执行器饱和控制研究
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摘要
饱和是控制系统中最为普遍的非线性现象之一，大多数执行器不可避免的会出现饱和。如果执行器的输入量达到一定限制，就进入了饱和状态，因为进一步增加输入不能对执行器的输出产生任何影响，执行器的饱和将使系统的动态性能降低，甚至导致闭环系统不稳定。
随着现代技术的发展，控制系统的精度要求越来越高，例如数控机床、机器人操作手、微电子装配单元、高速硬盘等都需要进行高精度控制。但是由于饱和等非线性的存在，经典的控制算法很难保证所要求的设计精度。为消除饱和非线性的影响而采用更高精密的仪器设备将使得整个控制系统造价昂贵；然而，如果能够采用先进的补偿策略，使得采用相对廉价的仪器设备来满足精度要求成为可能。小型和微型计算机及其电力电子技术的发展为各种控制算法的实现提供了更大空间，寻求更高性能和更高适应性控制算法成为实现高精度控制的捷径。本文针对具有执行器饱和的系统进行控制器的设计研究，寻求理想的饱和补偿策略，实现高精度的跟踪控制。
本文首先对当前的饱和补偿策略研究进行了回顾，接着针对不同的应用对象提出了两种不同的控制策略实现了饱和补偿，完成系统的高性能跟踪控制器的设计。两种方法为神经网络自适应方法和复合控制方法，其中神经网络自适应方法可以应用于时变系统，复合控制设计方法是针对线性时不变系统设计。
神经网络设计对于具有Brunovsky标准型的非线性时变系统提出一种权系数可在线调节的神经网络饱和补偿算法，采用了RBF神经网络对控制器输出超出饱和部分进行估计补偿。该算法的另一突出优点是考虑了网络重构误差和外部干扰，利用Lyapunov理论证明了该算法能够保证系统半全局一致最终有界，且跟踪误差以已知的形式可以自由调节。由于所考虑的系统具有未知函数，使神经网络设计方法具有广泛的应用性。复合控制设计方法以经典控制理论为基础，通过极点配置使系统达到期望的跟踪性能指标，然后设计具有抑制超调能力的非线性律，达到既能提高系统的响应速度又能保证输出有较小的超调量，实现较好的跟踪性能的目的。所提出的两种设计方法，均给出了稳定性的证明和仿真算例及结果，仿真结果表明两种方法都是有效的。
The problem of actuator saturation appears in many practical control systems, saturation nonlinearity is unavoidable in most actuators. When an actuator reached such an input limit, it is said to be "saturated", since efforts to further increase the actuator output would not result in any variation in the output. The presence of saturation can debase the performance even lead the closed-loop system to an unstable behavior.
With the development of modern technology, the precision of control systems require more and more highly, for example, ultra-precision machining, robot manipulator, assembly of small components and micro devices and hard disk drive system are all needed highly precision. It is very difficult to assure designing accuracy using conventional control system under the influence of saturation. To eliminate the saturation effect, designing and make a more precise mechanical components may lead to a high cost for the over system. However, adopting the advanced saturation compensation scheme makes the use of cheaper mechanical components to meet high-precision need possible. A remarkable progress in mini- and micro computers and power electronics technology has generated more room for control algorithms; designing higher performance and flexibility control strategy becomes a royal road for realizing high-precision control. This paper explores the methods of designing controller for nonlinear systems with input saturation and seeks strategy preferable to compensate the saturation for realizing high-precision tracking control.
Some control strategies were reviewed firstly in this paper; in the following, two saturation compensation schemes are presented for different nonlinear systems with input saturation to decrease the influence of saturations and realize tracking control, i.e. the Design of Neural Network Controller. And The Design of Composite Controller.The first design can be applied linear time-variant control systems and the second strategy can be applied linear time-invariant control systems.
A neural net-based actuator saturation composition scheme with on-line weights tuning law for nonlinear systems in Brnovsky form is presented in the third method. RBF neural network is adopted to approximate the part exceeding the saturation limit of controller's output. Another most prominent feature of the scheme is which can ensure the system is uniformly ultimately bounded which is proved by Lyapunov theory, and considering the network reconstruction error and the system's external disturbance. The tracking error can be freely adjusted by known form. Considering the plant with unknown function, the method has more extensively practical application. The Design of Composite Controller base on classical control theory, first make the system meeting the expecting control objective by pole placement and then design a nonlinear control law to reduce the overshoot caused by the linear part. This design can guaranteed the closed-loop system with a small damping ratio for a quick response, while the nonlinear control law can increase the damping ratio as the output approaches the target reference.
