网络控制系统的时延分析及PID控制器的设计
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摘要
网络控制系统(NCS),又称网络化的控制系统,它通过物理通信网络来实现控制器—执行器和传感器—控制器之间的数据交换,使某一区域内不同地点的设备和用户实现资源共享和协调操作,提高了系统的模块性、可靠性,减少安装和维护费用,在工业上得到了广泛应用。与此同时,网络的引入也带来了时延、数据丢包、资源优化调度等一系列问题,使得对网络控制系统的研究分析日益迫切。
本文主要针对网络控制系统中的网络时延问题,在不考虑其他网络影响因素的条件下分析了网络时延对NCS性能的影响,说明随着时延的增大NCS的动态性能和稳定性都降低,因此在NCS的设计过程中不可忽略时延给系统带来的影响。继而讨论了NCS采用PID控制时PID参数稳定域的确定,即先确定Kp的稳定范围,然后寻找给定Kp下K(?)-Kd平面的稳定域,最后通过遍历Kp得到整个PID参数稳定域。该稳定域为NCS智能控制器的设计提供了参数调整范围。
PID控制器在各种工业过程控制中显示出很多优点,但其无自适应能力,当网络时延和系统参数发生变化时不能调整控制参数,使系统性能下降。本文在PID控制的基础上引入模糊控制,采用模糊控制器根据系统误差对PID的控制参数进行在线调节,实现了对时延的良好补偿,提高了系统对参数变化的适应性,增强了抗干扰能力。
最后,运用TrueTime工具箱建立了NCS仿真平台,模拟实际网络控制系统的运行,对所设计的控制策略进行验证,结果表明设计的模糊PID控制器能够对时延进行有效补偿,使系统输出快速跟踪输入。同时还分析了网络速率和丢包率不同对NCS响应性能的影响,说明了联合网络和控制特性对NCS进行综合设计的重要性。
Networked Control System (NCS) which transmits data from controller to actuator and sensor to controller by network has been widely used in industry since it implements resource sharing and co-operation for equipments and users in different areas. It increases the modularity and reliability of system while decreasing costs of installation and maintanance. Meanwhile, the introduction of network to control system makes it quite important to analize NCS because it results in several questions, such as network induced time-delay, data loss, scheduling of resources and so on.
Without considering other factors of network, the impact of time-delay on NCS performance is analized which indicates that both dynamic performance and stability of system decreases with increasing time-delay, so that time-delay can't be ignored while designing a NCS. Then, the method to determine the stability region of PID controllers in NCS with PID control has been studied. Based on this method, the stability region of Kp is firstly found, then the stability region in K(？)-Kλplane can be determined under a fixed Kp, all stability region of (Kp, Ki, Kd) will be obtained by sweeping over Kp.The obtained stability region provides parameter regulating range for intelligent controller design of NCS.
The performance of NCS using PID control decreases for PID controller doesn't have self-adaptive ability to adjust control parameters with variable time-delay and system parameters. A Fuzzy-PID controller has been designed which can adjust PID parameters according to system error so that the impact of time-delay on NCS gets mostly compensated, improving system ability to adapt parameter variation and resist disturbance.
Finally, a NCS simulation platform is established by TrueTime toolbox which provides a simulated network environment to verify the validity of signed controllor. The simulation results evidence that Fuzzy-PID controller makes a good compensation to the impact of time-delay on NCS and output can quickly track input signal of system. In addition, the impact of data loss probability and network rate on NCS is also analized to demonstrate the importance of design NCS combining network and control.
