Active Disturbance Rejection Control For Piezo-Driven Nanopositioning Stage

With the rapid development of micro-nano scale science and technology, micro/nano-manipulating systems are widely used in various advanced technology fields, such as ultra-precision imaging systems, semiconductor manufacturing systems, biomedical science and data storage systems. However, micro/nano-manipulating systems suffer from the inherent hysteresis effect of the smart actuators, system uncertainties, as well as various environmental disturbances, which seriously affect the motion precision and closed-loop stability. These multifarious uncertainties have brought significant challenge to the control strategy to achieve the ultrahigh motion with nanometer resolution. To address such challenges, this dissertation proposes a modified active disturbance rejection control (ADRC) for piezo-driven nanopositioning stage in order to improve the system performance including accuracy, speed, robustness and disturbance rejection. Based on the traditional ADRC method, the composite nonlinear feedback and the gain-variable extended state observer (ESO) are proposed and the theoretical proofs of the convergence and stability are given. In particular, the main research works are listed as follows:(1)A general electromechanical model is proposed to characterize the dynamic behaviors of the customize-designed nano-stage driven by a piezoelectric (PZT) actuator, including the electric and mechanical behavior, the hysteresis nonlinearity and the piezoelectric effect. The system parameters are identified online through the discrete Fourier transform algorithm, which is confirmed by the experimental results and lays the foundation of controller design.(2) According to the basic principle of ADRC, the control algorithm is deployed on the customize-designed nano-stage to deal with the multifarious uncertainties including the nonlinear characteristics of the smart actuators, model uncertainties, sensor noise, environmental disturbances. Simulation and experimental results demonstrate the validity of the control method.(3) Considering the limitations on the parameter adjustment and performance optimization of traditional ADRC, a modified ADRC with composite nonlinear feedback is proposed to improve the closed-loop system transient response performance and tracking performance in presence of multifarious uncertainties without increasing the difficulty of controller design. In addition, the asymptotic stability of the closed loop system and the convergence of the tracking error of the augmented system are proved in this thesis.(4) The parameters of the extended state observer is optimized through genetic algorithm. Then, a modified ESO with the plant model information is developed, where the convergence of the observer error is proved. On this basis, a gain-variable ESO is further proposed in order to reduce the burden of the extended state observer and avoid the peaking phenomenon in the initial instants. The convergence of the gain-variable ESO is given through the coordinate transformation and Lyapunov method. Simulation and experimental results show the superiority of the modified ESO.