Abstract:The input-output variable pairing and the control-loop configuration are the first steps in designing a decentralized control configuration for multivariable processes. The relative gain array (RGA) method and improved variations have been widely used for control system designs, but they generally utilize time domain process information that create challenges when dealing with long lag times, integrators, and unstable systems. This work describes a relative frequency gain method as the ratio of the open-loop frequency gain to the close-loop frequency gain. An interaction measurement index is given through averaging the differences between the relative frequency gain and (1, j0) in the full frequency domain. The interaction measurement index array is used to create a new control-loop pairing criterion for the control structure selection. This method makes better use of the dynamic process characteristics than existing methods through frequency domain analysis. The method is simple and effective, with long lag times, integrators, and unstable systems.
许锋, 潘琦, 王一岚, 罗雄麟. 工业过程多变量系统常规控制结构的频域设计[J]. 清华大学学报(自然科学版), 2016, 56(4): 448-452.
XU Feng, PAN Qi, WANG Yilan, LUO Xionglin. Frequency domain design method for decentralized control of multivariable processes. Journal of Tsinghua University(Science and Technology), 2016, 56(4): 448-452.
[1] 罗雄麟, 王海群, 许锋. 工业过程多变量系统的辅助常规控制设计[J]. 化工自动化及仪表, 2009, 36(4):33-37.LUO Xionglin, WANG Haiqun, XU Feng. Auxiliary regulatory control design of multivariable system in industrial process[J]. Control and Instruments in Chemical Industry, 2009, 36(4):33-37. (in Chinese)
[2] Bristol E. On a new measure of interaction for multivariable process control[J]. IEEE Transactions on Automatic Control, 1966, 11(1):133-134.
[3] Niederlinski A. A heuristic approach to the design of linear multivariable interacting control systems[J]. Automatica, 1971, 7(6):691-701.
[4] Grosdldler P, Morari M, Holt B R. Closed-loop properties from steady state gain information[J]. Industrial & Engineering Chemistry Fundamentals, 1985, 24(2):221-235.
[5] Gagnepain J P, Seborg D E. Analysis of process interactions with application to multiloop control system design[J]. Industrial & Engineering Chemistry Process Design and Development, 1982, 21(1):5-11.
[6] 叶凌箭, 宋执环. 多变量控制系统的一种变量配对方法[J]. 控制与决策, 2009, 24(12):1795-1800.YE Lingjian, SONG Zhihuan. Variable pairing method for multivariable control systems[J]. Control and Decision, 2009, 24(12):1795-1800. (in Chinese)
[7] 罗雄麟, 任丽红, 周晓龙, 等. 常规控制系统配对设计的动态相对增益阵研究[J]. 化工自动化及仪表, 2012, 39(3):295-300.LUO Xionglin, REN Lihong, ZHOU Xiaolong, et al. Dynamic RGA for control system configuration of multivariable process[J]. Control and Instruments in Chemical Industry, 2012, 39(3):295-300. (in Chinese)
[8] Meeuse F M, Huesman A E M. Analyzing dynamic interaction of control loops in the time domain[J]. Industrial & Engineering Chemistry Research, 2002, 41(18):4585-4590.
[9] McAoy T, Arkun Y, Chen R, et al. A new approach to defining a dynamic relative gain[J]. Control Engineering Practice, 2003, 11(8):907-914.
[10] XIONG Qiang, CAI Wenjian, HE Maojun. A practical loop pairing criterion for multivariable processes[J]. Journal of Process Control, 2005, 15(7):741-747.
[11] XIONG Qiang, CAI Wenjian, HE Maojun, et al. Decentralized control system design for multivariable processes-A novel method based on effective relative gain array[J]. Industrial & Engineering Chemistry Research, 2006, 45(8):2769-2776.
[12] XIONG Qiang, CAI Wenjian. Effective transfer function method for decentralized control system design for multi-input multi-output processes[J]. Journal of Process Control, 2006, 16(8):773-784.
[13] XIONG Qiang, CAI Wenjian, HE Maojun. Equivalent transfer function method for PI/PID controller design of MIMO processes[J]. Journal of Process Control, 2007, 17(8):665-673.
[14] HE Maojun, CAI Wenjian, NI Wei, et al. RNGA based control system configuration for multivariable processes[J]. Journal of Process Control, 2009, 19(6):1036-1042.
[15] 任丽红, 刘雨波, 罗雄麟, 等. 多变量时滞系统的关联分析与变量配对[J]. 化工自动化及仪表, 2012, 39(6):743-746.REN Lihong, LIU Yubo, LUO Xionglin, et al. Association analysis and variable pairing for multivariable system with time delay[J]. Control and Instruments in Chemical Industry, 2012, 39(6):743-746. (in Chinese)
[16] Hovd M, Scogestad S. Pairing criteria for decentralized control of unstable plants[J]. Industrial & Engineering Chemistry Research, 1994, 33(9):2134-2139.
[17] Arkun Y, Downs J. A general method to calculate input-output gains and the relative gain array for integrating processes[J]. Computers & Chemical Engineering, 1990, 14(10):1101-1110.
[18] HUANG Hsiaoping, LIN Fengyi, JENG Jyhcheng. Multi-loop PID controllers design for MIMO processes containing integrators[J]. Journal of Chemical Engineering of Japan, 2005, 38(9):742-756.
[19] HU Wuhua, CAI Wenjian, XIAO Gaoxi. Decentralized control system design for MIMO processes with integrators/differentiators[J]. Industrial & Engineering Chemistry Research, 2010, 49(24):12521-12528.
[20] 许锋, 魏小丽, 任丽红, 等. 基于多变量广义预测控制的不稳定系统控制结构选择方法[J]. 自动化学报, 2013, 39(9):1547-1551. XU Feng, WEI Xiaoli, REN Lihong, et al. A control structure selection method based on multivariable generalized predictive control for unstable processes[J]. Acta Automatica Sinica, 2013, 39(9):1547-1551. (in Chinese)