本文主要针对网络控制系统中的网络时延问题,在不考虑其他网络影响因素的条件下分析了网络时延对NCS性能的影响,说明随着时延的增大NCS的动态性能和稳定性都降低,因此在NCS的设计过程中不可忽略时延给系统带来的影响。继而讨论了NCS采用PID控制时PID参数稳定域的确定,即先确定Kp的稳定范围,然后寻找给定Kp下K(?)-Kd平面的稳定域,最后通过遍历Kp得到整个PID参数稳定域。该稳定域为NCS智能控制器的设计提供了参数调整范围。
PID控制器在各种工业过程控制中显示出很多优点,但其无自适应能力,当网络时延和系统参数发生变化时不能调整控制参数,使系统性能下降。本文在PID控制的基础上引入模糊控制,采用模糊控制器根据系统误差对PID的控制参数进行在线调节,实现了对时延的良好补偿,提高了系统对参数变化的适应性,增强了抗干扰能力。
最后,运用TrueTime工具箱建立了NCS仿真平台,模拟实际网络控制系统的运行,对所设计的控制策略进行验证,结果表明设计的模糊PID控制器能够对时延进行有效补偿,使系统输出快速跟踪输入。同时还分析了网络速率和丢包率不同对NCS响应性能的影响,说明了联合网络和控制特性对NCS进行综合设计的重要性。
Networked Control System (NCS) which transmits data from controller to actuator and sensor to controller by network has been widely used in industry since it implements resource sharing and co-operation for equipments and users in different areas. It increases the modularity and reliability of system while decreasing costs of installation and maintanance. Meanwhile, the introduction of network to control system makes it quite important to analize NCS because it results in several questions, such as network induced time-delay, data loss, scheduling of resources and so on.
Without considering other factors of network, the impact of time-delay on NCS performance is analized which indicates that both dynamic performance and stability of system decreases with increasing time-delay, so that time-delay can't be ignored while designing a NCS. Then, the method to determine the stability region of PID controllers in NCS with PID control has been studied. Based on this method, the stability region of Kp is firstly found, then the stability region in K(？)-Kλplane can be determined under a fixed Kp, all stability region of (Kp, Ki, Kd) will be obtained by sweeping over Kp.The obtained stability region provides parameter regulating range for intelligent controller design of NCS.
The performance of NCS using PID control decreases for PID controller doesn't have self-adaptive ability to adjust control parameters with variable time-delay and system parameters. A Fuzzy-PID controller has been designed which can adjust PID parameters according to system error so that the impact of time-delay on NCS gets mostly compensated, improving system ability to adapt parameter variation and resist disturbance.
Finally, a NCS simulation platform is established by TrueTime toolbox which provides a simulated network environment to verify the validity of signed controllor. The simulation results evidence that Fuzzy-PID controller makes a good compensation to the impact of time-delay on NCS and output can quickly track input signal of system. In addition, the impact of data loss probability and network rate on NCS is also analized to demonstrate the importance of design NCS combining network and control.
引文
[1]吴迎年,张建华,侯国莲,杨建平.网络控制系统研究综述[J].现代电力,2003,20(5)：74～74.
[2]Walsh G C, Ye H, Bushnell L G. Stability Analysis of Networked Control Systems [A]. Proceedings of the 1999 American Control Conference [C]. Piscataway, NJ, USA:IEEE,1999: 2876～2880.
[3]傅磊,戴冠中.网络控制系统研究综述[J].计算机工程与应用,2005,41(25)：221～225.
[4]朱其新,胡寿松.网络控制系统的能控性和能观性[J].控制与决策,2004,19(2)：157～161.
[5]顾洪军.网络控制系统建模及性能分析方法的研究[D].北京：清华大学,2001.
[6]熊远生,钱苏翔,吴伟雄.网络控制系统的研究现状综述[J].工业仪表与自动化装置,2006(1)：11～11.
[7]Johan Nilsson, Bo Bernhardsson.Real-Time Control Systems with Delays [D]. Sweden, Lund Institute of Technology, Lund,1998,1 (1):1-90.
[8]GC Walsh, O Beldiman, L Bushnell. Scheduling of Networked Control Systems [J]. IEEE Control Systems Magazine,2002,21(1):57～65.
[9]Liars Fengli, Moyne J, Tilbury D. Analysis and Modeling of Networked Control Systems: MIMO Case with Mutiple Time Delays [C]. Proceedings of the American Control Conferrence, Arlington, VA,2001,6 (1):4306-4312.
