Output Feedback Bounded Control for Unidirectional Input Constrained Hysteretic Systems With Application to Piezoelectric-Driven Micropositioning Stage

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.