proposed control methods will be proved on smart-material actuator actuated positioning stages.The main work of this thesis are as follows:1.In this section,an adaptive implicit inverse control scheme for a class of discrete-time hysteretic nonlinear systems is proposed.The Prandtl-Ishlinskii(PI)model is employed to characterize the hysteresis loop in piezoelectric actuator.The main contributions are:1)by using the dynamic surface control technique which introduces the digital first-order low-pass filter,the original control system are not required to be transformed into an unknown special form;2)The hysteresis implicit inverse compensator is constructed to overcome the hysteresis which implies that the hysteresis item coupled with control signal is treated as the temporary control signal from which the method of searching the optimal control signal is designed;3)by employing the experimental platform of the piezoelectric positioning stage,the experimental verifications of the designed discrete-time adaptive controller are implemented.It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded(SUUB)and the experimental results show the effectiveness of the proposed scheme.2.In this section,an adaptive neural digital implicit inverse motion control scheme is proposed for a class of asymmetric hysteretic systems,the high-precision position digital control problem of asymmetric hysteretic nonlinear systems is solved.Firstly,by designing the signal quantizer and the discrete-time controller with implicit inverse compensator,the digital control problem of hysteretic system is overcome which has made the proposed digital dynamic surface control scheme more applicable in practical computer control cases.Secondly,by constructing the implicit inverse compensator where the optimal control law is computed from the hysteresis output,the exact inverse hysteresis model is not required.Thirdly,by designing the digital first-order low-pass filter,the model of discrete-time controlled plant is not needed to be converted into an unknown special form.Finally,experimental results show that the proposed control scheme achieves satisfactory tracking performance and can mitigate the hysteresis and the quantizer error.