[10]G. C.Walsh, HongYe, LindaG. Bushnell. Stability Analysis of Networked Control Systems [J]. IEEE Transactions on Control Systems Technology. May 2002,10 (3):438-446.
[11]Babak Azimi-Sadjadi. Stability of Networked Control Systems in the Presence of Packet Losses. ECSE Department, Rensselaer Polytechnic Institute, Troy, New York,12180 and Institute for Systems Research University of Maryland, College Park, MD 20742,2003:676-6812.
[12]Q Ling, M D Lemmon. Robust Performance of Soft Real-time Networked Control Systems with Data Dropouts [A]. IEEE Conference on Decision and Control, Las Vegas,2002,1(1): 1225～1235.
[13]Zhang Wei. Stability Analysis of Networked Control Systems [D]. Case Western Reserve University, August 2001.
[14]李琦,王坚,张浩等.Multi—agent技术在远程诊断与维护系统中的应用[J].计算机工程,2002.28(2)：137～139.
[15]Sally Floyd, Vem Paxson. Difficulties in Simulating the Intemet. IEEE/ACM Transaction on Networking. August 2001,9 (4):392～403.
[16]DeePak Bansal, Hari Balakrishnan, Sally Floyd and Scott Shenker. Dynamic Behavior of Slowly-Responsive Congestion Control Algorithms [C]. SIGCOMM'01, August 27-31,2001, SanDiego, California, USA.
[17]Brady.K and Tarn T.J. Internet-based Remote Teleoperation [J]. Proeeeding of the IEEE International Conference on Robotics and Automation, Leuven, Beigium,1998.
[18]Xi.N and Tarn T.J. Action Synchronization and Control of Internet Based Telerobotic Systems [C]. IEEE International Conference on Robotics and Automation,1999,1:219～224.
[19]Walsh G, Beldiman O, Bushnell L. Asymptotic Behavior of Nonlinear Networked Control Systems [J]. IEEE Transactions on Automatic Control,2001,46:1093～1097.
[20]Zhang W, Branicky M S, Phillips S M. Stability of Networked Control Systems [J]. IEEE Control Systems Magazine.2001,21:84～99.
[21]Montestruque L, Antsaklis P. On the Model-based Control of Networked Sytems [J]. Automatica.2003,39:1837～1843.
[22]Nilsson J, Bernhardsson B, Wittenmark B. Stability Result for Networked Control Systems Subject To Packet Dropouts. In Proceedings of the 16th IFAC World Congress.2005. Prague, July.
[23]Hu S, Zhu Q. Stochastic Optimal Control and Analysis of Stability of Networked Control Systems with Long Delay [J]. Automatic,2003,39:1877-1884.
[24]于之训,陈辉堂,王月娟.基于Markov延迟特性的闭环网络控制系统研究[J].控制理论与应用,2002,19：263～267.
[25]Zhivoglyadov P, Middleton R. Networked control design for linear systems [J]. Automatica, 2003,39:743～750.
[26]Mu S M, Chu T G, Wang L. Impulsive control of discrete-time networked systems the communication delays[C]. In Proceedings of the 16th IFAC World Congress. Prague. July 2005.
[27]胡寿松.自动控制原理[M].第4版.北京：科学出版社,2005.
[28]Martelli G. Comments on "New Results on the Synthesis of PID Controller". IEEE Transactions on Automatic Control,2005,50 (9):1468～1469.
[29]Tan N. Computation of Stabilizing PI and PID Controllers for Processs with Time Delay [J]. ISA Trans,2005,44 (2):215～223.
[30]王德进.一种确定PID参数稳定域的图解法[J].控制与决策,2007,22(6)：663～666.
[31]欧林林,顾诞英,张卫东.一类时滞对象的PID控制器参数稳定域计算[J].控制与决策,2006,21(9)：1021～1023.
[32]Naim Bajcinca. Design of Robust PID Controllers Using Decoupling at Singular Frequencies [J]. Automatica,2006,42:1943-1949.
