化工过程多回路PID控制系统模式切换参数自整定

doi:10.11949/0438-1157.20211473

摘要/Abstract

摘要：

化工过程一般为多变量系统，但其主要控制方案为分散多回路PID常规控制。由于多变量系统内部存在不同程度的耦合作用，各控制回路之间存在相互影响，当其他回路进行手动/自动模式切换时，本回路等效被控对象将会发生突变，导致本回路的原有控制参数不能适应等效被控对象的变化，造成控制性能下降，甚至闭环系统不稳定。为避免这种情况的发生，从整个系统的角度研究控制回路模式切换时的稳定性，采用多变量频域Nyquist阵列设计法。基于对角优势下正Nyquist稳定性判据，从Gershgorin圆边界点的角度定量分析各个控制回路在模式切换前后的稳定性变化程度，从而确定各回路控制器增益的调整方向及程度，实现各回路的控制器参数在控制回路模式切换瞬间的自动整定，尽可能抵消控制回路模式切换对整个系统的扰动，保证整个系统的闭环稳定性。以Shell公司重油分馏塔的多回路PID控制系统为例，将3个PID控制回路依次投用时，根据Gershgorin圆边界点进行控制参数的自整定，闭环系统仍能保持一定的控制性能，否则闭环系统将不稳定。

关键词: 过程控制, 多变量系统, 多回路控制, PID, 自整定, Nyquist阵列设计法

Abstract:

Chemical process is generally a multivariable system, but its main control scheme is decentralized multi-loop PID conventional control. Since there are different degrees of coupling in the multivariable system, there are mutual influences between the control loops. When the other control loops switch between the manual/automatic modes, the equivalent controlled object of this loop will mutate so that the original control parameters of this loop will be inappropriate and the control performance will become worse even the closed-loop system is unstable. In order to avoid this situation, the stability of the control loop mode switching should be studied from the perspective of the whole system, so the multivariable frequency domain Nyquist array design method is adopted. Based on the Nyquist stability criterion under diagonal dominance, the stability changing of each control loop before and after mode switching is quantitatively analyzed from the Gershgorin circle boundary points, so as to determine the adjustment direction and size of the controller gain for each loop. The controller parameter self-tuning of each loop at the moment of control loop mode switching is realized to compensate the disturbance caused by the control loop mode switching and ensure the closed-loop stability of the whole system. The multi-loop PID control system of Shell heavy oil fractionator is used as an example, when the three PID control loops are put into use in turn, the control parameter self-tuning according to the boundary points of Gershgorin circle makes the closed-loop system still maintain certain control performance, otherwise the closed-loop system will be unstable.

Key words: process control, multi-variable system, multi-loop control, PID, self-tuning, Nyquist array design method

中图分类号:

TP 273

王建松, 许锋, 罗雄麟. 化工过程多回路PID控制系统模式切换参数自整定[J]. 化工学报, 2022, 73(4): 1647-1657.

Jiansong WANG, Feng XU, Xionglin LUO. Controller parameter self-tuning when control loop mode switching for multi-loop PID control system of chemical process[J]. CIESC Journal, 2022, 73(4): 1647-1657.

图/表 14

图1 多变量解耦控制

Fig.1 Multivariable decoupling control

图2 多变量分散控制

Fig.2 Multivariate decentralized control

图3 仅第一个控制回路闭合时系统结构

Fig.3 Block diagram of the system structure when only the first control loop is closed

图4 第二个控制回路闭合时系统结构

Fig.4 Block diagram of system structure when the second control loop is closed

图5 系统的控制结构

Fig.5 System control chart

图6 正Nyquist判据与稳定性之间的Venn图

Fig.6 The Venn diagram between direct Nyquist criterion and system stability

图7 校正前后Gershgorin圆情况

Fig.7 The situation of Gershgorin circle before and after correction

图8 计算机辅助设计流程图

Fig.8 Computer-aided flowchart

图9 重油分馏塔流程图

Fig.9 Flowchart of heavy oil fractionator

图10 控制回路u1-y1闭合时输出曲线

Fig.10 Output curve when control loop u1-y1 is closed

表1 控制回路u2-y2模式切换时控制器参数及Gershgorin圆边界点校正前后数据

Table 1 Control loop u2-y2 mode switching controller parameters and Gershgorin circle before and after correction

控制器参数		列Gershgorin圆边界点
校正前	校正后	校正前	校正后
c₁=(0.3, 0.01, 0.3)	c₁=(0.2037, 0.0068, 0.2037)	h $1, - 1'$ = -1.1780	h $1, - 1'$ = -0.8
c₂=(0.5, 0.03, 0.3)	c₂=(0.5, 0.03, 0.3)	h $2, - 1'$ = -0.8685	h $2, - 1'$ = -0.8685

