基于等价传递函数的多变量控制系统分析与设计
|
摘要
由于大多数的工业过程都可以描述成多变量系统,因此,多变量控制系统一直是工业过程控制领域中的研究热点之一。工业过程中常用的控制策略,比如分散PI/PID控制和解耦控制,都因为其便利的现场调试操控性而得到了广泛的应用。对于耦合不严重的多变量系统,在合理配对的前提下,分散控制就可以得到满意的控制性能。而对于耦合严重的多变量系统,解耦控制策略则更加适合。如何真正有效地解除多变量回路之间的耦合作用,将复杂的多变量控制问题转换成简单的单变量控制问题,一直是工程师和学者们思索的焦点。本文在等价传递函数理论的基础上,结合经典单变量PID控制技术,对多变量控制系统进行深入分析,并进行多变量控制系统设计研究,大量的数学仿真和实验结果表明本论文提出的方法是简单有效的,在工业过程领域具有很好的应用前景。
本论文的主要内容包括:
1)系统阐述了多变量系统等价传递函数的概念、含义和性质,以及等价传递函数模型的参数化方法,在此基础上提出一种基于特性序列的等价传递函数的参数化方法,定义了特性序列来描述过程的动态特性,推导出了开环的特性序列和等价传递函数的特性序列之间的关系,并根据特性序列和模型参数之间的对应关系建立方程组,可以求解出等价传递函数的模型参数。另外,本文还给出了几类特殊的多变量过程的等价传递函数模型参数化方法。
2)提出基于等价传递函数的多变量系统集中式PI/PID控制器设计。集中式多变量控制器结构中的每个PI/PID控制器元素都是分开独立地针对每一个等价传递函数描述的单变量过程设计,可以保证在满足各个单变量控制目标的同时满足整个多变量系统的控制目标。因此,与分散式PI/PID控制器相比,集中式PI/PID控制器可以提供更好的总体控制性能。
3)提出基于等价传递函数矩阵的多变量系统解耦控制器设计方法。根据控制器结构的不同,又分为两种:一种是一体式或全矩阵结构的解耦控制器,解耦控制器由闭环期望传递函数矩阵和等价传递函数矩阵综合推导得到;另外一种是分体式的解耦控制器,由解耦器和PI/PID控制器两部分组成。首先,利用等价传递函数矩阵和传递函数逆阵之间的关系,选择合理的解耦后的前向通道的期望传递函数矩阵,可以直接推导出解耦控制器的解析形式。接着,运用经典的单回路PI/PID控制器设计方法,针对开环期望传递函数矩阵的元素分别设计PI/PID控制器,组成多变量系统的分散控制器。
4)提出基于等价传递函数矩阵的多变量系统部分解耦控制器设计方法,该方法和解耦控制器设计方法的不同点主要在于,解耦器结构的不同。部分解耦器主要考虑在控制性能和控制结构的复杂程度之间的折衷,引入了结构选择标准,在不影响控制性能的前提下尽可能地简化解耦器的结构。另外,该方法还分析了等价传递函数矩阵和传递函数逆阵之间的近似等价关系对总体控制性能可能带来的消极影响,为了避免这种影响,引入了对等价传递函数模型参数的约束,从而保证了等价传递函数的合理性。
5)针对提出的两种解耦控制器的设计方法,分别设计了两个仿真平台验证实验:双容液位控制实验和中央空调恒温控制实验。无论数学仿真还是实物仿真结果,均验证了基于ETF的解耦控制器设计方法的有效性。
As most of the industrial processes can be described as multivariable systems, the research of multivariable control systems is one of the hotspots in industrial process control area. The two commonly used strategies are decentralized control and decoupling control, which are easy to operate on the spot and easy to understand by the local engineers. As for the processes with slight coupling, decentralized control is competent to get satisfactory control results after the optimal paring solution is selected. Decoupling control mehod is more perferable to the decentralized control for the processes with serious coupling. How to handle the interactions among loops is always a headache question for the control engineers. In this thesis, several effective multivarible control strategies are proposed, which is based on the ETF therories and classical PID control technique. It includes:
1) The concept of equivalent transfer function for multivarible processes is introduced. Furthermore, the important property of ETF and its parameterization methods are also presented. A brand-new approach for high-order ETF model parameterization is involved, which is based on the open-loop charateristic sequence. The relationship between the open-loop charateristic sequence and charateristic sequence of the ETF matrix is derived. The parameters of ETF models are uniquely determined by solving the equation sets about the charateristic sequence. In addition, the parameteriazation methods for some special multivariable processes are also involved.
2) A ETF based centralized PI/PID controller design method for multivariable processes is presented, in which each element of the controller is designed individualy for corresponding ETF element. The control target of multivariable process can be attained simultaneously when the control targets of the single variable processes are achieved. Thus, centralized PI/PID controller can provide better overall control performance , particularly compared to the decentralized PI/PID controller.
3) A systematic ETF based decoupling control scheme is brought up, which can be divided into one-piece type and split type according to the different control structure.The one-piece decoupling controller can be derived by the desired closed-loop transfer fucntion matrix and the ETF matrix, while the split one is composed of two parts: the decoupler and multiloop PI/PID controller. By using the approximation relationship between ETF matrix and the inverse matrix and selecting the desirable forward transfer function matrix after decoupled, the decoulper will be derived directly. After that, the decentralized PI/PID controller is easily designed for the desirable transfer function matrix by available single loop controller design methods.
4) A novel ETF based partial decoupling control strategy is raised. The obvious difference from the former one is the structure of decoupler. By measuring the effect of each ETF element in decoupling control, a partial decoupling control structure selection criterion is proposed with the aim for the decoupler to have least complexity and satisfied overall system performance. Besides, the possible negative effect caused by the approximation between ETF matrix and the inverse matrix is also considered. To gurantee the reasonability, the ETF parameters are obtained under certain constraints.
5) Two experimental tests are designed to verify the effectiveness of ETF based decoupling control methods. The controlled plants are respectively double-level control system and 4-room constant temperature control system. The results of both mathematical simulation and the experimental test demonstrate that the ETF based decoupling control strategies are simple and effective.
