This study focused on finite-time adaptive motion control for nonlinear pure-feedback systems subject to unknown asymmetric hysteresis and immeasurable states. Accordingly, a finite-time output-feedback dynamic surface control algorithm based on the inverse hysteresis compensator was developed. A fuzzy state observer was utilized to estimate the immeasurable states. A rate-dependent asymmetric Prandtl–Ishlinskii model-based direct inverse compensator was developed to overcome the actuator hysteresis behavior. The finite-time command filter was designed to avoid the “differential explosion” problem due to the repetitive derivatives of the virtual control law. The finite-time compensated signals were designed to eliminate the filtering errors caused by the command filters. The proposed control strategy ensured that all signals in the closed-loop system were finite-time bounded. The effectiveness of the investigated method was demonstrated on the piezoelectric micro-positioning stage, which is a mechanical system with unknown actuator rate-dependent asymmetric hysteresis.

A piezoelectric micropositioning stage (PMPS), which is a type of piezoelectric-driven system, exhibits hysteresis characteristics that affect its positioning precision. In addition, the system is sensitive to disturbances, such as environmental noise, system uncertainties, and sensor uncertainties or faults. This study investigated a new hysteresis-compensation fault-tolerant control strategy for a PMPS. To compensate for the hysteresis caused by the piezoelectric actuator, an observer-based hysteresis compensator (HC) was proposed to avoid the need to model the hysteresis and calculate the hysteresis inverse. Subsequently, an extended state observer (ESO) was constructed to simultaneously estimate the unmeasurable states and generalized disturbances, including the HC compensation error, external disturbances, and uncertainties. The HC and ESO constitute a new compound estimation method to further enhance estimation performance. Moreover, to address sensor faults, a reconstruction sensor was developed to reconstruct the feedback loop and mask faults. Furthermore, a Nussbaum function was incorporated into the fault-tolerant controller to address the unknown actuator gain caused by hysteresis and hence avoid singularities that could occur in the controller design because of the adaptive estimation of the unknown gain. Finally, comparative experiments were conducted on the PMPS to demonstrate the effectiveness of the developed control method.

The piezoceramic actuated stages have rate-dependent hysteresis nonlinearity, which is not simply related to the current and historical input, but also related to the frequency of the input signal, seriously affects its positioning accuracy. Consider the influence of frequency on hysteresis modeling, a rate-dependent hysteresis nonlinearity model that is based on Krasnoselskii–Pokrovskii (KP) operator is proposed in this paper. A hybrid optimization algorithm of improved particle swarm optimization and cuckoo search is employed in order to identify the density function of rate-dependent KP model, avoiding the blind search process caused by the high randomness of Levy’s flight in the cuckoo search algorithm, and improving the parameter identification performance. For the sake of eliminating the hysteresis characteristics, an inverse feed-forward compensation control that is based on recursive method is proposed without any additional conditions, and a feed-forward compensation controller is designed accordingly. The experimental results show that, under different frequency input signals, as compared with the classic KP model, the proposed rate-dependent KP model can accurately describe the rate-dependent hysteresis characteristics of the piezoceramic actuated stages, and the recursive inverse feed-forward compensation control method can effectively mitigate the hysteresis behaviors.

In this study, an observer-based output feedback bounded control strategy is investigated for states unmeasurable nonlinear systems subjected to actuator hysteresis and unidirectional input constraints. The inevitable complex actuators restrictions and hysteresis that exist in practice are considered and transformed by applying a new model transformation operations. To cope with the challenge introduced by the coupling of control inputs and an actuator nonlinear term, a new fuzzy state observer is constructed by introducing a signal filter so that the unmeasurable states and generalized uncertainties, including the hysteresis term, disturbances, and uncertainties, can be estimated synchronously. An output feedback bounded control strategy is proposed that achieves high-precision positioning using a performance-prespecified dynamic surface controller and guarantees that the control signal is bounded within the input constraints by constructing the logarithm Lyapunov functions. The stability of the closed-loop system is proven. Furthermore, the investigated scheme is validated on the piezoelectric micropositioning stage, which is a mechanical system with unknown actuator hysteresis and unidirectional input constraints. Note to Practitioners —This study is motivated by the problem of bounded motion control for smart material-driven micropositioning stages with hysteresis and unidirectional input constraints. The development of micro/nano technology places higher requirements on micro/nanopositioning control. As one of the most commonly used smart material-driven micropositioning stages, piezoelectric micropositioning stage is widely used in mechanical engineering, aerospace technology, bioengineering and other fields. However, influenced by the inherent properties of materials, piezoelectric actuators have complex hysteresis nonlinearity and are subject to unidirectional input constraints, which impair the positioning accuracy and the equipment operation safety. Existing control methods for hysteretic systems are either limited in control performance due to the hysteresis modeling accuracy or difficult to be applied to practical systems with only measurable outputs, and all of existing methods ignore the effect of unidirectional input constraints on the control performance. This study proposes an output feedback bounded control strategy that eliminates the negative effects of hysteresis without constructing an inverse hysteresis model, and realizes high-precision positioning control with prespecified performance, where the bounds of control input is known a priori and satisfy the input constraints.