In this paper, every method is given stability provability and simulation example as well results respectively, the results illustrate the effectiveness of the three methods.
随着现代技术的发展，控制系统的精度要求越来越高，例如数控机床、机器人操作手、微电子装配单元、高速硬盘等都需要进行高精度控制。但是由于饱和等非线性的存在，经典的控制算法很难保证所要求的设计精度。为消除饱和非线性的影响而采用更高精密的仪器设备将使得整个控制系统造价昂贵；然而，如果能够采用先进的补偿策略，使得采用相对廉价的仪器设备来满足精度要求成为可能。小型和微型计算机及其电力电子技术的发展为各种控制算法的实现提供了更大空间，寻求更高性能和更高适应性控制算法成为实现高精度控制的捷径。本文针对具有执行器饱和的系统进行控制器的设计研究，寻求理想的饱和补偿策略，实现高精度的跟踪控制。
本文首先对当前的饱和补偿策略研究进行了回顾，接着针对不同的应用对象提出了两种不同的控制策略实现了饱和补偿，完成系统的高性能跟踪控制器的设计。两种方法为神经网络自适应方法和复合控制方法，其中神经网络自适应方法可以应用于时变系统，复合控制设计方法是针对线性时不变系统设计。
神经网络设计对于具有Brunovsky标准型的非线性时变系统提出一种权系数可在线调节的神经网络饱和补偿算法，采用了RBF神经网络对控制器输出超出饱和部分进行估计补偿。该算法的另一突出优点是考虑了网络重构误差和外部干扰，利用Lyapunov理论证明了该算法能够保证系统半全局一致最终有界，且跟踪误差以已知的形式可以自由调节。由于所考虑的系统具有未知函数，使神经网络设计方法具有广泛的应用性。复合控制设计方法以经典控制理论为基础，通过极点配置使系统达到期望的跟踪性能指标，然后设计具有抑制超调能力的非线性律，达到既能提高系统的响应速度又能保证输出有较小的超调量，实现较好的跟踪性能的目的。所提出的两种设计方法，均给出了稳定性的证明和仿真算例及结果，仿真结果表明两种方法都是有效的。
The problem of actuator saturation appears in many practical control systems, saturation nonlinearity is unavoidable in most actuators. When an actuator reached such an input limit, it is said to be "saturated", since efforts to further increase the actuator output would not result in any variation in the output. The presence of saturation can debase the performance even lead the closed-loop system to an unstable behavior.
With the development of modern technology, the precision of control systems require more and more highly, for example, ultra-precision machining, robot manipulator, assembly of small components and micro devices and hard disk drive system are all needed highly precision. It is very difficult to assure designing accuracy using conventional control system under the influence of saturation. To eliminate the saturation effect, designing and make a more precise mechanical components may lead to a high cost for the over system. However, adopting the advanced saturation compensation scheme makes the use of cheaper mechanical components to meet high-precision need possible. A remarkable progress in mini- and micro computers and power electronics technology has generated more room for control algorithms; designing higher performance and flexibility control strategy becomes a royal road for realizing high-precision control. This paper explores the methods of designing controller for nonlinear systems with input saturation and seeks strategy preferable to compensate the saturation for realizing high-precision tracking control.
Some control strategies were reviewed firstly in this paper; in the following, two saturation compensation schemes are presented for different nonlinear systems with input saturation to decrease the influence of saturations and realize tracking control, i.e. the Design of Neural Network Controller. And The Design of Composite Controller.The first design can be applied linear time-variant control systems and the second strategy can be applied linear time-invariant control systems.
A neural net-based actuator saturation composition scheme with on-line weights tuning law for nonlinear systems in Brnovsky form is presented in the third method. RBF neural network is adopted to approximate the part exceeding the saturation limit of controller's output. Another most prominent feature of the scheme is which can ensure the system is uniformly ultimately bounded which is proved by Lyapunov theory, and considering the network reconstruction error and the system's external disturbance. The tracking error can be freely adjusted by known form. Considering the plant with unknown function, the method has more extensively practical application. The Design of Composite Controller base on classical control theory, first make the system meeting the expecting control objective by pole placement and then design a nonlinear control law to reduce the overshoot caused by the linear part. This design can guaranteed the closed-loop system with a small damping ratio for a quick response, while the nonlinear control law can increase the damping ratio as the output approaches the target reference.
In this paper, every method is given stability provability and simulation example as well results respectively, the results illustrate the effectiveness of the three methods.