[33]Hwang C, Hwang J H. Stabilization of First-order Plus Dead-time Unstable Processes Using PID Controllers [J]. IEE Proceedings:Control Theory and Applications,2004,15 (1):89～94.
[34]Vilma A. Oliveira, Marcelo C.M. Teixeira, Lucia Cossi. Stabilizing a Class of Time Delay Systems Using the Hermite-Biehler Theorem [J]. Linear Algebra and its Applications,2003, 369:203-216.
[35]欧林林,顾诞英,张卫东.线性时滞系统的P和PI控制器稳定参数集算法[J].上海交通大学学报,2006,40(7)：1112～1116.
[36]Lee Kyung Chang, Lee Suk. Remote Controller Design of Networked Control System Using Genetic Alnorithm [C]. IEEE 2001, Pusan, Korea in IEEE.2001:1845～1850.
[37]Lee Suk, Lee Sang Ho, Lee Kyung Chang. Remote Fuzzy Logic Control for Networked Control System [C]. IECON'01:The 27th Annual Conference of the IEEE Industrial Electronics Society.2001:1822-1827.
[38]黎善斌,王智,孙优贤.网络控制系统的自整定鲁棒数字PID控制[J].浙江大学学报,2004,38(12)：1579～1584.
[39]Almutairi Naif B, Chow Moyuen. PI Parameterization Using Adaptive Fuzzy Modulation
(APM)for Networked Control Systems-Part 1:Partial Adaptation [C].IEEE Proceedings of IECON 2002. Sevilla, Spain,2002:3152～3157.
[40]Yodyium Tipsuwan, Mo-Yuen Chow. On the Gain Scheduling for Networked PI Controller Over IP Network [J]. IEEE/ASME Transactions on Mechatronics,2004,9 (3):491～498.
[41]Mikael Pohjola. PID Controller Design in Networked Control Systems [D]. Helsinki: Department of Automation and Systems Technology, Helsinki University of Technology,2006.
[42]姜学军.计算机控制技术[M].第1版.北京：清华大学出版社,2005.
[43]刘金琨.先进PID控制及其MATLAB仿真[M].第1版.北京：电子工业出版社,2003.
[44]Martin Ohlin, Dan Henriksson, Anton Cervin. Truetime 1.4Reference Manual [M]. Department of Automatic Control, Lund Institute of Technology, September 2006:1～104.
[45]Justin Ray Hartman. Networked Control System Co-Simulation for Co-Design [D]. Department of Electrical Engineering and Computer Science, Case Western Reserve University,2004.
[46]于之训.闭环网络控制系统的理论与实验研究[D].同济大学,上海,2001.
[47]Kim Young Shin, Kim Hyung Seok, Kwon Wook Hyun. A Design of a Network-based Robot Control System Using FIP. In Proceedings of the 3rd Asian Control Conference.2000, Shanghai, China.
[48]Lee Kyung Chang, Lee Sul, Lee Man Hyung. Remote Fuzzy Logic Control of Networked Control System Via Profibus-DP [J]. IEEE Transactions on Industrial Electronics,2003,50 (4): 784～792.
[49]岳东,彭晨,Qinglong Han.网络控制系统的分析与综合[M].第1版.北京：科学出版社,2007.
[50]邱占芝,张庆灵,杨春雨.网络控制系统分析与控制[M].第1版.北京：科学出版社,2009.
[2]Walsh G C, Ye H, Bushnell L G. Stability Analysis of Networked Control Systems [A]. Proceedings of the 1999 American Control Conference [C]. Piscataway, NJ, USA:IEEE,1999: 2876～2880.
[3]傅磊,戴冠中.网络控制系统研究综述[J].计算机工程与应用,2005,41(25)：221～225.
[4]朱其新,胡寿松.网络控制系统的能控性和能观性[J].控制与决策,2004,19(2)：157～161.
[5]顾洪军.网络控制系统建模及性能分析方法的研究[D].北京：清华大学,2001.
[6]熊远生,钱苏翔,吴伟雄.网络控制系统的研究现状综述[J].工业仪表与自动化装置,2006(1)：11～11.