本论文的主要内容包括:
1)系统阐述了多变量系统等价传递函数的概念、含义和性质,以及等价传递函数模型的参数化方法,在此基础上提出一种基于特性序列的等价传递函数的参数化方法,定义了特性序列来描述过程的动态特性,推导出了开环的特性序列和等价传递函数的特性序列之间的关系,并根据特性序列和模型参数之间的对应关系建立方程组,可以求解出等价传递函数的模型参数。另外,本文还给出了几类特殊的多变量过程的等价传递函数模型参数化方法。
2)提出基于等价传递函数的多变量系统集中式PI/PID控制器设计。集中式多变量控制器结构中的每个PI/PID控制器元素都是分开独立地针对每一个等价传递函数描述的单变量过程设计,可以保证在满足各个单变量控制目标的同时满足整个多变量系统的控制目标。因此,与分散式PI/PID控制器相比,集中式PI/PID控制器可以提供更好的总体控制性能。
3)提出基于等价传递函数矩阵的多变量系统解耦控制器设计方法。根据控制器结构的不同,又分为两种:一种是一体式或全矩阵结构的解耦控制器,解耦控制器由闭环期望传递函数矩阵和等价传递函数矩阵综合推导得到;另外一种是分体式的解耦控制器,由解耦器和PI/PID控制器两部分组成。首先,利用等价传递函数矩阵和传递函数逆阵之间的关系,选择合理的解耦后的前向通道的期望传递函数矩阵,可以直接推导出解耦控制器的解析形式。接着,运用经典的单回路PI/PID控制器设计方法,针对开环期望传递函数矩阵的元素分别设计PI/PID控制器,组成多变量系统的分散控制器。
4)提出基于等价传递函数矩阵的多变量系统部分解耦控制器设计方法,该方法和解耦控制器设计方法的不同点主要在于,解耦器结构的不同。部分解耦器主要考虑在控制性能和控制结构的复杂程度之间的折衷,引入了结构选择标准,在不影响控制性能的前提下尽可能地简化解耦器的结构。另外,该方法还分析了等价传递函数矩阵和传递函数逆阵之间的近似等价关系对总体控制性能可能带来的消极影响,为了避免这种影响,引入了对等价传递函数模型参数的约束,从而保证了等价传递函数的合理性。
5)针对提出的两种解耦控制器的设计方法,分别设计了两个仿真平台验证实验:双容液位控制实验和中央空调恒温控制实验。无论数学仿真还是实物仿真结果,均验证了基于ETF的解耦控制器设计方法的有效性。
As most of the industrial processes can be described as multivariable systems, the research of multivariable control systems is one of the hotspots in industrial process control area. The two commonly used strategies are decentralized control and decoupling control, which are easy to operate on the spot and easy to understand by the local engineers. As for the processes with slight coupling, decentralized control is competent to get satisfactory control results after the optimal paring solution is selected. Decoupling control mehod is more perferable to the decentralized control for the processes with serious coupling. How to handle the interactions among loops is always a headache question for the control engineers. In this thesis, several effective multivarible control strategies are proposed, which is based on the ETF therories and classical PID control technique. It includes:
1) The concept of equivalent transfer function for multivarible processes is introduced. Furthermore, the important property of ETF and its parameterization methods are also presented. A brand-new approach for high-order ETF model parameterization is involved, which is based on the open-loop charateristic sequence. The relationship between the open-loop charateristic sequence and charateristic sequence of the ETF matrix is derived. The parameters of ETF models are uniquely determined by solving the equation sets about the charateristic sequence. In addition, the parameteriazation methods for some special multivariable processes are also involved.
2) A ETF based centralized PI/PID controller design method for multivariable processes is presented, in which each element of the controller is designed individualy for corresponding ETF element. The control target of multivariable process can be attained simultaneously when the control targets of the single variable processes are achieved. Thus, centralized PI/PID controller can provide better overall control performance , particularly compared to the decentralized PI/PID controller.
3) A systematic ETF based decoupling control scheme is brought up, which can be divided into one-piece type and split type according to the different control structure.The one-piece decoupling controller can be derived by the desired closed-loop transfer fucntion matrix and the ETF matrix, while the split one is composed of two parts: the decoupler and multiloop PI/PID controller. By using the approximation relationship between ETF matrix and the inverse matrix and selecting the desirable forward transfer function matrix after decoupled, the decoulper will be derived directly. After that, the decentralized PI/PID controller is easily designed for the desirable transfer function matrix by available single loop controller design methods.
4) A novel ETF based partial decoupling control strategy is raised. The obvious difference from the former one is the structure of decoupler. By measuring the effect of each ETF element in decoupling control, a partial decoupling control structure selection criterion is proposed with the aim for the decoupler to have least complexity and satisfied overall system performance. Besides, the possible negative effect caused by the approximation between ETF matrix and the inverse matrix is also considered. To gurantee the reasonability, the ETF parameters are obtained under certain constraints.
5) Two experimental tests are designed to verify the effectiveness of ETF based decoupling control methods. The controlled plants are respectively double-level control system and 4-room constant temperature control system. The results of both mathematical simulation and the experimental test demonstrate that the ETF based decoupling control strategies are simple and effective.
引文
[1]. Labibi, B. Marquez, H. Z., Chen, T. Decentralized robust PI controller design for an industrial boiler. Journal of Process Control. 2009, 19(2): 216-230.
[2]. Larsson, T., Skogestad, S. Plantwide control-a review and a new design procedure. Modeling , Identification and Control. 2000, 21(4):209-240.
[3]. Vaes, D., Swevers, J. Sas, P. Experimental validation of different MIMO-feedback controller design methods. Control Engineering Practice. 2005, 13(11): 1439-1451.
[4]. Bi. Q.,Cai, W.-J., WANG, Q.-G., Hang,C.-C., Lee, E.-L., Yong, S., Liu, K.-D., Zhang, Y., Zou, B. Advanced controller auto-tuning and its application in HVAC systems. Control Engineering Practice. 2000, 8(6): 633-644.
[5]. He, M., Cai, W.-J., Li, S.-Y., Multiple fuzzy model-based temperature predictive control for HVAC systems. Information Sciences. 2005, 169(1-2): 155-174.
[6]. Li, S., Liu, H., Cai, W.-J., Soh, Y.-C., Xie, L.-H. A new coordinated control strategy for boiler-turbine system of coal-fired power plant. IEEE Transactions on Control Systems Technology. 2005, 13(6): 943-954.
[7]. Wang, Y.-W., Cai, W.-J., Soh, Y.-C., Li, S.-J., Lu, L., Xie, L.-H. A simplified modeling of cooling coils for control and optimization of HVAC systems. Energy Conversion and Management. 2004, 45(18-19):2915-2930.
[8]. Wang, Y.-G., Shi, Z.-G., Cai, W.-J. PID autotuner and its application in HVAC systems. Proceedings of American Control Conference. 2001, 3: 2192-2196.
[9].李少远,蔡文剑.工业过程辨识与控制,北京:化学工业出版社,2011.
[10]. Wang, Q.-G., Zhen, Y., Cai, W.-J. PID control for multivariable processes. Springer, 2008.
[11]. Bao, J., Lee, P. L. Process control: the passive systems approach, Advances in Industrial Control, Springer-Verlag, London, 2007.
[12].金以慧.过程控制,北京:清华大学出版社,1993.
[13]. Vu, T.N.L., Lee, J., Lee, M. Design of multiloop PID controllers based on the generalized IMC-PID method with Mp criterion. International Journal of Control, Automation and Systems. 2007, 5(2): 212-217.
[14]. Lee, M., Lee, K., Kim, C., Lee, J. Analytical design of multiloop PID controllers for desired closed-loop responses. AIChE Journal. 2004, 50(7): 1631-1635.
[15]. Ho, W.K., Lee, T.H., Gan, O.P. Tuning of multiloop Proportional-Integral-Derivative controllers based on gain and phase margin specifications. Industrial & Engineering Chemistry Research. 1997, 36(6): 2231-2238.
[16]. Dong, J., Brosilow, C. B. Design of robust multivariable PID controllers via IMC. Proceedings of the American Control Conference. 1997, 3380-3384.
