Hysteresis is an inherent characteristic of piezoelectric materials that can be determined by not only the historical input but also the input signal frequency. Hysteresis severely degrades the positioning precision of piezoelectric micropositioning stages. In this study, the hysteresis characteristics and the excitation frequency effects on the hysteresis behaviors of the piezoelectric micropositioning stage are investigated. Accordingly, a rate-dependent asymmetric hysteresis Prandtl–Ishlinskii (RDAPI) model is developed by introducing a dynamic envelope function into the play operators of the Prandtl–Ishlinskii (PI) model. The RDAPI model uses a relatively simple analytical structure with fewer parameters and then other modified PI models to characterize the rate-dependent and asymmetric hysteresis behavior in piezoelectric micropositioning stages. Considering practical situations with the uncertainties and external disturbances associated with the piezoelectric micropositioning stages, the system dynamics are described using a second-order differential equation. On this basis, a corresponding robust adaptive control method that does not involve the construction of a complex hysteretic inverse model is developed. The Lyapunov analysis method proves the stability of the entire closed-loop control system. Experiments confirm that the proposed RDAPI model achieves a significantly improved accuracy compared with the PI model. Furthermore, compared with the inverse RDAPI model-based feedforward compensation and the inverse RDAPI model-based proportional–integral–derivative control methods, the proposed robust adaptive control strategy exhibits improved tracking performance. 

/pdf/rate-dependent-asymmetric-hysteresis-modeling-and-robust-1sqxf23x.pdf

Rate-dependent asymmetric hysteresis modeling and robust adaptive trajectory tracking for piezoelectric micropositioning stages


 Hysteresis is an inherent characteristic of piezoelectric materials that can be determined by not only the historical input but also the input signal frequency. Hysteresis severely degrades the positioning precision of piezoelectric micropositioning stages. In this study, the hysteresis characteristics and the excitation frequency effects on the hysteresis behaviors of the piezoelectric micropositioning stage are investigated. Accordingly, a rate-dependent asymmetric hysteresis Prandtl-Ishlinskii (RDAPI) model is developed by introducing a dynamic envelope function into the play operators of the Prandtl-Ishlinskii (PI) model. The RDAPI model uses a relatively simple analytical structure with fewer parameters then other modified PI model to characterize the rate-dependent and asymmetric hysteresis behavior in piezoelectric micropositioning stages. Considering practical situations with the uncertainties and external disturbances associated with the piezoelectric micropositioning stages, the system dynamics are described using a second-order differential equation. On this basis, a corresponding adaptive robust control method that does not involve the construction of a complex hysteretic inverse model is developed. The Lyapunov analysis method proves the stability of the entire closed-loop control system. Experiments confirm that the proposed RDAPI model achieves a significantly improved accuracy compared with the PI model. Furthermore, compared with the inverse RDAPI model-based feedforward compensation and the inverse RDAPI model-based proportional-integral-derivative control methods, the proposed robust adaptive control strategy exhibits improved tracking performance.

/pdf/rate-dependent-asymmetric-hysteresis-modeling-and-robust-4ct8u6cmko.pdf

Rate-dependent Asymmetric Hysteresis Modeling and Robust Adaptive Trajectory Tracking for Piezoelectric Micropositioning Stages

The magnetic shape memory alloy (MSMA) is a new family of smart materials, which exhibits great strain deformation and high energy density. Based on these properties, the MSMA has excellent potential to represent an available means for developing a novel generation of actuators in the micro-positioning application. However, the MSMA-based actuator suffers from the inherent hysteresis and it has become a bottleneck in the industrial application. A hybrid hysteresis model, which consists of a simple dynamic hysteresis operator (SDHO) and chaotic neural network (CNN), is proposed in this article. This developed model possesses a concise construction and distinguished generalization capability. By conducting comparative experiments, the proposed approach has a superior ability to predict the hysteresis behaviors under various input signals.

Chaotic Neural Network-Based Hysteresis Modeling With Dynamic Operator for Magnetic Shape Memory Alloy Actuator

Adaptive sliding mode control with hysteresis compensation-based neuroevolution for motion tracking of piezoelectric actuator

For a class of high-order nonlinear multi-agent systems with input hysteresis, an adaptive consensus output-feedback quantized control scheme with full state constraints is investigated. The major properties of the proposed control scheme are: 1) According to the different hysteresis input characteristics of each agent in the multi-agent system, a hysteresis quantization inverse compensator is designed to eliminate the influence of hysteresis characteristics on the system while ensuring that the quantized signal maintains the desired value. 2) A barrier Lyapunov function is introduced for the first time in the hysteretic multi-agent system. By constructing state constraint control strategy for the hysteretic multi-agent system, it ensures that all the states of the system are always maintained within a predetermined range. 3) The designed adaptive consensus output-feedback quantization control scheme allows the hysteretic system to have unknown parameters and unknown disturbance, and ensures that the input signal transmitted between agents is the quantization value, and the introduced quantizer is implemented under the condition that only its sector bound property is required. The stability analysis has proved that all signals of the closed-loop are semi-globally uniformly bounded. The StarSim hardware-in-the-loop simulation certificates the effectiveness of the proposed adaptive quantized control scheme.

Yannan Zhang

Papers

Hysteresis inverse compensation-based model reference adaptive control for a piezoelectric micro-positioning platform