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Parallel piezostages have been prevalently applied in the micro-/nano-positioning field, but, unluckily, suffer from the undesired effects, like creep, hysteresis, vibration, cross coupling, and input saturation. To eliminate these nonlinearities, a new discrete-time sliding mode predictive control (DSMPC) with decoupling and damping properties (DSMPC-DDP) is proposed for a parallel six-axis piezostage devoted to cell micromanipulation. Firstly, a state-space-based decoupler is applied to make the MIMO system decoupled into six SISO subsystems, and then a damping compensator via the notch filter principle is selected to suppress the high-frequency vibration dynamics of six subsystems. After that, a feedback DSMPC law is designed for each decoupled and damped subsystem. Unlike the traditional linear model predictive control (MPC), the feedback DSMPC is developed based on a nonlinear discrete-time terminal sliding mode prediction model, leading to stronger robustness and faster convergence speed. Through the utilization of the receding horizon optimization, the sliding mode states are optimized to explicitly deal with the input constraints. The stability of the closed-loop subsystems is analyzed based on the terminal constraint theory. Finally, the effectiveness and superiority of the proposed controller is validated by a series of experimental tests. Results show that the proposed DSMPC-DDP scheme can achieve higher tracking accuracy and control bandwidth than the existing proportional–integral (PI) and MPC methods in the context of abovementioned nonlinearities. • A new DSMPC-DDP is proposed for a parallel six-axis piezostage. • Attenuating the creep, hysteresis, cross coupling, vibration, and input saturation simultaneously. • Providing rigorous stability analysis for the closed-loop control system. • Comprehensive comparative experiments are conducted for validating the superiority. [ABSTRACT FROM AUTHOR]

Parallel micropositioning piezostages are widely used in the micro-/nano-manipulation applications, but also subject to the nonlinear disturbances, like hysteresis, creep and cross-coupling effects. In this paper, a new fractional robust adaptive decoupled control (FRADC) is synthesized for a six-axis parallel micropositioning piezostage to improve the positioning accuracy. The proposed FRADC contains three intuitional terms: (1) a decoupling term that alleviates the coupled motions among different axes, making the controller implementation more convenient and efficient; (2) a feedforward compensation term based on a fractional normalized Bouc-Wen (FONBW) model, compensating for the rate-dependent hysteresis effect induced by the piezoelectric actuators; (3) a feedback model reference adaptive control (MRAC) term with fractional proportional-plus-integral-type updating rules that suppresses the creep effect, parameters uncertainty and external disturbances, further enhancing the robustness and positioning accuracy. The stability of the closed-loop system is analyzed in theory. The effectiveness of the proposed FRADC is experimentally validated by comparing with the standalone inverse-FONBW-based feedforward control, the standalone feedback fractional MRAC, and the traditional integer-order control methods. Results demonstrate that the proposed FRADC can guarantee higher positioning accuracy for the piezostage system in wider control bandwidth. [ABSTRACT FROM AUTHOR]