Nano-positioning And Tracking Control Of Piezoelectric Actuators

As the rapid development of nano-science and nano-technology,there are urge demands for micro-nano actuators with high precision and stability in industry areas such as micro-electronics,optical-fiber communication,precision machining,and so on.Piezoelectric actuator is an ideal micro-actuator,which has advantages of fast response,high resolution,noise free,friction free,small size,and so on.Therefore,it gradually developed to the key component to achieve micro-manipulation and machining in high precision manufacturing equipment.However,piezoelectric actuator itself also has some complex nonlinear properties like hysteresis,which could greatly degrade the performance of piezoelectric actuator nano-positioning systems,and thus bring some inconvenience into its practical applications.In addition,because of the existence of hystere-sis nonlinear property,the dynamic system of piezoelectric actuator includes complex dynamics property that is difficult to be exactly described by mathematical model.This makes the modeling of piezoelectric actuator very complex,and very difficult to obtain accurate model parameters.As a result,the model based invert-model control strategy will increase the complexity of the con-trol system,and may even degrade the performance of the controller.To deal with the above mentioned problem,this thesis is focused on the theoretical study and experimental verification of nano-positioning and tracking control problems.The main contents can be summarized as follows:One of the most popular and mature control methods for nonlinear system control is the clas-sic sliding mode control because of its advantages such as simple structure,easy implementation,and great suitability for nonlinear system control problems that include uncertainties.Therefore,it often treats the piezoelectric actuator as second-order linear system in piezoelectric actuator con-trol.The model parameters are obtained by system model identification methods.The hysteresis and the differences between second order linear piezoelectric actuator model and actual nonlinear model are treated as the uncertainty part in the system,and then compensated robustly using s-liding mode control.However,the discontinuous control part in the classic sliding mode control methods brings undesired chattering into the system.An integral part is then added to classic PD sliding surface,which eliminates the steady-state error caused by chattering and provides a smooth control input.The improved sliding mode controller and a single input-double output high gain observer are designed basing on the second-order simplified model of piezoelectric actuator.The proposed observer is able to estimate the full states of the system based on position measurements.The stability of the proposed controller is proved using Lyapunov based methods.The controller designed by this method not only suppresses system disturbances such as nonlinearity brought by hysteresis and system uncertainties brought by modeling error,but also achieves better control of piezoelectric actuator by using observed full-state information,overcomes the limitation that the piezoelectric actuator only has one position sensor.The effectiveness of the method is experimen-tally verified on the experimental platform.In order to further improve the controller robustness to unmodeled dynamics and external disturbances,the thesis combined the concept of robust compensation and nonlinear sliding mode observer techniques,proposed the sliding mode observer based piezoelectric actuator robust out-put feedback control method,which added the compensation term for external disturbances and uncertainties on top of the piezoelectric actuator sliding mode controller.The method in some degree overcomes the limitation of high gain observer,improves the controller performance.The sliding mode observer in this method is designed using equivalent control concept,makes all the system states converging to sliding surface one by one in finite time,until the full system states are estimated in finite time.The finite time convergence of the estimated value to the actual val-ue is proved using Lyapunov based method.In order to verify the effectiveness of this method,the piezoelectric actuator nano-positioning system experimental platform is also used here.The controller was applied on this experimental platform and the experimental data was analyzed and discussed.The aforementioned high order sliding mode observer is designed according to the system model,it estimates high order states(velocity signal)by mimic the system dynamics.However,the model based observer is often limited by the requirement of exact system model,and the un-known unmodeling dynamics and nonlinearities are difficult to be accurately recovered by numer-ical simulation,the positioning and tracking control precision will also be degraded.Therefore,to further improve the performance and stability of output feedback controller,the thesis proposed a piezoelectric actuator nonlinear robust output feedback integral control method,which is based on the recently developed novel robust integral of the sign of the error(RISE)method.The proposed method uses simplified second-order piezoelectric actuator identified model of small rotor-craft UAVs which only includes limited nonlinear dynamics.An auxiliary filtering auxiliary system is firstly designed,then the filtered error signals and the control law are developed based on the Lya-punov stability analysis results,and the expression of uncertainty and disturbance estimation term is also obtained by using the integral of the sign of filtered error signal.By using Lyapunov based analysis method,it is proved that the proposed controller is able to achieve semi-global asymptotic tracking of any bounded and second-order differentiable reference signal.The convergence of the estimated uncertainty and disturbance to the real values is also proved.In order to verify the effec-tiveness of the proposed method,the piezoelectric actuator nano-positioning system experimental platform is also used here,and the experimental results are analyzed and compared.The stability of above mentioned three proposed methods are all system asymptotic stable,the designed control law gives useful results.However,it is known now that the finite time stability of known dynamic system will improve the system accuracy of positioning and tracking,acceler-ate convergence speed,and insensitive to system uncertainty and external disturbance.Terminal sliding mode control method is a revised sliding mode control approach,which can achieve finite time stability.Therefore,the thesis proposed a novel continuous finite time terminal sliding mode control method,which has global finite time stability.To improve the robustness of control system,here uses a sliding mode disturbance observer to estimate the bounded uncertainty and disturbance in finite time.In here the piezoelectric actuator is treated as a second order nonlinear system to design the controller.Hysteresis is treated as the main nonlinearity in system and the simple hys-teresis model is given to obtain more accurate simulation result.Similarly,the stability of this controller is proved using Lyapunov analysis method.At last,the effectiveness of the proposed method is verified through numerical simulations,and useful conclusions are obtained.