[17]. Yu, C.-C., Luyben, W. L. Design of multiloop SISO controllers in multivariable processes. Industrial and Engineering Chemistry Process Design and Development. 1986, 25(2):498-503.
[18]. Toh, W. K., Rangaiah, G. P. A methodology for autotuning of multivariable systems. Industrial & Engineering Chemistry Research. 2002, 41(18):4605-4615.
[19]. Loh, A. P., Vasnani, V. U. Describing function matrix for multivariable systems and its use in multiloop PI design. Journal of Process Control. 1994,4(3),115-120.
[20].席裕庚.预测控制.北京:国防工业出版社, 1993.
[21]. Morari, M., Lee, J. H. Model predictive control: Past, present and future. Computers & Chemical Engineering, 1999, 23(4): 667-682.
[22]. Hu, X. B., Chen, W. H. Model predictive control for constrained systems with uncertain state-delays. International Journal of Robust and Nonlinear Control, 2004, 14(7):1421-1432.
[23]. Rodrigues, M. A., Odloak, D. Robust MPC for systems with output feedback and input saturation. Journal of Process Control, 2005, 15(7):837-846.
[24]. Li, N., Li, S. Y., Xi, Y. G. Multiple model predictive control for MIMO systems. Acta Automatica Sinica, 2003, 29(4): 516-523.
[25]. Xiong, Q., Cai, W. -J., He, M. -J. Equivalent transfer function method for PI/PID controller design of MIMO processes. Journal of Process Control. 2007, 17(8): 665-673.
[26]. Huang, H.-P, Jeng, J.-C. Monitoring and assessment of control performance for single loop systems. Industrial & Engineering Chemistry Research. 2002, 41(5): 1297-1309.
[27]. Xiong, Q., Cai, W.-J., He, M.-J., He, M. Decentralized control system design for multivariable processes-a novel method based on effective relative gain array. Industrial & Engineering Chemistry Research. 2006, 45 (8): 2769-2776.
[28]. Xiong, Q., Cai, W.-J. Effective transfer function method for decentralized control system design of multi-input multi-output processes. Journal of Process Control. 2006, 16(8): 773-784.
[29]. Cai, W. -J., Ni, W., He, M. -J., Ni, C.-Y. Normalized decoupling-a new approach for MIMO processes control system design. Industrial & Engineering Chemistry Research. 2008, 47 (19):7347-7356.
[30]. Xiong, Q., Cai, W.-J., He, M. -J., He, M. Decentralized control system design for multivariable processes- A novel method based on effective relative gain array. Industrial & Engineering Chemistry Research. 2006, 45 (8): 2769-2776.
[31].王诗宓.多变量控制系统的分析和设计,北京:中国电力出版社,1996.
[32]. He, M.-J., Cai, W.-J., Li, S.-Y. Evaluation of the decentralized closed-loop integrity for multivariable control systems. Industrial & Engineering Chemistry Research. 2005, 44 (10): 3567-3574.
[33]. Doyle, J. C., Francis, B. A., Tannenbaum, A. R. Feedback control theory. New York, NY: Macmillan, 1992.
[34]. Wang, Q.-G., Zhang, Y., Chiu, M.-S. Decoupling internal model control for multivariable systems with multiple time delays. Chemical Engineering Science. 2002, 57(1): 115-124.
[35]. Jerome, N. F., Ray, W. H. Model-predictive control of linear multivariable systems having time delays and right-half-plane zeros. Chemical Engineering Science, 1992, 47(4): 763-785.
[36]. Wang, Q.-G., Zou, B., Zhang, Y. Decoupling Smith predictor design for multivariable systems with multiple time delays. Chemical Engineering Research and Design Transactions of the Institute of Chemical Engineers, Part A, 2000, 78(4):565-572.
[37]. Xue, F. Z., Pang, G. Z., Hu, J. H. Multivariable control for beer fermentation temperature. Acta Automatica Sinica, 2002, 28(1): 150-154.
[38]. Desbiens, A., Pomerleau, A., Hodouin, D. Frequency based tuning of SISO controllers for two-by-two processes. IEE Proceedings- Control Theory& Applications, 1996, 143(1):25-32.
[39]. Jerome, N. F., Ray, W. H. High-performance multivariable control strategies for systems having time delays. AIChE Journal, 1986, 32(6):914-931.
[40]. Watanabe, K.M Ishiyama, Y., Ito, M. Modified Smith predictor control for multivariable systems with delays and unmeasurable step disturbances. International Journal of Control, 1983, 37(5): 959-973.
[41]. Orunnaike, B. A., Ray, W. H. Multivariable controller design for linear systems having multiple time delays. AIChE Journal, 1979, 25(6):1043-1056.
[42]. Garelli, F., Mantz, R. J., De Battista, H. Limiting interactions in decentralized control of MIMO systems. Journal of Process Control. 2006, 16(5): 473-483.
[43]. Cui, H., Jacobsen, E. W. Performance limitations in decentralized control. Journal of ProcessControl. 2002, 12(4): 485-494.
[44]. Campo, P. J.; Morari, M. Achievable closed-loop properties of systems under decentralized control: conditions involving the steady-state gain. IEEE Transactions on Automatic Control. 1994, 39(5): 932-943.
[45]. Monica, T.J., Yu, C.C., Luyben, W.L. Improved muliloop single-input/single-output (SISO) controllers for multivariable processes. Industrial & Engineering Chemistry Research. 1988, 27(6): 969-973.
[46]. Luyben, W.L. Simple method for tuning SISO controllers in multivariable systems. Industrial & Engineering Chemistry Process Design and Development. 1986, 25(3): 654-660.
[47]. Mayne, D. Q. The design of linear multivariable systems. Automatica. 1973, 9(2): 201-207.
[48]. Chiu, M.S., Arkun, Y. A methodology for sequential design of robust decentralized control systems. Automatica. 1992, 28(5): 997-1001.
[49]. Hovd, M., Skogestad, S. Sequential design of decentralized controllers. Automatica. 1994, 30(10):1601-1607.
[50]. Shiu, S.J., Hwang, S.H. Sequential design method for multivariable decoupling and multiloop PID controllers. Industrial & Engineering Chemistry Research. 1998, 37(1): 107-119.
[51]. Shiu, S.-J., Hwang, S.-H. Sequential design method for multivariable decoupling and multiloop PID controllers. Industrial & Engineering Chemistry Research. 1998, 37(1):107-119.
[52]. Shen, S.H., Yu, C.C. Use of relay-feedback test for antomatic tuning of multivariable systems. AIChE Journal. 1994, 40(4): 627-646.
[53]. Lee, J., Cho, W., Edgar, T.F. Multiloop PI controller tuning for interacting multivariable processes. Computers & Chemical Engineering. 1998, 22(11):1711-1723.
[54]. Wang, Q.G., Lee, T.H., Zhang, Y. Multi-loop version of modified Ziegler-Nichols method for two input two output process. Industrial & Engineering Chemistry Research. 1998, 37(12): 4725-4733.
[55]. Bao, J., Forbes, J.F., Mclellan, P.J. Robust multiloop PID controller design: a successive semidefinite programming approach. Industrial & Engineering Chemistry Research. 1999, 38(9): 3407-3419.
