优化滤波器在内模控制中的应用
摘要
时滞系统是过程工业领域里的控制难题,内模控制由于具有良好鲁棒性和控制性能而被广泛采用在时滞系统的控制中。本文以时滞系统工业过程为研究对象,采用目前在工业应用中实用的内模控制方法为主要控制手段,针对内模控制器设计中的滤波器的设计,分析了其对控制系统性能的影响,得出为提高系统的鲁棒性和闭环性能,滤波器的设计是至关重要的,因此,可以通过对系统的鲁棒性和闭环性能的分析,来设计控制器中的滤波器。
本文针对内模控制器中的滤波器的设计进行了深入研究,分析了标准Butterworth滤波器的基本原理、时域及频域特性,阶数n截止频率ωc。对控制性能的影响,给出了提高控制系统性能的改进型Butterworth滤波器的设计方法,并分别从时域、频域特性上分析了改进型Butterworth滤波器的三个可调参数：阶数n、截止频率ωc以及最靠近虚轴的极点所在的半径与虚轴之间的夹角θ对控制性能的影响,针对一阶时滞系统和二阶时滞系统,给出了改进型Butterworth滤波器的控制设计方案并进行了仿真实验研究。
其次,分析了滤波器中的可调参数λ(即1／ωc)对控制系统的影响,提出了采用伸缩因子变论域的滤波器时间常数λ自调整模糊内模控制。给出了滤波器时间常数的变论域模糊控制改进方法,由e指数伸缩因子导出工程上可实用的幂指数伸缩因子。针对工业过程中常见的一阶、二阶时滞过程,并分别在模型匹配、模型失配以及模型不确定和干扰的情况下,分别采用传统模糊控制、改进变论域模糊控制及采用幂函数型伸缩因子的变论域模糊控制进行了仿真实验研究。
最后,本文将卡尔曼滤波器引入到内模控制的结构中,针对被控对象的模型不确定,同时考虑到系统的随机噪声和测量噪声进而构建内模控制器,使控制系统及具有较强的鲁棒性又达到了较强的快速性,大大的提升了控制系统的控制性能,为内模控制器的进一步优化设计提供了一条有效的方法。
Time-delay system is a problem in process control industrial, the internal model control (IMC) has been widely used in time-delay systems control because of its good robustness and control performance. In this paper, industrial process of time-delay system is used as the research object, the current IMC method is applied to the main control means, for the filter of IMC design, analyzes its effect on control system performance. Filter design is crucial for the improvement of the robustness of the system and closed-loop performance. Therefore, performance analysis of the system robustness and closed-loop performance analysis can be used to design the filter of the controller.
This paper did in-depth research in the filter design of the IMC, analyzed the basic principles of the standard Butterworth filter, also the effect to the control properties of time and frequency domain characteristics, n the order,ωc the cut-off frequency, given improved Butterworth filter design methods which can improve control system performance, and from time domain. It also analyzed the control performance of the three adjustable parameters of improved Butterworth filter from frequency domain characteristics, which are:n the order,ωc cut-off frequency andθincluded-angle between radii of pole which next to the imaginary axis and the imaginary axis. For a 1st and 2nd order delay system, simulation experiment of the improved Butterworth filter control design was carried out.
Secondly, we analyzed the impact of the control system of the filter adjustable parametersλ(as 1/ωc), and proposed a fuzzy self-tuning IMC using variable universe expansion factor of filter time constantλ. Offered a improve fuzzy control method of the variable universe expansion factor for the filter time constant, advanced the exponential expansion factor derived from the e index which can be useful for the works. In connection with the first order, second order delay process which is common in industrial process, when model matched, model mismatch and model uncertainty and disturbance cases, we did simulation experiments using, respectively, the standard fuzzy control, the improved variable universe fuzzy control and the power function variable universe expansion factor fuzzy control.
Finally, the Kalman filter is introduced into the structure of IMC, when the model is uncertainty, remaining the system's random noise and measurement noise then build an IMC, the control system has strong robustness and fast, greatly improved the control system performance, it provides a method for the further optimization of the IMC design.
