Multivariable control system based on PID diagonal dominant compensation matrix

doi:10.11949/j.issn.0438-1157.20171137

Abstract

Abstract:

Chemical processes are multivariable systems with often coupled interactions between input and output variables, which conventional decentralized PID control system is difficult to maintain good control performance. In order to weaken coupling effect in multivariable system, PID dynamic pre-compensation matrix was designed by weighted optimization of many frequency points and diagonal dominance design criterion. A controller of the compensated diagonal dominance system was designed using positive Nyquist array design method. According to Nyquist stability criterion of diagonal dominance system, stable parameter range of feedback matrix was determined by plotting dominance degree curve and Gershgorin band. After that, dynamic compensator was designed by following single input single output system principle, which made the closed-loop system meet performance requirements of dynamic controls. Case studies show that centralized control systems designed by this method are more advantageous, simpler, and easier than decentralized control system.

Key words: process control, multivariable systems, diagonal dominance, centralized control, PID

摘要：

化工过程一般为多变量系统，输入输出变量之间往往存在耦合作用，常规分散PID控制系统难以保证控制质量。为了削弱多变量系统的耦合作用，基于对角优势的设计准则，通过在若干频率点加权优化，设计PID动态预补偿阵。然后利用正Nyquist阵列设计法对补偿后的系统设计控制器，基于对角优势系统的Nyquist稳定判据，通过绘制优势度曲线和Gershgorin带判断系统的优势程度，初步确定反馈矩阵的稳定参数范围，再按照单输入单输出系统设计动态补偿器，使得系统满足动态控制品质要求。最后通过示例说明，该方法设计的集中控制系统与分散控制相比，控制性能具有一定的优势，且方法简便，容易实现。

关键词: 过程控制, 多变量系统, 对角优势, 集中控制, PID

CLC Number:

TP273

WANG Qihang, XU Feng, LUO Xionglin. Multivariable control system based on PID diagonal dominant compensation matrix[J]. CIESC Journal, 2018, 69(3): 1092-1101.

王启航, 许锋, 罗雄麟. 基于PID对角优势补偿阵的过程多变量控制系统设计[J]. 化工学报, 2018, 69(3): 1092-1101.