[56]. Economou, C.G.., Morari, M. Internal model control: multi-loop design, Industrial & Engineering Chemistry Process Design and Development. 1986, 25(2):411-419.
[57]. Grosdidier, P., Morara, M. Interaction measures for systems under decentralized control.Automatica. 1986, 22(3):309-319.
[58]. Skogestad, S., Morari, M. Robust performance of decentralized control systems by independent designs. Automatica. 1989, 25(1):119-125.
[59]. Hovd, M., Skogestad, S. Improved independent design of robust decentralized controllers. Journal of Process Control. 1993, 3(1):43-51.
[60]. Vu, T. N. L., Lee, M. Independent design of multi-loop PI/PID controllers for interacting multivariable processes. Journal of Process Control. 2010, 20(8): 922-933.
[61].吴国垣,李东海,薛亚丽,唐多元.多变量系统分散PID控制器设计.清华大学学报. 2004, 44(11): 1567-1570.
[62]. Huang, H. -P., Jeng, J.-C., Chiang, C.-H., Pan, W. A direct method for multi-loop PI/PID controller design. Journal of Process Control. 2003, 13(8): 769-786.
[63]. Bao, J., Zhang, W. Z., Lee, P. L. Passivity-based decentralized failure-tolerant control. Industrial & Engineering Chemistry Research. 2002, 41(23): 5702-5715.
[64]. He, M.-J., Cai, W.-J.,Wu, B.-F., He, M. Simple decentralized PID controller design method based on dynamic relative interaction analysis. Industrial & Engineering Chemistry Research. 2005, 44(22): 8334-8344.
[65]. Shen, S. H., Yu, C. C. Use of relay-feedback test for automatic tuning of multivariable systems. AIChE Journal. 1994. 40(4): 627-646.
[66]. Semino, D., Scali, C. Improved identification and autotuning of PI controllers for MIMO processes by relay techniques. Journal of Process Control. 1998, 8(3):219-227.
[67]. Wang, Q. -G., Zou, B., Lee, T. -H., Bi, Q. Auto-tuning of multivariable PID controllers from decentralized relay feedback. Automatica. 1997, 33(3): 319-330.
[68]. Morrilla, F., Vázquez. F., Garrido, J. Centralized PID control by decoupling for TITO processes. Proceedings of the 13th IEEE International Conference on Emerging Technologies and Factory Automation, 2008, 1318-1225.
[69].刘涛,张卫东,顾诞英,蔡云泽.化工多变量时滞过程的频域解耦控制设计的研究进展.自动化学报. 2006, 32(1): 73-81.
[70]. Chen, D., Seborg, D. E. Design of decentralized PI control systems based on nyquist stability analysis. Journal of Process Control. 2003, 13(1): 27-39.
[71]. Lee, J., Kim, D. H., Edgar, T. F. Static decouplers for control of multivariable processes. AIChE Journal. 2005, 51(10): 2712-2720.
[72]. Astr?m. K. J., Johansson, K.H., Wang, Q.-G. Design of decoupled PID controllers for MIMO systems. Proceedings of the American Control Conference. 2001, 25-27.
[73]. Walter, M., Walter, J., Walter, K. V. Decoupling revisited. Industrial and Engineering Chemistry Research. 2003, 13(3): 253-265.
[74]. Perng, M. H., Ju, J. S. Optimally decoupled robust control MIMO plants with multiple delays. IEE Proceedings-Control Theory and Applications. 1994, 141(1): 49-56.
[75]. Sun, X., Sun, Y. X. Basis weight and moisture content analysis for papermaking process. Control Theory and Applications. 2000, 18(suppl): 121-124.
[76]. Guo, Q. D., Tang, G. P. Research on synchrodrive technology based on decoupling control. Control and Decision. 2001, 16(1): 72-75.
[77]. Chen, S. P., Sun, Y. X. Lower-order robust decoupler design. Acta Automatica Sinica. 1998, 24(4): 543-547.
[78]. Shiu, S. J., Hwang, S. H. Sequential design method for multivariable decoupling and multiloop PID controllers. Industrial and Engineering Chemical Research. 1998, 37(1): 107-119.
[79]. Yeung, L. F., Yang, W. K., Ng, W. H. Y., Bryant, G. F. Sequential design of MIMO systems with parametric uncertainties. IEE Proceedings-Control Theory and Applications. 2002, 149(6): 511-519.
[80]. Shiu, S.-J., Hwang, S.-H. Sequential design method for multivariable decoupling and multiloop PID controllers. Industrial & Engineering Chemistry Research. 1998, 37 (1): 107-119.
[81]. Gilbert, A. F., Yousef, A., Natarajan, K., Deighton, S. Tuning of PI controllers with one-way decoupling in 2×2 MIMO systems based on finite frequency response data. Journal of Process Control. 2003, 13(6): 553-567.
[82]. Wang, Q. -G. Decoupling Control. Berlin: Springer-Verlag. 2003.
[83]. Pomerleau, D., Pomerleau, A. Guide lines for the tuning and the evaluation of decentralized and decoupling controllers for processes with recirculation. ISA Transaction. 2001, 40(4): 341-351.
[84]. Vrancic, D. Design of MIMO controllers with inverted decoupling. Proceedings of the 8th Asian Control Conference. 2011, 1153-1158.
[85]. Garrido, J., Vázquez. F., Morrilla, F. An extended approach of inverted decoupling. Journal of Process Control. 2011, 21(1): 55-68.
[86]. Chen, P., Zhang, W. Improvement on an inverted decoupling technique for a class of stable linear multivariable processes. ISA Transactions. 2007, 46(2): 199-210.
[87]. Gagnon, E., Pomerleau, A., Desbiens, A. Simplified, ideal or inverted decoupling? ISA Transactions. 1998, 37(4): 265-276.
[88]. Lieslehto, J. MIMO controller design using SISO controller design methods. Proceeding of the 13th IFAC World Congress. 1996, 169-173.
[89]. Wang, Q.-G., Zhang, Y., Chiu, M.-S. Non-interacting control design for multivariable industrial processes. Journal of Process Control. 2003, 13(3): 253-265.
[90]. Liu, T., Zhang, W., Gao, F. Analytical decoupling control strategy using a feedback control structure for MIMO processes with time delays. Journal of Process Control. 2007, 17(2): 173-186.
[91].刘涛,张卫东,顾诞英.多变量时滞过程的解耦控制设计.自动化学报. 2005, 31(6): 881-889.
[92]. Q.-G. Wang, T.H. Lee, Y. Zhang, Multi-loop version of the modified Ziegler–Nichols method for two input two output process, Industrial and Engineering Chemistry Research. 1998,37(12): 4725–4733.
[93]. Grosdidier, P., Morari, M. Closed-loop properties from steady-state gain information. Industrial & Engineering Chemistry Research. 1985, 24 (2): 221-235.
[94]. Avoy, T. M., Arkun, Y., Chen, R., Robinson, Derek., Schnelle, D. A new approach to defining a dynamic relative gain. Control Engineering Practice. 2003, 11(8): 907-914.