[7]Johan Nilsson, Bo Bernhardsson.Real-Time Control Systems with Delays [D]. Sweden, Lund Institute of Technology, Lund,1998,1 (1):1-90.
[8]GC Walsh, O Beldiman, L Bushnell. Scheduling of Networked Control Systems [J]. IEEE Control Systems Magazine,2002,21(1):57～65.
[9]Liars Fengli, Moyne J, Tilbury D. Analysis and Modeling of Networked Control Systems: MIMO Case with Mutiple Time Delays [C]. Proceedings of the American Control Conferrence, Arlington, VA,2001,6 (1):4306-4312.
[10]G. C.Walsh, HongYe, LindaG. Bushnell. Stability Analysis of Networked Control Systems [J]. IEEE Transactions on Control Systems Technology. May 2002,10 (3):438-446.
[11]Babak Azimi-Sadjadi. Stability of Networked Control Systems in the Presence of Packet Losses. ECSE Department, Rensselaer Polytechnic Institute, Troy, New York,12180 and Institute for Systems Research University of Maryland, College Park, MD 20742,2003:676-6812.
[12]Q Ling, M D Lemmon. Robust Performance of Soft Real-time Networked Control Systems with Data Dropouts [A]. IEEE Conference on Decision and Control, Las Vegas,2002,1(1): 1225～1235.
[13]Zhang Wei. Stability Analysis of Networked Control Systems [D]. Case Western Reserve University, August 2001.
[14]李琦,王坚,张浩等.Multi—agent技术在远程诊断与维护系统中的应用[J].计算机工程,2002.28(2)：137～139.
[15]Sally Floyd, Vem Paxson. Difficulties in Simulating the Intemet. IEEE/ACM Transaction on Networking. August 2001,9 (4):392～403.
[16]DeePak Bansal, Hari Balakrishnan, Sally Floyd and Scott Shenker. Dynamic Behavior of Slowly-Responsive Congestion Control Algorithms [C]. SIGCOMM'01, August 27-31,2001, SanDiego, California, USA.
[17]Brady.K and Tarn T.J. Internet-based Remote Teleoperation [J]. Proeeeding of the IEEE International Conference on Robotics and Automation, Leuven, Beigium,1998.
[18]Xi.N and Tarn T.J. Action Synchronization and Control of Internet Based Telerobotic Systems [C]. IEEE International Conference on Robotics and Automation,1999,1:219～224.
[19]Walsh G, Beldiman O, Bushnell L. Asymptotic Behavior of Nonlinear Networked Control Systems [J]. IEEE Transactions on Automatic Control,2001,46:1093～1097.
[20]Zhang W, Branicky M S, Phillips S M. Stability of Networked Control Systems [J]. IEEE Control Systems Magazine.2001,21:84～99.
[21]Montestruque L, Antsaklis P. On the Model-based Control of Networked Sytems [J]. Automatica.2003,39:1837～1843.
[22]Nilsson J, Bernhardsson B, Wittenmark B. Stability Result for Networked Control Systems Subject To Packet Dropouts. In Proceedings of the 16th IFAC World Congress.2005. Prague, July.
[23]Hu S, Zhu Q. Stochastic Optimal Control and Analysis of Stability of Networked Control Systems with Long Delay [J]. Automatic,2003,39:1877-1884.
[24]于之训,陈辉堂,王月娟.基于Markov延迟特性的闭环网络控制系统研究[J].控制理论与应用,2002,19：263～267.
[25]Zhivoglyadov P, Middleton R. Networked control design for linear systems [J]. Automatica, 2003,39:743～750.
[26]Mu S M, Chu T G, Wang L. Impulsive control of discrete-time networked systems the communication delays[C]. In Proceedings of the 16th IFAC World Congress. Prague. July 2005.
[27]胡寿松.自动控制原理[M].第4版.北京：科学出版社,2005.
[28]Martelli G. Comments on "New Results on the Synthesis of PID Controller". IEEE Transactions on Automatic Control,2005,50 (9):1468～1469.
