Adaptive Quantized Control Research for Hysteresis Nonlinear Systems in Piezoelectric Positioning Stages

Background Introduction

In modern high-precision positioning systems, smart materials (such as piezoelectric ceramics) are widely used in micro/nano manufacturing and soft robotics due to their excellent performance. However, the inherent hysteresis nonlinearity of these materials leads to complex cyclic relationships between system input and output, causing inaccurate positioning and even potential system instability. Therefore, effectively controlling hysteresis nonlinear systems has become a hot research topic. Additionally, practical applications face the issue of irregular constraints, where the system is constrained at certain times and unconstrained at others. Traditional control methods typically address only full-time constrained or unconstrained scenarios, making them ineffective for handling such intermittent constraints. To address this, researchers Heyu Hu et al. proposed an adaptive quantized control scheme to solve the tracking control problem of hysteresis nonlinear systems under irregular constraints.

Source of the Paper

This paper was co-authored by Heyu Hu (Zhongyuan-Petersburg Aviation College, Zhongyuan University of Technology), Shengjun Wen (Zhongyuan-Petersburg Aviation College, Zhongyuan University of Technology), Jun Yu (Zhongyuan-Petersburg Aviation College, Zhongyuan University of Technology), and Changan Jiang (Department of Robotics, Osaka Institute of Technology). It was published in the Journal of LaTeX Class Files, Volume XX, Issue X, 2024. The research was supported by multiple projects, including the Natural Science Foundation of Shandong Province (ZR2023MF024) and the Support Plan for Science and Technology Innovation Teams in Higher Education Institutions of Henan Province (24IRTSTHN024).

Research Content and Methods

1. Problem Description

The research focuses on smart material-driven systems with hysteresis nonlinearity, addressing the following issues: 1. Irregular Constraints: The system’s output error and state need to meet constraints at certain times, while being unconstrained at other times. 2. Quantized Control: To reduce communication costs, control signals must be quantized. However, existing quantizers introduce significant errors when the signal amplitude is large, affecting system performance.

2. Control Scheme Design

The researchers proposed an adaptive quantized control scheme, with the following steps: 1. System Transformation: By introducing a barrier function, the original system’s constraints are transformed into an unconstrained system. Specifically, transformation functions for error and state variables are designed to incorporate constraint boundaries into the system model. 2. Controller Design: Combining backstepping and dynamic surface control techniques, an adaptive quantized controller is designed. The controller adjusts the control signal threshold to integrate logarithmic and uniform quantizers, reducing communication overhead while minimizing quantization error. 3. Quantizer Design: A novel quantizer is proposed, which switches to uniform quantization mode when the control signal amplitude is large, effectively controlling quantization error.

3. Experimental Validation

The researchers validated the proposed control method on a physical experimental platform based on a piezoelectric actuator. The experiments were divided into two parts: 1. Control Performance Under Irregular Constraints: Experimental results showed that the system could effectively track the desired trajectory under irregular constraints, with errors and speeds consistently staying within the constraint range. 2. Comparison with Traditional Methods: Compared to existing methods, the proposed controller performed better in preset performance control, especially when handling mixed signals (e.g., 1Hz and 5Hz), with more stable tracking errors.

Research Results and Conclusions

1. Control Performance: Experiments demonstrated that the proposed controller could effectively track the desired trajectory under irregular constraints, with quantization error kept at a low level.
2. Innovation: The study introduced irregular constraint boundaries into a unified form of barrier function for the first time and designed a novel quantizer combining the advantages of logarithmic and uniform quantization.
3. Application Value: The control method can be applied to micro/nano-level high-precision control systems, such as piezoelectric positioning platforms, with broad practical application prospects.

Highlights

1. Irregular Constraint Handling: A unified form of barrier function is proposed, capable of handling both conventional constraints and partial state constraints, avoiding the selection of feasibility conditions in traditional methods.
2. Quantizer Innovation: A novel quantizer is designed to adaptively switch quantization modes based on the control signal amplitude, significantly reducing communication overhead and quantization error.
3. Experimental Validation: The effectiveness and superiority of the control method were verified through a physical experimental platform, providing reliable technical support for practical applications.

Research Significance

This study provides a new solution for tracking control of hysteresis nonlinear systems, particularly in handling irregular constraints and quantized control. The research results not only fill gaps in existing control methods but also offer theoretical and experimental validation for the design of high-precision control systems driven by smart materials. In the future, the research team plans to further explore the system’s dynamic models to enhance control performance.