引文
[1] Ben M. Chen, Senior Member, IEEE, Tong H. Lee, Kemao Peng, and V. Venkataramanan. Composite Nonlinear Feedback Control for Linear Systems With Input Saturation: Theory and an Application ,IEEE Transactions on Automatic Control,Vol.48, no.3, march 2003.
[2] 董锡君，姚郁，王子才．基于滤波器的Anti-windup设计及其在伺服系统中的应用．哈尔滨工业大学学报 2002年01期
[3] 方敏．具有执行器饱和系统的控制器合成设计理论及应用．轻工业学院学报，2006，no3。
[4] Whitake H P. Design of Model-Reference Adaptive Control System for Aircaft.R- 164. Instrumentation Laboratory, MIT, Cambridge, Mass, 1958.
[5] Drossber R W. An approach to Model-Reference Adaptive Control System. IEEE Transactions on Automatic Control, 1967: 7580.
[6] Shachcloth B, Butchart R L. Synthesis of Model Reference Adaptive Control System by Lyapunov second Method. IFAC Aymposium Jeddinglon, 1965.
[7] T. Fliegner, H. Logemann, E.P. Ryan. Adaptive Low-gain Integral Control in The Presence of Input and Output Nonlinearities. Department of Mathematical sciences, University of Bath Calverton Down, Bath BA2 7AY, U.K.
[8] Y. -S.Zhong.Globally stable adaptive system design for minimum phase SISO plants with saturation. Automatic, no.41, 2005,pp. 1539-1547.
[9] 余文，M．DelaSen2，柴天佑．具有任意非线性输入的鲁棒模型参考自适应控制．自动化学报．Vol．23，No．1，January，1997
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[12] 李涛，冯勇，安澄全．变边界饱和特性减小抖振的设计方法．自动化学报．Vol．26，No．1，Jan．，2000
[13] Eric N. Johnson and Anthony J. Calise. Neural Network Adaptive Control of Systems with Input Saturation. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150
[14] Wenzhi Gao and Rastko R. Selmic. Neural Network Control of a Class of Nonlinear Systems With Actuator Saturation. Proceeding of 2004 American Control Conference Boston, Massachusetts June 30-July 2,2004.pp: 2569-2574.
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[16] 俞立．有控制约束的不确定离散系统最优保性能控制．统工程与电子技术，vol．26，no．10，2004．
[17] Stuart Crawshaw. Control of systems with actuator nonlinearities, Trinity College, Department of Engineering University of Cambridge. A dissertation submitted for the degree of Doctor of Philosophy, May 26,2000
[18] I-Kong Fong and Chih-Chin Hsu。 State Feedback Stabilization of single Input Systems Through Actuators with Saturation and Deadzone Characteristics, proceedings of the 39th IEEE conference on Decision and Control Sydney, Australia.December 2000.
[19] 王福忠，姚波，张嗣瀛．具有执行器故障的保成本可靠控制．东北大学学报．Vol．24，no．7，2003．
[20] 张桂香，曾利权．输入具有饱和非线性的离散系统闭环稳定性．湖南大学学报．Vol．25，No．6，1998．12．
[21] 周腊吾，朱英浩．输入具有饱和非线性的离散系统闭环稳定性．湘潭大学自然科学学报．2003．9，Vol．25，No．3
[22] F. Z . Chaoui, F. Giri, M. Saad.Asymptotic stabilization of linear plants in presence of input and output saturations. Automatica 37 (2001)
[23] 王毅，曾鸣，苏宝库．具有多个饱和非线性的系统分析与设计．电机与控制学报．2002，Vol．6，No．2
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[32] J-H. Horng. Neural adaptive tracking control of a DC motor. Information Sciences.1999,(118): 1-13
[33] Y. H. Kim. F. L. Lewis. Reinforcement Adaptive Learning Neural-Net-Based Friction Compensation Control for High Speed and Precision. IEEE Trans. Contr.Sys. Tech., 2000, 8(1): 118-126.
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[2] 董锡君，姚郁，王子才．基于滤波器的Anti-windup设计及其在伺服系统中的应用．哈尔滨工业大学学报 2002年01期
[3] 方敏．具有执行器饱和系统的控制器合成设计理论及应用．轻工业学院学报，2006，no3。
[4] Whitake H P. Design of Model-Reference Adaptive Control System for Aircaft.R- 164. Instrumentation Laboratory, MIT, Cambridge, Mass, 1958.
[5] Drossber R W. An approach to Model-Reference Adaptive Control System. IEEE Transactions on Automatic Control, 1967: 7580.
