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In this paper, a new composite controller (feedforward + feedback) is proposed for the trajectory tracking control of a piezo-driven bridge displacement amplifier. A hysteresis model considering dynamic effects is established based on the modified Bouc–Wen (MBW) model, which can describe the asymmetry and frequency-dependence behaviors. The effectiveness of the modified model is verified by the experimental comparison. A feedforward controller is designed to compensate for hysteresis nonlinearity based on the inverse multiplicative structure of the modified model. A feedback controller with the Kalman observer is designed based on a modified model predictive control (MMPC). The proportional term and integral term of feedback error are introduced into the MPC control law to improve the response speed and reduce the steady-state error. The proposed MBW + MMPC is compared with MBW + proportional–integral–derivative (PID), and MBW + MPC. The experimental tracking results of continuously differentiable signals and non-differentiable signals verify MBW + MMPC feasibility and show that it can improve tracking performance. [ABSTRACT FROM AUTHOR]

Continuum robot has great advantages in minimally invasive surgery (MIS) due to the slenderness and dexterity. But the friction and backlash result in the low trajectory tracking accuracy. This paper aims to study the transmission process of the driving force and the error compensation method. The statics is performed considering the frictional transmission process, and the variation of friction force with driving force is revealed by the model. The hysteresis effect of the tip trajectory is revealed. Then the relationship between the load history and the robot shape is studied, next, the deflection of the robot subject to the different loading forces can be predicted. The correctness of the mechanical model is verified by numerical simulation and experiments. Furthermore, the control methods according to the cable length and the driving force are compared respectively, and a method of error compensation according to the cable length is worked out considering the mechanical model. The rationality of the compensation method is validated by experiment. The results show that the compensation method based on cable length greatly improves the control accuracy, and the maximum deviation is 1.08 mm. The established model and compensation method create conditions for clinical application of the proposed continuum robot. [ABSTRACT FROM AUTHOR]

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]

This article presents a new fractional-order normalized Bouc–Wen (BW) (FONBW) model to describe the asymmetric and rate-dependent hysteresis nonlinearity of piezoelectric actuators (PEAs). In view of the fact that the classical BW (CBW) model is only efficient for the symmetric and rate-independent hysteresis description, the FONBW model is devoted to characterizing the asymmetric and rate-dependent behaviors of the hysteresis in PEAs by adopting an $N$ th-order polynomial input function and two fractional operators, respectively. Different from the traditional modified BW models, the proposed FONBW model also eliminates the redundancy of parameters in the CBW model via the normalization processing. By this way, the developed FONBW model has a relatively simple mathematic expression with fewer parameters to simultaneously characterize the asymmetric and rate-dependent hysteresis behaviors of PEAs. Model parameters are identified by the self-adaptive differential evolution algorithm. To validate the effectiveness of the proposed model, a series of model verification and inverse-multiplicative-structure-based feedforward control experiments are carried out on a PEA system. Results show that the proposed model is superior to the CBW model and traditional modified BW model in modeling accuracy and hysteresis compensation. [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]