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基于牛顿定律设计的无模型不确定性控制系统

开平安1, 申忠利2   

  1. 1. 国家发展改革委能源研究所, 北京 100053;
    2. 长沙理工大学电气与信息工程学院, 长沙 410114
  • 收稿日期:2020-06-07 修回日期:2021-10-01 出版日期:2022-02-25 发布日期:2022-03-21
  • 通讯作者: 申忠利,Email:www-lieon@126.com.
  • 基金资助:
    国家自然科学基金(51977012)资助课题.

开平安, 申忠利. 基于牛顿定律设计的无模型不确定性控制系统[J]. 系统科学与数学, 2022, 42(2): 206-223.

KAI Ping'an, SHEN Zhongli. A Model-Free Design Method of Uncertainty Control System Based on Newton's Laws of Motion[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(2): 206-223.

A Model-Free Design Method of Uncertainty Control System Based on Newton's Laws of Motion

KAI Ping'an1, SHEN Zhongli2   

  1. 1. Energy Research Institute, State Development and Reform Committee of China, Beijing 100053;
    2. School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114
  • Received:2020-06-07 Revised:2021-10-01 Online:2022-02-25 Published:2022-03-21
在工程实践中,针对工业过程的不确定性设计便于使用和维护的控制器具有重要意义.牛顿定律是广大工程技术人员最熟悉的物理定律之一,文章基于牛顿定律提出了一种无模型不确定性控制系统及其设计方法,该方法通过构建被控系统的位置、速度和加速度三个状态变量,应用卡尔曼滤波器理论设计了牛顿运动力学观测器ONLM,并基于观测到的位置、速度和加速度设计了闭环系统补偿器,构成MFCNLM (Model-Free Control based on Newton's Laws of Motion)无模型控制系统,使得系统输出跟踪期望的输出轨迹.本文更进一步地提出了PID (Proportional IntegralDerivative)控制器设计的牛顿力学原理,分析和论证了MFCNLM控制方法与PID控制方法在控制系统设计上的牛顿力学统一性原理.文章所提出的设计方法不需要被控对象的数学模型,仅需控制工程师给出闭环控制系统期望的过渡过程时间$T$.文章给出了4个仿真研究和工程应用例子,具体展示了基于牛顿定律的MFCNLM控制系统与PID控制器的设计方法,结果表明所提方法对不确定系统具有良好的控制品质和鲁棒性能.
In engineering practice, it is of great significance to design a controller which is easy to use and maintain for the uncertainty of industrial process. Newton's law was one of the most familiar physical laws for engineers and technicians. Based on Newton's law, this paper proposes a model-free uncertainty control system and its design method. By constructing three state variables of the controlled system, i.e., position, velocity and acceleration, and applying Kalman filter theory, an observer based on Newton motion law (ONLM) is designed. And then a closed-loop compensator is designed according to the position, velocity and acceleration, and then a model free control system (MFCNLM) is brought into being, which makes the system output track the desired output trajectory. Furtherly, this paper puts forward a PID controller design method based on the principle of Newton motion law, and analyzes and demonstrates the Newton motion law of MFCNLM control method and PID control method in control system design. The design method proposed in this paper does not need the mathematical model of the controlled object, but only needs the control engineer to give the expected transition time $T$ of the closed-loop control system. The results show that the proposed method has good control quality and robust performance for uncertain systems.

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