[29]Tan N. Computation of Stabilizing PI and PID Controllers for Processs with Time Delay [J]. ISA Trans,2005,44 (2):215～223.
[30]王德进.一种确定PID参数稳定域的图解法[J].控制与决策,2007,22(6)：663～666.
[31]欧林林,顾诞英,张卫东.一类时滞对象的PID控制器参数稳定域计算[J].控制与决策,2006,21(9)：1021～1023.
[32]Naim Bajcinca. Design of Robust PID Controllers Using Decoupling at Singular Frequencies [J]. Automatica,2006,42:1943-1949.
[33]Hwang C, Hwang J H. Stabilization of First-order Plus Dead-time Unstable Processes Using PID Controllers [J]. IEE Proceedings:Control Theory and Applications,2004,15 (1):89～94.
[34]Vilma A. Oliveira, Marcelo C.M. Teixeira, Lucia Cossi. Stabilizing a Class of Time Delay Systems Using the Hermite-Biehler Theorem [J]. Linear Algebra and its Applications,2003, 369:203-216.
[35]欧林林,顾诞英,张卫东.线性时滞系统的P和PI控制器稳定参数集算法[J].上海交通大学学报,2006,40(7)：1112～1116.
[36]Lee Kyung Chang, Lee Suk. Remote Controller Design of Networked Control System Using Genetic Alnorithm [C]. IEEE 2001, Pusan, Korea in IEEE.2001:1845～1850.
[37]Lee Suk, Lee Sang Ho, Lee Kyung Chang. Remote Fuzzy Logic Control for Networked Control System [C]. IECON'01:The 27th Annual Conference of the IEEE Industrial Electronics Society.2001:1822-1827.
[38]黎善斌,王智,孙优贤.网络控制系统的自整定鲁棒数字PID控制[J].浙江大学学报,2004,38(12)：1579～1584.
[39]Almutairi Naif B, Chow Moyuen. PI Parameterization Using Adaptive Fuzzy Modulation
(APM)for Networked Control Systems-Part 1:Partial Adaptation [C].IEEE Proceedings of IECON 2002. Sevilla, Spain,2002:3152～3157.
[40]Yodyium Tipsuwan, Mo-Yuen Chow. On the Gain Scheduling for Networked PI Controller Over IP Network [J]. IEEE/ASME Transactions on Mechatronics,2004,9 (3):491～498.
[41]Mikael Pohjola. PID Controller Design in Networked Control Systems [D]. Helsinki: Department of Automation and Systems Technology, Helsinki University of Technology,2006.
[42]姜学军.计算机控制技术[M].第1版.北京：清华大学出版社,2005.
[43]刘金琨.先进PID控制及其MATLAB仿真[M].第1版.北京：电子工业出版社,2003.
[44]Martin Ohlin, Dan Henriksson, Anton Cervin. Truetime 1.4Reference Manual [M]. Department of Automatic Control, Lund Institute of Technology, September 2006:1～104.
[45]Justin Ray Hartman. Networked Control System Co-Simulation for Co-Design [D]. Department of Electrical Engineering and Computer Science, Case Western Reserve University,2004.
[46]于之训.闭环网络控制系统的理论与实验研究[D].同济大学,上海,2001.
[47]Kim Young Shin, Kim Hyung Seok, Kwon Wook Hyun. A Design of a Network-based Robot Control System Using FIP. In Proceedings of the 3rd Asian Control Conference.2000, Shanghai, China.
[48]Lee Kyung Chang, Lee Sul, Lee Man Hyung. Remote Fuzzy Logic Control of Networked Control System Via Profibus-DP [J]. IEEE Transactions on Industrial Electronics,2003,50 (4): 784～792.
[49]岳东,彭晨,Qinglong Han.网络控制系统的分析与综合[M].第1版.北京：科学出版社,2007.
[50]邱占芝,张庆灵,杨春雨.网络控制系统分析与控制[M].第1版.北京：科学出版社,2009.