[6] Shachcloth B, Butchart R L. Synthesis of Model Reference Adaptive Control System by Lyapunov second Method. IFAC Aymposium Jeddinglon, 1965.
[7] T. Fliegner, H. Logemann, E.P. Ryan. Adaptive Low-gain Integral Control in The Presence of Input and Output Nonlinearities. Department of Mathematical sciences, University of Bath Calverton Down, Bath BA2 7AY, U.K.
[8] Y. -S.Zhong.Globally stable adaptive system design for minimum phase SISO plants with saturation. Automatic, no.41, 2005,pp. 1539-1547.
[9] 余文，M．DelaSen2，柴天佑．具有任意非线性输入的鲁棒模型参考自适应控制．自动化学报．Vol．23，No．1，January，1997
[10] 游少鹏．一种模糊自适应控制器．成都科技大学学报．Vol．77，No．3，1994
[11] 张天平，冯纯伯．一类非线性系统的自适应模糊滑模控制．自动化学报．Vol．23，No．3May，1997．
[12] 李涛，冯勇，安澄全．变边界饱和特性减小抖振的设计方法．自动化学报．Vol．26，No．1，Jan．，2000
[13] Eric N. Johnson and Anthony J. Calise. Neural Network Adaptive Control of Systems with Input Saturation. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150
[14] Wenzhi Gao and Rastko R. Selmic. Neural Network Control of a Class of Nonlinear Systems With Actuator Saturation. Proceeding of 2004 American Control Conference Boston, Massachusetts June 30-July 2,2004.pp: 2569-2574.
[15] 郭小勤，金西岳．考虑控制输入饱和限制的飞控系统设计．飞行力学1996年03期
[16] 俞立．有控制约束的不确定离散系统最优保性能控制．统工程与电子技术，vol．26，no．10，2004．
[17] Stuart Crawshaw. Control of systems with actuator nonlinearities, Trinity College, Department of Engineering University of Cambridge. A dissertation submitted for the degree of Doctor of Philosophy, May 26,2000
[18] I-Kong Fong and Chih-Chin Hsu。 State Feedback Stabilization of single Input Systems Through Actuators with Saturation and Deadzone Characteristics, proceedings of the 39th IEEE conference on Decision and Control Sydney, Australia.December 2000.
[19] 王福忠，姚波，张嗣瀛．具有执行器故障的保成本可靠控制．东北大学学报．Vol．24，no．7，2003．
[20] 张桂香，曾利权．输入具有饱和非线性的离散系统闭环稳定性．湖南大学学报．Vol．25，No．6，1998．12．
[21] 周腊吾，朱英浩．输入具有饱和非线性的离散系统闭环稳定性．湘潭大学自然科学学报．2003．9，Vol．25，No．3
[22] F. Z . Chaoui, F. Giri, M. Saad.Asymptotic stabilization of linear plants in presence of input and output saturations. Automatica 37 (2001)
[23] 王毅，曾鸣，苏宝库．具有多个饱和非线性的系统分析与设计．电机与控制学报．2002，Vol．6，No．2
[24] Fu K S. Learning Control Systems and Intelligent Control System: An Intersection of Artificial Intelligence and Automatic Control. IEEE Trans. on Automatic Control, 1971, AC-16 (1): 70-72
[25] Hunt K J, Sbarbaro D, Zbikowski R, et al. Neural networks for control systems-a survey[J]. Automatica, 1992, 28 (6): 1083-1112
[26] F. Scarselli, H. Tsoi. Universal approximation using feedforward neural networks: A survey of some existing methods, and some new results. Neural Networks. 1998, 11(1): 15-37
[27] K. Krishna Kumar, K. Nishita. Robustness analysis of neural networks with an application to system identification. J. Guidance Contr. And Dynamics, 1999, 22 (5):695-701
[28] N. Sadegh. A perceptron network for functional identification and control of nonlinear systems. IEEE Trans. Neural Networks, 1993,4 (6): 982-988
[29] J. C. Patra, R. N. Pal, B. N. Chatterji et al. Identification of nonlinear dynamic systems using functional link artificial neural networks. IEEE Trans. Systems Man and Cybernetics-Part B: Cybernetics. 1999, 29 (2): 254-262
[30] S. Bhama, H. Singh. Single layer neural networks for linear system identification using gradient descent technique. IEEE Trans. Neural Networks, 1993,4 (5):884-888
[31] F. L. Lewis, A. Yesildirek, K. Liu. Multiplayer neural-net robot controller with guaranteed tracking performance. IEEE Trans. Neural Networks, 1996, 7 (2):388-399
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