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This article proposes a new discrete-time predictive sliding mode control (DPSMC) for a parallel micropositioning piezostage to improve the motion accuracy in the presence of cross-coupling hysteresis nonlinearities and input constraints. Unlike the traditional linear discrete-time sliding mode control (DSMC), the proposed DPSMC is chattering free and has a faster convergence rate thanks to the design of a nonlinear discrete-time fast integral terminal sliding mode surface. Moreover, by combining with the receding horizon optimization, the sliding mode state is predicted to follow the expected trajectory of a predefined continuous sliding mode reaching law, which also allows the proposed controller to explicitly deal with constraints. The stability of the closed-loop system is analyzed under the model disturbances and constraints, and proves that the proposed DPSMC can offer a smaller quasi-sliding mode bandwidth than the traditional DSMC. The effectiveness of the proposed controller is validated by a series of numerical simulations and experiments. Results demonstrate the advantages of proposed DPSMC over the traditional DSMC method. [ABSTRACT FROM AUTHOR]

A robust and practical force control system is crucial to the sensitive piezo-driven micromanipulation applications. This paper presents a new model-free robust finite-time force tracking controller for piezoelectric actuators (PEAs). The proposed controller composes of three intuitive terms: (1) a time-delay estimation (TDE) term that eliminates the requirement of detailed information about the PEA system, realizing model-free control; (2) a fast integral terminal sliding mode-based desired error dynamics injection term that ensures fast convergence and high tracking precision; (3) a correcting term based on adaptive fuzzy logic system that compensates for TDE errors caused by discontinuous nonlinearities and improves the robustness of the system. Force differential signal used in the controller is estimated online by a force state estimator. Stability of the closed-loop system and finite-time convergence are analyzed in theory. Comparative experiments are carried out on a PEA system with two superposed PEAs. Results show that the proposed control strategy has faster convergence, higher tracking accuracy and stronger robustness compared with the traditional TDE-based force controllers. [ABSTRACT FROM AUTHOR]

Improving the control performance of active vibration isolation systems is crucial to provide an ultra-quiet environment for precision instruments. This paper presents a new fractional-order robust model reference adaptive controller for the piezo-actuated active vibration isolation systems with a relative-degree-one model. One advantage of the proposed controller lies in that its controller parameters are adjusted online by fractional proportional–integral-type adaptive laws, which not only speeds up the convergence of the closed-loop system, but also improves the control energy efficiency. Moreover, the proposed controller only uses the measurable input and output of the plant as feedback signals, which is convenient for controller implementation. The stability of the closed-loop system is proved based on the Lyapunov theory in detail. The optimal values of the fractional order and adaptive gains for adaptive laws are determined using the multi-objective genetic algorithm through off-line simulation. Comparative experiments on the piezo-actuated active vibration isolation systems are conducted to verify the effectiveness of the proposed controller. Results show that the proposed controller achieves satisfactory isolation performance in a wider frequency band of 20–500 Hz, and simultaneously reduces the control effort compared with the traditional MRAC methods. [ABSTRACT FROM AUTHOR]

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]

This paper presents an adaptive proportional-integral-derivative fractional-order nonsingular terminal sliding mode (PID-FONTSM) control for the cable-driven manipulators using time-delay estimation (TDE). The proposed control uses TDE technique to obtain the lumped system dynamics and brings in an effective model-free structure. Then, a PID-FONTSM surface is designed to further enhance the control performance. The proposed PID-FONTSM surface uses the FONTSM error dynamic as its inner loop and utilises a PID-type surface with FONTSM variable as its outer loop. Benefitting from this structure, the proposed PID-FONTSM surface enjoys the advantages from both PID and FONTSM simultaneously. Afterwards, an adaptive algorithm is developed, to timely and precisely regulate the control gain for the robust term. The proposed control method is model-free, highly accurate and essentially continuous thanks to the TDE technique and developed PID-FONTSM surface and adaptive algorithm. The stability of the closed-loop control system under TDE and PID-FONTSM dynamics is proved using Lyapunov stability theory. Finally, comparative simulations were conducted to verify the effectiveness and superiorities of our proposed control method over the existing methods. [ABSTRACT FROM AUTHOR]

To ensure satisfactory control performance for the cable-driven manipulators under complex lumped uncertainties, a new continuous fractional-order nonsingular terminal sliding mode (CFONTSM) control scheme based on time delay estimation (TDE) is proposed and studied in this paper. The proposed control scheme contains three elements, a TDE element adopted to suitably cancel out the unknown lumped dynamics with purposely time-delayed signals of the closed-loop control system, a newly proposed FONTSM manifold adopted to realize finite-time convergence in the sliding mode phase and a fast-TSM-type reaching law adopted to ensure finite-time convergence in the reaching phase. The proposed control scheme is model-free and no longer needs system dynamics benefiting from TDE, which is very suitable and easy to use in practical applications. Meanwhile, high precision, fast convergence and good robustness against lumped uncertainties are ensured thanks to the newly proposed FONTSM manifold and adopted fast-TSM-type reaching law. Integrated stability analysis of the closed-loop control system is presented based on Lyapunov stability theory. Finally, the effectiveness of our proposed control scheme is demonstrated by comparative 2-DoFs (degrees-of-freedom) simulation and experiments. [ABSTRACT FROM AUTHOR]

• Propose a novel robust control with feedforward compensation. • Prove the stability of the closed-loop control system considering the proposed dynamics. • Demonstrate the validity of proposed method through both simulations and experiments. For the trajectory tracking purpose of cable-driven robots, a novel robust control method is proposed and investigated in this paper. The proposed method consists of three elements, i.e. a time-delay estimation (TDE) element and a nonsingular fast terminal sliding mode (NFTSM) control element and a feedforward compensation. The TDE technique is utilized to estimate the lumped system dynamics in a simple but effective way, and then ensures an attractive model-free control scheme. The NFTSM control element is adopted to guarantee precise and robust control performance with continuous and singularity-free control efforts. Moreover, the feedforward compensation is also utilized to further enhance the control performance by taking advantages of the system dynamics. Due to this feedforward compensation element, higher control performance has been ensured compared with the traditional TDE-based control. Thanks to above three elements, the proposed method is practical to use and highly accurate and strongly robust. Comparative simulations and experiments were conducted to verify the effectiveness and superiorities of our proposed control method over the recently proposed one. [ABSTRACT FROM AUTHOR]