[95]. Astr?m, K. J., H?gglund, T. PID controller: theory, design and tuning. Instrument Society of America, 1995.
[96]. Bristol, E. H. On a new measure of interactions for multivariable process control. IEEE Transactions on Automatic Control. 1966, 11: 133-134.
[97]. Loh, A. P., Vasnani, V. U. Describing function matrix for multivariable systems and its use in multiloop PI design. Journal of Process Control. 1994, 4(3): 115-120.
[98]. Lee, T.K., Chiu, M.-S. Arkun, Y. Interaction measure for the selection of partially decentralized control structures. Industrial & Engineering Chemistry Research. 1998, 37 (12): 4734-4739.
[99]. Lin, C.-A., Wu, C.-M. Block-decoupling linear multivariable systems: necessary and sufficient conditions. Automatica. 1998, 34(2): 237-243.
[100]. Linnemann, A., Wang, Q. -G. Block decoupling with stability by unity output feedback–solution and performance limitations. Automatica. 1993, 29(3): 735-744.
[101]. Commault, C., Dion, J. M. Transfer matrix approach to the triangular block decoupling problem. Automatica. 1983, 19(5): 533-542.
[102]. Grosdidler, P., Morari, M., Holt, B. R. Closed-loop properties from steady-state gain information. Industrial & Engineering Chemistry Fundamentals. 1985, 24(2):221-235.
[103]. Skogestad, S. Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control. 2003, 13(4):291-309.
[104]. Lee, Y., Park, S., Lee, M., Brosilow, C. PID controller tuning for desired closed-loop responses for SI/SO systems. AIChE Journal. 1998, 44(1):106-115.
[105]. Carvajal, J., Chen, G., Ogmen, H. Fuzzy PID controller: design, performance evaluation and stability analysis. Information Sciences. 2000, 123(3-4): 249-270.
[106]. Chen, D., Seborg, D. E. PI/PID controller design based on direct synthesis and disturbance rejection. Industrial & Engineering Chemistry Research. 2002, 41(19): 4807-4822.
[107]. Huang, H. P., Lee, M. W., Chen, C. L. Inverse based design for a modified PID controller. Journal of the Chinese Institute of Chemical Engineers. 2000,31(3): 225-236.
[108]. Rivera, D. E., Morari, M., Skogestad, S. Internal model control: PID controller design. Industrial & Engineering Chemistry Process Design and Development. 1986, 25(1): 252-265.
[109]. Wang, Y.-G., Cai, W.-J. Advanced proportional-integral-derivative tuning for integrating and unstable processes with gain and phase margin specifications. Industrial & Engineering Chemistry Research. 2002, 41(9): 2910-2914.
[110].柴天佑,张贵军.基于给定的相角裕度和幅值裕度的PID参数自整定新方法.自动化学报. 1997, 23(2): 167-172.
[111]. Panda, R. C., Yu, C.-C., Huang, H.-P. PID rules for SOPDT systems: review and some new results. ISA Transactions.2004, 43(2):283-295.
[112]. Lee, Y., Park, S., Lee, M., Brosilow, C. PID controller tuning for desired closed-loop responses for SI/SO systems. AIChE Journal. 1998, 44(1):106-115.
[113]. Wood, R. K., Berry, M. W. Terminal composition control of a binary distillation column. Chemical Engineering Science. 1973, 28(9):1707-1717.
[114]. Zhang, Y., Wang, Q.-G., Astrom, K. J. Dominant pole placement for multi-loop control systems. Automatica. 2002, 38(7):1213-1220.
[115]. Ogunnaike, B. A., Ray, W. H. Multivariable controller design for linear systems having multiple time delays. AIChE Journal. 1979, 25(6):1043-1057.
[116]. Morari, M., Zafiriou, E. Robust process control. New Jersey: Prentice-Hall, 1989.
[117]. Skogestad, S., Postlethwaite, I. Multivariable feedback control, John Wiley&Sons, Chichester,1996.
[118]. Chien, I. -L., Huang, H. -P., Yang, J. -C. A simple multiloop tuning method for PID controllers with no proportional kick. Industrial & Engineering Chemistry Research. 1999, 38(4):1456-1468.
[119]. Lyben, W. L. Simple method for tuning SISO controllers in multivariable system. Industrial & Engineering Chemistry Process Design and Development. 1986, 25(3): 654-660.
[120]. Mei, H., Li, S., Cai, W.-J., Xiong, Q. Decentralized closed-loop parameter identification for multivariable processes from step responses. Mathematics and Computers in Simulation. 2005, 68(2): 171-192.
[121]. Mei, H., Li, S., Cai, W.-J., Xiong, Q. Decentralized closed-loop parameter identification for multivariable processes from step responses. Mathematics and Computers in Simulation. 2005, 68(2): 171-192.
[122]. Willjuice Iruthayarajan, M., Baskar, S. Covriance matrix adaption evolution strategy based design of centralized PID controller. Expert Systems with Applications. 2010, 37(8): 5775-5781.
[123]. Hu, W., Cai, W.-J., Xiao G. Decentralized control system design for MIMO processes with integrators/differentiators. Industrial & Engineering Chemistry Research. 2010, 49(24): 12521-12528.
[124]. Gundes, A. N., Ozbay, H., Ozguler, A. B. PID controller synthesis for a class of unstable MIMO plants with I/O delays. Automatica. 2007,43(1):135-142.
[125]. Liu, T., Zhang, W., Gu, D. Analytical design of decoupling internal model (IMC) scheme for two-input–two-output (TITO) processes with time delays. Industrial & Engineering Chemistry Research. 2006, 45(9): 3149-3160.
[126]. Doukas, N., Luyben, W. L. Control of sidestream columns separating ternary mixtures. Instrumentation Technology. 1978, 25: 43-48.
[2]. Larsson, T., Skogestad, S. Plantwide control-a review and a new design procedure. Modeling , Identification and Control. 2000, 21(4):209-240.
[3]. Vaes, D., Swevers, J. Sas, P. Experimental validation of different MIMO-feedback controller design methods. Control Engineering Practice. 2005, 13(11): 1439-1451.
[4]. Bi. Q.,Cai, W.-J., WANG, Q.-G., Hang,C.-C., Lee, E.-L., Yong, S., Liu, K.-D., Zhang, Y., Zou, B. Advanced controller auto-tuning and its application in HVAC systems. Control Engineering Practice. 2000, 8(6): 633-644.
[5]. He, M., Cai, W.-J., Li, S.-Y., Multiple fuzzy model-based temperature predictive control for HVAC systems. Information Sciences. 2005, 169(1-2): 155-174.
[6]. Li, S., Liu, H., Cai, W.-J., Soh, Y.-C., Xie, L.-H. A new coordinated control strategy for boiler-turbine system of coal-fired power plant. IEEE Transactions on Control Systems Technology. 2005, 13(6): 943-954.
[7]. Wang, Y.-W., Cai, W.-J., Soh, Y.-C., Li, S.-J., Lu, L., Xie, L.-H. A simplified modeling of cooling coils for control and optimization of HVAC systems. Energy Conversion and Management. 2004, 45(18-19):2915-2930.
