基于最小角回归的稀疏辨识与优化PID控制

doi:10.12305/j.issn.1001-506X.2025.08.28

系统工程与电子技术 ›› 2025, Vol. 47 ›› Issue (8): 2706-2714.doi: 10.12305/j.issn.1001-506X.2025.08.28

• 制导、导航与控制 • 上一篇

基于最小角回归的稀疏辨识与优化PID控制

刘艳君¹^,²^,*, 武禹辰¹, 陈晶², 丁锋¹^,²

1. 江南大学物联网工程学院，江苏无锡 214122
2. 江南大学轻工过程先进控制教育部重点实验室，江苏无锡 214122

收稿日期:2024-05-06 出版日期:2025-08-25 发布日期:2025-09-04
通讯作者: 刘艳君
作者简介:武禹辰（2000—），男，硕士研究生，主要研究方向为系统辨识
陈　晶（1981—），男，教授，博士，主要研究方向为系统辨识、模式识别
丁　锋（1963—），男，教授，博士，主要研究方向为系统建模、系统辨识、过程控制、多率控制
基金资助:
国家自然科学基金（62373165）；江苏省自然科学基金（BK20201339）；中国博士后科学基金（2022M711361）；近地面探测技术重点实验室基金（6142414220203）资助课题

Sparse identification based on least angle regression and optimal PID control

Yanjun LIU¹^,²^,*, Yuchen WU¹, Jing CHEN², Feng DING¹^,²

1. School of Internet of Things Engineering，Jiangnan University，Wuxi 214122，China
2. Ministry of Education Laboratory of Advanced Process Control for Light Industry，Jiangnan University，Wuxi 214122，China

Received:2024-05-06 Online:2025-08-25 Published:2025-09-04
Contact: Yanjun LIU

摘要/Abstract

摘要：

针对过程复杂且结构未知的对象，在保证模型有效性的前提下，根据数据信息构建简单模型来简化控制器的求解是亟待解决的问题。以受控自回归模型为例，提出一种基于修正最小角回归算法的稀疏辨识方法。首先将系统模型转化为过参数化的高维稀疏模型，然后将最小角回归算法用于稀疏系统辨识，并提出绝对角度停止准则，使算法经过少量的迭代即可获得模型的稀疏参数估计，并同时获得有效的时滞和阶次估计。结合辨识得到的受控自回归模型，引入一种基于指定相位点频率和增益的比例-积分-微分（proportional integral derivative，PID）控制器。数值仿真和平衡机器人的姿态控制仿真表明，该稀疏辨识算法在低数据量下具有较高的辨识精度，建立的模型具有较好的泛化性能，控制器具有良好的控制效果。

关键词: 最小角回归, 稀疏系统辨识, 时滞阶次联合估计, 停止准则, 优化PID控制

Abstract:

For complex processes and unknown structures, it is an urgent problem to be solved to construct a simple model based on data information to simplify the solution of controllers for objects, while ensuring the effectiveness of the model. Taking the controlled autoregressive model as an example, a sparse identification method based on the modified minimum angle regression algorithm is proposed. Firstly, the system model is transformed into a hyperparameter high-dimensional sparse model. Then, the minimum angle regression algorithm is used for sparse system identification, and the absolute angle stopping criterion is proposed. The algorithm can obtain sparse parameter estimates of the model after a small number of iterations, and obtain effective time delay and order estimates at the same time. Combining the identified controlled autoregressive model, a proportional integral derivative （PID） controller based on specified phase point frequency and gain is introduced. Numerical simulation and attitude control simulation of the balancing robot show that the sparse identification algorithm has high identification accuracy under low data volume, the established model has good generalization performance, and the controller has good control effect.

Key words: least angle regression, sparse system identification, time-delay and order joint estimation, stopping criterion, optimal proportional integral derivative （PID） control

中图分类号:

TP 273

刘艳君, 武禹辰, 陈晶, 丁锋. 基于最小角回归的稀疏辨识与优化PID控制[J]. 系统工程与电子技术, 2025, 47(8): 2706-2714.

Yanjun LIU, Yuchen WU, Jing CHEN, Feng DING. Sparse identification based on least angle regression and optimal PID control[J]. Systems Engineering and Electronics, 2025, 47(8): 2706-2714.

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基于最小角回归的稀疏辨识与优化PID控制

Sparse identification based on least angle regression and optimal PID control

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