References 29

[1]	XIONG Q, CAI W J, HE M J, 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.
[2]	XIONG Q, CAI W J. Effective transfer function method for decentralized control system design of multi-input multi-output processes[J]. Journal of Process Control, 2006, 16(8):773-784.
[3]	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 X L, WANG H Q, XU F. Auxiliary regulatory control design of multivariable system in industrial process[J]. Control and Instruments in Chemical Industry, 2009, 36(4):33-37.
[4]	ROSENBROCK H H. Design of multivariable control systems using the inverse Nyquist array[J]. Proceedings of the Institution of Electrical Engineers, 1969, 116(11):1929-1936.
[5]	HO W K, LEE T H, XU W. The direct nyquist array design of PID controllers[J]. IEEE Transactions on Industrial Electronics, 2000, 47(1):175-185.
[6]	CHEN D, SEBORG D E. Multiloop PI/PID controller design based on Gershgorin bands[J]. IEE Proc.-Control Theory Appl., 2002, 149(1):68-73.
[7]	ROSENBROCK H H. Computer-Aided Control System Design[M]. New York:Academic Press, 1974.
[8]	LIMEBEER D J N. The application of generalized diagonal dominance to linear system stability theory[J]. International Journal of Control, 1982, 36(2):185-212.
[9]	HAWKINS D J. Pseudodiagonalisation and the inverse-Nyquist array method[J]. Proceedings of the Institution of Electrical Engineers, 1972, 119(3):337-342.
[10]	江青茵. 对角优势的常数阵实现[J]. 控制理论与应用, 1988, 5(1):89-94. JIANG Q Y. Achieving diagonal dominance via constant compensation[J]. Control Theory and Applications, 1988, 5(1):89-94.
[11]	FORD M P, DALY K C. Dominance improvement by pseudodecoupling[J]. Proceedings of the Institution of Electrical Engineers, 1980, 126(12):1316-1320.
[12]	WANG Q G, HUANG B, GUO X. Auto-tuning of TITO decoupling controllers from step tests[J]. ISA Transactions, 2000, 39(4):407-418.
[13]	NOBAKHTI A, MUNRO N. Achieving diagonal dominance by frequency interpolation[C]//American Control Conference. Boston:IEEE Xplore, 2004:3065-3069.
[14]	SHEN Y, CAI W J, LI S. Multivariable process control:decentralized, decoupling, or sparse?[J]. Industrial & Engineering Chemistry Research, 2010, 49(2):761-771.
[15]	李康伟, 王宏力. 多变量线性系统解耦控制算法研究[J]. 计算机测量与控制, 2007, 15(3):346-348. LI K W, WANG H L. Research on decoupling control algorithm of multi-variable linear systems[J]. Computer Measurement and Control, 2007, 15 (3):346-348.
[16]	ÅSTRÖM K J, JOHANSSON K H, WANG Q G. Design of decoupled PI controller for two-by-two systems[J]. IEE Proceedings-Control Theory and Applications, 2002, 149(1):74-81.
[17]	CAI W J, NI W, HE M J, et al. Normalized decoupling-a new approach for MIMO process control system design[J]. Ind. Eng. Chem. Res., 2008, 47(19):7347-7356.
[18]	SHEN Y, CAI W J, LI S. Normalized decoupling control for high-dimensional MIMO processes for application in room temperature control HVAC systems[J]. Control Engineering Practice, 2010, 18(6):652-664.
[19]	庞国仲, 鲍远律. "自加权"准优势化方法[J]. 控制与决策, 1989, (2):1-7. PANG G Z, BAO Y L. The self weighting pseudo-domination algorithm[J]. Control and Decision, 1989, (2):1-7.
[20]	LUYBEN W L. Simple method for tuning SISO controllers in multivariable systems[J]. Industrial & Engineering Chemistry Process Design & Development, 1986, 25(3):654-660.
[21]	HO W K, LEE T H, GAN O P. Tuning of multiloop proportional-integral-derivative controllers based on gain and phase margin specifications[J]. Industrial & Engineering Chemistry Research, 1997, 36(6):2231-2238.
[22]	CHEN D, SEBORG D E. Design of decentralized PI control systems based on Nyquist stability analysis[J]. Journal of Process Control, 2003, 13(1):27-39.
[23]	HUANG H P, JENG J C, CHIANG C H, et al. A direct method for multi-loop PI/PID controller design[J]. Journal of Process Control, 2003, 13(8):769-786.
[24]	CHIEN I L, HUANG H P, YANG J C. A simple multiloop tuning method for PID controllers with no proportional kick[J]. Ind.Eng.Chem.Res., 1999, 38(4):1456-1468.
[25]	XIONG Q, CAI W J, HE M J. Equivalent transfer function method for PI/PID controller design of MIMO processes[J]. Journal of Process Control, 2007, 17(8):665-673.
[26]	吴晓威, 张井岗, 赵志诚. 多变量系统的PID控制器设计[J]. 信息与控制, 2008, 37(3):316-321. WU X W, ZHANG J G, ZHAO Z C. Design of a PID controller for multivariable systems[J]. Information and Control, 2008, 37(3):316-321.
[27]	王德普. 多变量频域控制理论的对角优势化发展[J]. 哈尔滨船舶工程学院学报, 1989, 10(4):418-424. WANG D P. Diagonal dominance for the design of multivariable control systems[J]. Journal of Harbin Shipbuilding Engineering Institute, 1989, 10 (4):418-424.
[28]	VLACHOS C, WILLIAMS D, GOMM J B. Solution to the Shell standard control problem using genetically tuned PID controllers[J]. Control Engineering Practice, 2002, 10(2):151-163.
[29]	段玉波, 周毅平, 陈广义, 等. 逆奈奎斯特阵列法在蒸汽锅炉温度控制系统设计中的应用[J]. 哈尔滨工程大学学报, 1995, 16(2):18-22. DUAN Y B, ZHOU Y P, CHEN G Y, et al. The application of inverse Nyquist array in boiler temperature control system design[J]. Journal of Harbin Engineering University, 1995, 16(2):18-22.