[8]. Wang, Y.-G., Shi, Z.-G., Cai, W.-J. PID autotuner and its application in HVAC systems. Proceedings of American Control Conference. 2001, 3: 2192-2196.
[9].李少远,蔡文剑.工业过程辨识与控制,北京:化学工业出版社,2011.
[10]. Wang, Q.-G., Zhen, Y., Cai, W.-J. PID control for multivariable processes. Springer, 2008.
[11]. Bao, J., Lee, P. L. Process control: the passive systems approach, Advances in Industrial Control, Springer-Verlag, London, 2007.
[12].金以慧.过程控制,北京:清华大学出版社,1993.
[13]. Vu, T.N.L., Lee, J., Lee, M. Design of multiloop PID controllers based on the generalized IMC-PID method with Mp criterion. International Journal of Control, Automation and Systems. 2007, 5(2): 212-217.
[14]. Lee, M., Lee, K., Kim, C., Lee, J. Analytical design of multiloop PID controllers for desired closed-loop responses. AIChE Journal. 2004, 50(7): 1631-1635.
[15]. Ho, W.K., Lee, T.H., Gan, O.P. Tuning of multiloop Proportional-Integral-Derivative controllers based on gain and phase margin specifications. Industrial & Engineering Chemistry Research. 1997, 36(6): 2231-2238.
[16]. Dong, J., Brosilow, C. B. Design of robust multivariable PID controllers via IMC. Proceedings of the American Control Conference. 1997, 3380-3384.
[17]. Yu, C.-C., Luyben, W. L. Design of multiloop SISO controllers in multivariable processes. Industrial and Engineering Chemistry Process Design and Development. 1986, 25(2):498-503.
[18]. Toh, W. K., Rangaiah, G. P. A methodology for autotuning of multivariable systems. Industrial & Engineering Chemistry Research. 2002, 41(18):4605-4615.
[19]. Loh, A. P., Vasnani, V. U. Describing function matrix for multivariable systems and its use in multiloop PI design. Journal of Process Control. 1994,4(3),115-120.
[20].席裕庚.预测控制.北京:国防工业出版社, 1993.
[21]. Morari, M., Lee, J. H. Model predictive control: Past, present and future. Computers & Chemical Engineering, 1999, 23(4): 667-682.
[22]. Hu, X. B., Chen, W. H. Model predictive control for constrained systems with uncertain state-delays. International Journal of Robust and Nonlinear Control, 2004, 14(7):1421-1432.
[23]. Rodrigues, M. A., Odloak, D. Robust MPC for systems with output feedback and input saturation. Journal of Process Control, 2005, 15(7):837-846.
[24]. Li, N., Li, S. Y., Xi, Y. G. Multiple model predictive control for MIMO systems. Acta Automatica Sinica, 2003, 29(4): 516-523.
[25]. Xiong, Q., Cai, W. -J., He, M. -J. Equivalent transfer function method for PI/PID controller design of MIMO processes. Journal of Process Control. 2007, 17(8): 665-673.
[26]. Huang, H.-P, Jeng, J.-C. Monitoring and assessment of control performance for single loop systems. Industrial & Engineering Chemistry Research. 2002, 41(5): 1297-1309.
[27]. Xiong, Q., Cai, W.-J., He, M.-J., He, M. Decentralized control system design for multivariable processes-a novel method based on effective relative gain array. Industrial & Engineering Chemistry Research. 2006, 45 (8): 2769-2776.
[28]. Xiong, Q., Cai, W.-J. Effective transfer function method for decentralized control system design of multi-input multi-output processes. Journal of Process Control. 2006, 16(8): 773-784.
[29]. Cai, W. -J., Ni, W., He, M. -J., Ni, C.-Y. Normalized decoupling-a new approach for MIMO processes control system design. Industrial & Engineering Chemistry Research. 2008, 47 (19):7347-7356.
[30]. Xiong, Q., Cai, W.-J., He, M. -J., He, M. Decentralized control system design for multivariable processes- A novel method based on effective relative gain array. Industrial & Engineering Chemistry Research. 2006, 45 (8): 2769-2776.
[31].王诗宓.多变量控制系统的分析和设计,北京:中国电力出版社,1996.
[32]. He, M.-J., Cai, W.-J., Li, S.-Y. Evaluation of the decentralized closed-loop integrity for multivariable control systems. Industrial & Engineering Chemistry Research. 2005, 44 (10): 3567-3574.
[33]. Doyle, J. C., Francis, B. A., Tannenbaum, A. R. Feedback control theory. New York, NY: Macmillan, 1992.
[34]. Wang, Q.-G., Zhang, Y., Chiu, M.-S. Decoupling internal model control for multivariable systems with multiple time delays. Chemical Engineering Science. 2002, 57(1): 115-124.
[35]. Jerome, N. F., Ray, W. H. Model-predictive control of linear multivariable systems having time delays and right-half-plane zeros. Chemical Engineering Science, 1992, 47(4): 763-785.
[36]. Wang, Q.-G., Zou, B., Zhang, Y. Decoupling Smith predictor design for multivariable systems with multiple time delays. Chemical Engineering Research and Design Transactions of the Institute of Chemical Engineers, Part A, 2000, 78(4):565-572.
[37]. Xue, F. Z., Pang, G. Z., Hu, J. H. Multivariable control for beer fermentation temperature. Acta Automatica Sinica, 2002, 28(1): 150-154.
[38]. Desbiens, A., Pomerleau, A., Hodouin, D. Frequency based tuning of SISO controllers for two-by-two processes. IEE Proceedings- Control Theory& Applications, 1996, 143(1):25-32.
[39]. Jerome, N. F., Ray, W. H. High-performance multivariable control strategies for systems having time delays. AIChE Journal, 1986, 32(6):914-931.
[40]. Watanabe, K.M Ishiyama, Y., Ito, M. Modified Smith predictor control for multivariable systems with delays and unmeasurable step disturbances. International Journal of Control, 1983, 37(5): 959-973.
[41]. Orunnaike, B. A., Ray, W. H. Multivariable controller design for linear systems having multiple time delays. AIChE Journal, 1979, 25(6):1043-1056.
[42]. Garelli, F., Mantz, R. J., De Battista, H. Limiting interactions in decentralized control of MIMO systems. Journal of Process Control. 2006, 16(5): 473-483.
[43]. Cui, H., Jacobsen, E. W. Performance limitations in decentralized control. Journal of ProcessControl. 2002, 12(4): 485-494.
[44]. Campo, P. J.; Morari, M. Achievable closed-loop properties of systems under decentralized control: conditions involving the steady-state gain. IEEE Transactions on Automatic Control. 1994, 39(5): 932-943.
[45]. Monica, T.J., Yu, C.C., Luyben, W.L. Improved muliloop single-input/single-output (SISO) controllers for multivariable processes. Industrial & Engineering Chemistry Research. 1988, 27(6): 969-973.
[46]. Luyben, W.L. Simple method for tuning SISO controllers in multivariable systems. Industrial & Engineering Chemistry Process Design and Development. 1986, 25(3): 654-660.
[47]. Mayne, D. Q. The design of linear multivariable systems. Automatica. 1973, 9(2): 201-207.
