Adaptive Quantized Control for a Class of Hysteresis Nonlinear System With Irregular Constraints and Its Application to Piezoelectric Positioning Stage

This paper investigates the tracking control problem of hysteresis nonlinear systems with irregular constraint boundaries. By blending the constraint boundary with the barrier function and using the system transformation technique, an adaptive quantized tracking control scheme is developed, in which three significant advantages are obtained: 1) Compared with traditional constraint control methods, the constraints considered in this work only need to satisfy the condition of piecewise differentiability, which may be time-varying, asymmetric, and may appear in stages; 2) The designed controller can maintain the state within the boundary range where constraints are active, effectively managing situations where constraints and non-constraints alternate. 3) The quantizer used combines logarithmic and uniform quantizers, effectively reducing communication costs and maintaining acceptable quantization errors, which ultimately improves the overall system performance. The method’s effectiveness and superiority are validated through experiments conducted on a piezoelectric-driven motion system. Note to Practitioners—Smart materials are crucial components in high-precision positioning applications and indispensable tools for the precision manufacturing processes of advanced equipment. Current research on tracking control of smart material actuation systems typically focuses on eliminating the effects of hysteresis nonlinearity to achieve stable tracking. However, there is a lack of attention on ensuring that the desired trajectory and system states consistently meet predetermined constraints. It is observed that most existing works consider scenarios where constraints on system output or state are either uniformly present or uniformly absent. Consequently, the control methods proposed in these works become ineffective when constraint boundary gaps appear. On the other hand, to reduce the communication burden between system modules while ensuring system performance, it becomes necessary to quantify control signals. The existing quantizers employ a logarithmic distribution for quantization density, which significantly reduces communication load and quantization error. However, when the quantized signal’s value is large, it results in considerable quantization error, thereby affecting the system’s control performance. Therefore, this paper addresses the smart material actuation system with hysteresis characteristics by considering irregular boundary constraints and improving the traditional quantizer. This approach is further combined with system state transformation and backstepping techniques to construct an adaptive quantized control scheme. Additionally, a physical experimental platform based on a piezoelectric actuator within smart materials is developed to validate the effectiveness and superiority of the proposed control method.