本文针对内模控制器中的滤波器的设计进行了深入研究,分析了标准Butterworth滤波器的基本原理、时域及频域特性,阶数n截止频率ωc。对控制性能的影响,给出了提高控制系统性能的改进型Butterworth滤波器的设计方法,并分别从时域、频域特性上分析了改进型Butterworth滤波器的三个可调参数：阶数n、截止频率ωc以及最靠近虚轴的极点所在的半径与虚轴之间的夹角θ对控制性能的影响,针对一阶时滞系统和二阶时滞系统,给出了改进型Butterworth滤波器的控制设计方案并进行了仿真实验研究。
其次,分析了滤波器中的可调参数λ(即1／ωc)对控制系统的影响,提出了采用伸缩因子变论域的滤波器时间常数λ自调整模糊内模控制。给出了滤波器时间常数的变论域模糊控制改进方法,由e指数伸缩因子导出工程上可实用的幂指数伸缩因子。针对工业过程中常见的一阶、二阶时滞过程,并分别在模型匹配、模型失配以及模型不确定和干扰的情况下,分别采用传统模糊控制、改进变论域模糊控制及采用幂函数型伸缩因子的变论域模糊控制进行了仿真实验研究。
最后,本文将卡尔曼滤波器引入到内模控制的结构中,针对被控对象的模型不确定,同时考虑到系统的随机噪声和测量噪声进而构建内模控制器,使控制系统及具有较强的鲁棒性又达到了较强的快速性,大大的提升了控制系统的控制性能,为内模控制器的进一步优化设计提供了一条有效的方法。
Time-delay system is a problem in process control industrial, the internal model control (IMC) has been widely used in time-delay systems control because of its good robustness and control performance. In this paper, industrial process of time-delay system is used as the research object, the current IMC method is applied to the main control means, for the filter of IMC design, analyzes its effect on control system performance. Filter design is crucial for the improvement of the robustness of the system and closed-loop performance. Therefore, performance analysis of the system robustness and closed-loop performance analysis can be used to design the filter of the controller.
This paper did in-depth research in the filter design of the IMC, analyzed the basic principles of the standard Butterworth filter, also the effect to the control properties of time and frequency domain characteristics, n the order,ωc the cut-off frequency, given improved Butterworth filter design methods which can improve control system performance, and from time domain. It also analyzed the control performance of the three adjustable parameters of improved Butterworth filter from frequency domain characteristics, which are:n the order,ωc cut-off frequency andθincluded-angle between radii of pole which next to the imaginary axis and the imaginary axis. For a 1st and 2nd order delay system, simulation experiment of the improved Butterworth filter control design was carried out.
Secondly, we analyzed the impact of the control system of the filter adjustable parametersλ(as 1/ωc), and proposed a fuzzy self-tuning IMC using variable universe expansion factor of filter time constantλ. Offered a improve fuzzy control method of the variable universe expansion factor for the filter time constant, advanced the exponential expansion factor derived from the e index which can be useful for the works. In connection with the first order, second order delay process which is common in industrial process, when model matched, model mismatch and model uncertainty and disturbance cases, we did simulation experiments using, respectively, the standard fuzzy control, the improved variable universe fuzzy control and the power function variable universe expansion factor fuzzy control.
Finally, the Kalman filter is introduced into the structure of IMC, when the model is uncertainty, remaining the system's random noise and measurement noise then build an IMC, the control system has strong robustness and fast, greatly improved the control system performance, it provides a method for the further optimization of the IMC design.
引文
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[37]李钟慎.基于Butterworth标准传递函数设计状态反馈系统[J].微计算机信息,2005,21(8-1)：46-48.
[38]洪健,李钟慎.改进的Butterworth最佳传递函数标准型[J].计算机技术与自动化,2005,24(2)：13-15.
[39]吕丹,陈文灵,张文夫,邓发升.基于改进的Butterworth传递函数的高阶低通有源滤波器的设计[J].弹箭与制导学报,2006,26(1)：784-788.
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[2]Deshpande P B, A sh R H著,张新薇,陈永译.计算机过程控制—先进控制策略的应用[M].中国科学技术出版社,1991
[3]Morari M, Zafiriou E. Robust Process Control[M]. Prentice-Hall,1988
[4]舒迪前1预测控制系统及其应用1[M].北京：机械工业出版社,1996
[5]赵曜1直流调速系统的2自由度内模控制方法1[J].电气传动,1997,27(1)：41-43
[6]赵曜1直流调速系统2自由度内模控制与PID控制的比较[J].1997中国控制会议论文集,武汉出版社,1997：1109-1112
[7]张井岗等1 直流电动机调速系统的内模控制1[J].电机与控制学报,1998,2(2)：126-128
[8]Garcia C E, Morari M. Internal Model Control 2. [J]. Design Procedure for multivariable system s. I & EC P rocess Des.Dev.,1985,24 (2):472-484
[9]Econmou C G, Morari M. Internal Model Control.5. [J]. Extension to Nonlinear Systems. I & EC Process Des. Dev.,1986,25 (2):403-411
[10]Garcia C E, Morari M. Internal Model Control.3 [J]. Multivariable Control Law Computation and Tuning Guidelines.I & EC Process Des. Dev.,1985,24 (2):484-494
[11]Garcia C E, Mo rari M. InternalModel Control.4 [J]. PID Controller Design. I & EC P rocessDes. Dev.,1986,25 (1):252-265
[12]舒迪前1自适应控制1[M],沈阳：东北大学出版社,1993
[13]谭永红,李松1自适应内模控制及其应用1[M].自动化仪表,1991,12(4)：8-10
[14]张井岗等1 模糊自适应内模控制1[J].第二届全球华人智能控制与智能自动化大会论文集,1997：1811-1814
[15]刘乐星,余文休1智能自适应内模控制器1[J].1996中国智能自动化会议论文集,1996：501-505
[16]李士勇1模糊控制、神经控制和智能控制论[M].哈尔滨工业大学出版社,1996
[17]赵曜,牛端燕1 内模控制系统反馈滤波器的在线智能调节[J].1999中国智能自动化会议论文集(待出版),清华大学出版社,1999：529-533
[18]A. DEHGHANI et al. Hoo design to generalize internal model control [J]. Automatica, 2006,42:1959-1968.