[48]. Chiu, M.S., Arkun, Y. A methodology for sequential design of robust decentralized control systems. Automatica. 1992, 28(5): 997-1001.
[49]. Hovd, M., Skogestad, S. Sequential design of decentralized controllers. Automatica. 1994, 30(10):1601-1607.
[50]. Shiu, S.J., Hwang, S.H. Sequential design method for multivariable decoupling and multiloop PID controllers. Industrial & Engineering Chemistry Research. 1998, 37(1): 107-119.
[51]. Shiu, S.-J., Hwang, S.-H. Sequential design method for multivariable decoupling and multiloop PID controllers. Industrial & Engineering Chemistry Research. 1998, 37(1):107-119.
[52]. Shen, S.H., Yu, C.C. Use of relay-feedback test for antomatic tuning of multivariable systems. AIChE Journal. 1994, 40(4): 627-646.
[53]. Lee, J., Cho, W., Edgar, T.F. Multiloop PI controller tuning for interacting multivariable processes. Computers & Chemical Engineering. 1998, 22(11):1711-1723.
[54]. Wang, Q.G., Lee, T.H., Zhang, Y. Multi-loop version of modified Ziegler-Nichols method for two input two output process. Industrial & Engineering Chemistry Research. 1998, 37(12): 4725-4733.
[55]. Bao, J., Forbes, J.F., Mclellan, P.J. Robust multiloop PID controller design: a successive semidefinite programming approach. Industrial & Engineering Chemistry Research. 1999, 38(9): 3407-3419.
[56]. Economou, C.G.., Morari, M. Internal model control: multi-loop design, Industrial & Engineering Chemistry Process Design and Development. 1986, 25(2):411-419.
[57]. Grosdidier, P., Morara, M. Interaction measures for systems under decentralized control.Automatica. 1986, 22(3):309-319.
[58]. Skogestad, S., Morari, M. Robust performance of decentralized control systems by independent designs. Automatica. 1989, 25(1):119-125.
[59]. Hovd, M., Skogestad, S. Improved independent design of robust decentralized controllers. Journal of Process Control. 1993, 3(1):43-51.
[60]. Vu, T. N. L., Lee, M. Independent design of multi-loop PI/PID controllers for interacting multivariable processes. Journal of Process Control. 2010, 20(8): 922-933.
[61].吴国垣,李东海,薛亚丽,唐多元.多变量系统分散PID控制器设计.清华大学学报. 2004, 44(11): 1567-1570.
[62]. Huang, H. -P., Jeng, J.-C., Chiang, C.-H., Pan, W. A direct method for multi-loop PI/PID controller design. Journal of Process Control. 2003, 13(8): 769-786.
[63]. Bao, J., Zhang, W. Z., Lee, P. L. Passivity-based decentralized failure-tolerant control. Industrial & Engineering Chemistry Research. 2002, 41(23): 5702-5715.
[64]. He, M.-J., Cai, W.-J.,Wu, B.-F., He, M. Simple decentralized PID controller design method based on dynamic relative interaction analysis. Industrial & Engineering Chemistry Research. 2005, 44(22): 8334-8344.
[65]. Shen, S. H., Yu, C. C. Use of relay-feedback test for automatic tuning of multivariable systems. AIChE Journal. 1994. 40(4): 627-646.
[66]. Semino, D., Scali, C. Improved identification and autotuning of PI controllers for MIMO processes by relay techniques. Journal of Process Control. 1998, 8(3):219-227.
[67]. Wang, Q. -G., Zou, B., Lee, T. -H., Bi, Q. Auto-tuning of multivariable PID controllers from decentralized relay feedback. Automatica. 1997, 33(3): 319-330.
[68]. Morrilla, F., Vázquez. F., Garrido, J. Centralized PID control by decoupling for TITO processes. Proceedings of the 13th IEEE International Conference on Emerging Technologies and Factory Automation, 2008, 1318-1225.
[69].刘涛,张卫东,顾诞英,蔡云泽.化工多变量时滞过程的频域解耦控制设计的研究进展.自动化学报. 2006, 32(1): 73-81.
[70]. Chen, D., Seborg, D. E. Design of decentralized PI control systems based on nyquist stability analysis. Journal of Process Control. 2003, 13(1): 27-39.
[71]. Lee, J., Kim, D. H., Edgar, T. F. Static decouplers for control of multivariable processes. AIChE Journal. 2005, 51(10): 2712-2720.
[72]. Astr?m. K. J., Johansson, K.H., Wang, Q.-G. Design of decoupled PID controllers for MIMO systems. Proceedings of the American Control Conference. 2001, 25-27.
[73]. Walter, M., Walter, J., Walter, K. V. Decoupling revisited. Industrial and Engineering Chemistry Research. 2003, 13(3): 253-265.
[74]. Perng, M. H., Ju, J. S. Optimally decoupled robust control MIMO plants with multiple delays. IEE Proceedings-Control Theory and Applications. 1994, 141(1): 49-56.
[75]. Sun, X., Sun, Y. X. Basis weight and moisture content analysis for papermaking process. Control Theory and Applications. 2000, 18(suppl): 121-124.
[76]. Guo, Q. D., Tang, G. P. Research on synchrodrive technology based on decoupling control. Control and Decision. 2001, 16(1): 72-75.
[77]. Chen, S. P., Sun, Y. X. Lower-order robust decoupler design. Acta Automatica Sinica. 1998, 24(4): 543-547.
[78]. Shiu, S. J., Hwang, S. H. Sequential design method for multivariable decoupling and multiloop PID controllers. Industrial and Engineering Chemical Research. 1998, 37(1): 107-119.
[79]. Yeung, L. F., Yang, W. K., Ng, W. H. Y., Bryant, G. F. Sequential design of MIMO systems with parametric uncertainties. IEE Proceedings-Control Theory and Applications. 2002, 149(6): 511-519.
[80]. Shiu, S.-J., Hwang, S.-H. Sequential design method for multivariable decoupling and multiloop PID controllers. Industrial & Engineering Chemistry Research. 1998, 37 (1): 107-119.
[81]. Gilbert, A. F., Yousef, A., Natarajan, K., Deighton, S. Tuning of PI controllers with one-way decoupling in 2×2 MIMO systems based on finite frequency response data. Journal of Process Control. 2003, 13(6): 553-567.
[82]. Wang, Q. -G. Decoupling Control. Berlin: Springer-Verlag. 2003.
[83]. Pomerleau, D., Pomerleau, A. Guide lines for the tuning and the evaluation of decentralized and decoupling controllers for processes with recirculation. ISA Transaction. 2001, 40(4): 341-351.
[84]. Vrancic, D. Design of MIMO controllers with inverted decoupling. Proceedings of the 8th Asian Control Conference. 2011, 1153-1158.
[85]. Garrido, J., Vázquez. F., Morrilla, F. An extended approach of inverted decoupling. Journal of Process Control. 2011, 21(1): 55-68.
[86]. Chen, P., Zhang, W. Improvement on an inverted decoupling technique for a class of stable linear multivariable processes. ISA Transactions. 2007, 46(2): 199-210.