[19]N. CHAWANKUL et al. The integration of design and control:IMC control and robustness [J]., Computers and Chemical Engineering,2005,29:261-271.
[20]I.D. LANDAU et al. Adaptive narrowband disturbance rejection applied to an active suspension-an internal model principle approach [J]. Automatica,2005,41:563-574.
[21]刘红军,韩璞,孙海蓉,姚万业.基于内模控制的PID控制器的设计[J].计算机仿真,2004,22(3)：207-210.
[22]IAN G H,J EFFERY R A, CHRISTOPHER J G. Improved filter de2sign in internal model control [J]. Industrial Engineering Chemistry Research,1996,35 (10):3437-3441.
[23]CAMPI M,LEE W S,ANAERSON B D O. Filters for internal mod2el control design for unstable plants [C]//Proc of the 32nd IEEE Conf on Decision and Control. San Antonio:IEEE Press,1993:1343-1348.
[24]RIVALS I, PERSONNAZ L. Nonlinear internal model control using neural networks: application to processes with delay and design issues [J]. IEEE Trans on Neural Networks, 2000,11 (1):80-90.
[25]CALVET J,ARKUN Y.Feed forward and feedback linearization of nonlinear systems and its implementation using internal model con2trol (IMC) [J]. Industrial Engineering Chemistry Research,1988,27(10):1822-1831.
[26]HU Q,SAHA P, RANGAIAH G P. Adaptive internal model control of nonlinear processes [J]. Chemical Engineering Science,1999,54(9):1205-1220.
[27]HU Q,RANGAIAH G P. Anti-windup schemes for uncertain nonlin2ear systems [J]. IEE Proc-Control Theory and Applications,2000,147(3):321-329.
[28]ROUX G,DAHHOU B. Multivariable nonlinear internal model control applied to a bioreactor [C]. Proc of the 14th IFAC World.
[29]袁德成,韩阳,王贵成,等.非线性辅助内模控制(NAIMC)系统研究[J].信息与控制,1995,24(4)：230-236.
[30]DAI X Z,LIU J, FENG C, et al. Neural network ath order inverse system method for the control of nonlinear continuous systems [J]. IEE Proc-Control Theory and Applications, 1998,145 (6):519-522.
[31]陈庆伟,吕朝霞,胡维礼,等.基于逆系统方法的非线性内模控制[J].自动化学报,2002,28(5)：715-721.
[32]LI Q, POO A N, LIM C M. Neuro-based adaptive internal model control for robot manipulators [C]. Proc of IEEE Int Conf on Neural Networks. Perth:IEEE Press,1995, 5:2353-2357.
[33]陈霞,陈广林.模糊控制理论的发展与应用[J].煤矿现代化,2004(3)：34.
[34]Zadeh.L.A "Fuzzy set" in format contras vol.85 Ostergaard J.J "Fuzzy control of a heat exchange process" [J]. International report. University of Demand,1976
[35]崔涛,赵莉.模糊控制理论和应用的发展概况[J].自动化仪表,2002,23 (7)：2-3.
[36]郭庆祝,孟维明.模糊控制技术发展现状及研究热点[J]. Extension广角,2005(4)：70-72.
[37]李钟慎.基于Butterworth标准传递函数设计状态反馈系统[J].微计算机信息,2005,21(8-1)：46-48.
[38]洪健,李钟慎.改进的Butterworth最佳传递函数标准型[J].计算机技术与自动化,2005,24(2)：13-15.
[39]吕丹,陈文灵,张文夫,邓发升.基于改进的Butterworth传递函数的高阶低通有源滤波器的设计[J].弹箭与制导学报,2006,26(1)：784-788.
[40]洪健.基于状态反馈的纯滞后对象的鲁棒优化控制[J].计算机测量与控制,2005,13(12)：1361-1384.
[41]陈娟,潘立登,曹柳林.时滞系统的滤波器时间常数自调整内模控制[J].系统仿真学报,2006,18(6)：1630-1633.
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