[87]. Gagnon, E., Pomerleau, A., Desbiens, A. Simplified, ideal or inverted decoupling? ISA Transactions. 1998, 37(4): 265-276.
[88]. Lieslehto, J. MIMO controller design using SISO controller design methods. Proceeding of the 13th IFAC World Congress. 1996, 169-173.
[89]. Wang, Q.-G., Zhang, Y., Chiu, M.-S. Non-interacting control design for multivariable industrial processes. Journal of Process Control. 2003, 13(3): 253-265.
[90]. Liu, T., Zhang, W., Gao, F. Analytical decoupling control strategy using a feedback control structure for MIMO processes with time delays. Journal of Process Control. 2007, 17(2): 173-186.
[91].刘涛,张卫东,顾诞英.多变量时滞过程的解耦控制设计.自动化学报. 2005, 31(6): 881-889.
[92]. Q.-G. Wang, T.H. Lee, Y. Zhang, Multi-loop version of the modified Ziegler–Nichols method for two input two output process, Industrial and Engineering Chemistry Research. 1998,37(12): 4725–4733.
[93]. Grosdidier, P., Morari, M. Closed-loop properties from steady-state gain information. Industrial & Engineering Chemistry Research. 1985, 24 (2): 221-235.
[94]. Avoy, T. M., Arkun, Y., Chen, R., Robinson, Derek., Schnelle, D. A new approach to defining a dynamic relative gain. Control Engineering Practice. 2003, 11(8): 907-914.
[95]. Astr?m, K. J., H?gglund, T. PID controller: theory, design and tuning. Instrument Society of America, 1995.
[96]. Bristol, E. H. On a new measure of interactions for multivariable process control. IEEE Transactions on Automatic Control. 1966, 11: 133-134.
[97]. Loh, A. P., Vasnani, V. U. Describing function matrix for multivariable systems and its use in multiloop PI design. Journal of Process Control. 1994, 4(3): 115-120.
[98]. Lee, T.K., Chiu, M.-S. Arkun, Y. Interaction measure for the selection of partially decentralized control structures. Industrial & Engineering Chemistry Research. 1998, 37 (12): 4734-4739.
[99]. Lin, C.-A., Wu, C.-M. Block-decoupling linear multivariable systems: necessary and sufficient conditions. Automatica. 1998, 34(2): 237-243.
[100]. Linnemann, A., Wang, Q. -G. Block decoupling with stability by unity output feedback–solution and performance limitations. Automatica. 1993, 29(3): 735-744.
[101]. Commault, C., Dion, J. M. Transfer matrix approach to the triangular block decoupling problem. Automatica. 1983, 19(5): 533-542.
[102]. Grosdidler, P., Morari, M., Holt, B. R. Closed-loop properties from steady-state gain information. Industrial & Engineering Chemistry Fundamentals. 1985, 24(2):221-235.
[103]. Skogestad, S. Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control. 2003, 13(4):291-309.
[104]. Lee, Y., Park, S., Lee, M., Brosilow, C. PID controller tuning for desired closed-loop responses for SI/SO systems. AIChE Journal. 1998, 44(1):106-115.
[105]. Carvajal, J., Chen, G., Ogmen, H. Fuzzy PID controller: design, performance evaluation and stability analysis. Information Sciences. 2000, 123(3-4): 249-270.
[106]. Chen, D., Seborg, D. E. PI/PID controller design based on direct synthesis and disturbance rejection. Industrial & Engineering Chemistry Research. 2002, 41(19): 4807-4822.
[107]. Huang, H. P., Lee, M. W., Chen, C. L. Inverse based design for a modified PID controller. Journal of the Chinese Institute of Chemical Engineers. 2000,31(3): 225-236.
[108]. Rivera, D. E., Morari, M., Skogestad, S. Internal model control: PID controller design. Industrial & Engineering Chemistry Process Design and Development. 1986, 25(1): 252-265.
[109]. Wang, Y.-G., Cai, W.-J. Advanced proportional-integral-derivative tuning for integrating and unstable processes with gain and phase margin specifications. Industrial & Engineering Chemistry Research. 2002, 41(9): 2910-2914.
[110].柴天佑,张贵军.基于给定的相角裕度和幅值裕度的PID参数自整定新方法.自动化学报. 1997, 23(2): 167-172.
[111]. Panda, R. C., Yu, C.-C., Huang, H.-P. PID rules for SOPDT systems: review and some new results. ISA Transactions.2004, 43(2):283-295.
[112]. Lee, Y., Park, S., Lee, M., Brosilow, C. PID controller tuning for desired closed-loop responses for SI/SO systems. AIChE Journal. 1998, 44(1):106-115.
[113]. Wood, R. K., Berry, M. W. Terminal composition control of a binary distillation column. Chemical Engineering Science. 1973, 28(9):1707-1717.
[114]. Zhang, Y., Wang, Q.-G., Astrom, K. J. Dominant pole placement for multi-loop control systems. Automatica. 2002, 38(7):1213-1220.
[115]. Ogunnaike, B. A., Ray, W. H. Multivariable controller design for linear systems having multiple time delays. AIChE Journal. 1979, 25(6):1043-1057.
[116]. Morari, M., Zafiriou, E. Robust process control. New Jersey: Prentice-Hall, 1989.
[117]. Skogestad, S., Postlethwaite, I. Multivariable feedback control, John Wiley&Sons, Chichester,1996.
[118]. Chien, I. -L., Huang, H. -P., Yang, J. -C. A simple multiloop tuning method for PID controllers with no proportional kick. Industrial & Engineering Chemistry Research. 1999, 38(4):1456-1468.
[119]. Lyben, W. L. Simple method for tuning SISO controllers in multivariable system. Industrial & Engineering Chemistry Process Design and Development. 1986, 25(3): 654-660.
[120]. Mei, H., Li, S., Cai, W.-J., Xiong, Q. Decentralized closed-loop parameter identification for multivariable processes from step responses. Mathematics and Computers in Simulation. 2005, 68(2): 171-192.
[121]. Mei, H., Li, S., Cai, W.-J., Xiong, Q. Decentralized closed-loop parameter identification for multivariable processes from step responses. Mathematics and Computers in Simulation. 2005, 68(2): 171-192.
[122]. Willjuice Iruthayarajan, M., Baskar, S. Covriance matrix adaption evolution strategy based design of centralized PID controller. Expert Systems with Applications. 2010, 37(8): 5775-5781.
[123]. Hu, W., Cai, W.-J., Xiao G. Decentralized control system design for MIMO processes with integrators/differentiators. Industrial & Engineering Chemistry Research. 2010, 49(24): 12521-12528.
[124]. Gundes, A. N., Ozbay, H., Ozguler, A. B. PID controller synthesis for a class of unstable MIMO plants with I/O delays. Automatica. 2007,43(1):135-142.
[125]. Liu, T., Zhang, W., Gu, D. Analytical design of decoupling internal model (IMC) scheme for two-input–two-output (TITO) processes with time delays. Industrial & Engineering Chemistry Research. 2006, 45(9): 3149-3160.
[126]. Doukas, N., Luyben, W. L. Control of sidestream columns separating ternary mixtures. Instrumentation Technology. 1978, 25: 43-48.