表1 控制回路u2-y2模式切换时控制器参数及Gershgorin圆边界点校正前后数据

Table 1 Control loop u2-y2 mode switching controller parameters and Gershgorin circle before and after correction

控制器参数		列Gershgorin圆边界点
校正前	校正后	校正前	校正后
c₁=(0.3, 0.01, 0.3)	c₁=(0.2037, 0.0068, 0.2037)	h $1, - 1'$ = -1.1780	h $1, - 1'$ = -0.8
c₂=(0.5, 0.03, 0.3)	c₂=(0.5, 0.03, 0.3)	h $2, - 1'$ = -0.8685	h $2, - 1'$ = -0.8685

图11 控制回路u2-y2切换时校正前后输出曲线

Fig.11 Output curve before and after correction when control loop u2-y2 is closed

图12 控制回路u3-y3切换时校正前后输出曲线

Fig.12 Output curve before and after correction when control loop u3-y3 is closed

表2 控制回路u3-y3模式切换时控制器参数及Gershgorin圆边界点校正前后数据

Table 2 Control loop u3-y3 mode switching controller parameters and Gershgorin circle before and after correction

控制器参数		列Gershgorin圆边界点
校正前	校正后	校正前	校正后
c₁=(0.2037, 0.0068, 0.2037)	c₁=(0.1234, 0.0041, 0.1234)	h $1, - 1'$ = -1.3206	h $1, - 1'$ = -0.8
c₂=(0.5, 0.03, 0.3)	c₂=(0.2570, 0.0154, 0.1542)	h $2, - 1'$ = -1.5565	h $2, - 1'$ = -0.8
c₃=(0.05, 0.004, 0.3)	c₃=(0.05, 0.004, 0.3)	h $3, - 1'$ = -0.2579	h $3, - 1'$ = -0.2579

表2 控制回路u3-y3模式切换时控制器参数及Gershgorin圆边界点校正前后数据

Table 2 Control loop u3-y3 mode switching controller parameters and Gershgorin circle before and after correction

控制器参数		列Gershgorin圆边界点
校正前	校正后	校正前	校正后
c₁=(0.2037, 0.0068, 0.2037)	c₁=(0.1234, 0.0041, 0.1234)	h $1, - 1'$ = -1.3206	h $1, - 1'$ = -0.8
c₂=(0.5, 0.03, 0.3)	c₂=(0.2570, 0.0154, 0.1542)	h $2, - 1'$ = -1.5565	h $2, - 1'$ = -0.8
c₃=(0.05, 0.004, 0.3)	c₃=(0.05, 0.004, 0.3)	h $3, - 1'$ = -0.2579	h $3, - 1'$ = -0.2579

参考文献 36

1	Mayne D Q. The design of linear multivariable systems[J]. Automatica, 1973, 9(2): 201-207.
2	Monica T J, Yu C C, Luyben W L. Improved multiloop single-input/single-output (SISO) controllers for multivariable processes[J]. Industrial & Engineering Chemistry Research, 1988, 27(6): 969-973.
3	Bao J, Forbes J F, McLellan P J. Robust multiloop PID controller design: a successive semidefinite programming approach[J]. Industrial & Engineering Chemistry Research, 1999, 38(9): 3407-3419.
4	Vu T N L, Lee M. Independent design of multi-loop PI/PID controllers for interacting multivariable processes[J]. Journal of Process Control, 2010, 20(8): 922-933.
5	Bristol E. On a new measure of interaction for multivariable process control[J]. IEEE Transactions on Automatic Control, 1966, 11(1): 133-134.
6	Wang S, Munro N. A complete proof of Bristol’s relative gain array[J]. Transactions of the Institute of Measurement & Control, 1982, 4(1): 53-56.
7	Niederlinski A. A heuristic approach to the design of linear multivariable interacting control systems[J]. Automatica, 1971, 7(6): 691-701.
8	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 L J, Song Z H. Variable pairing method for multivariable control systems[J]. Control and Decision, 2009, 24(12): 1795-1800.
9	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 X L, Ren L H, Zhou X L, et al. Dynamic RGA for control system configuration of multivariable process[J]. Control and Instruments in Chemical Industry, 2012, 39(3): 295-300.
10	许锋, 袁未未, 罗雄麟. 化工过程非方瘦系统的串级控制系统结构设计[J]. 化工学报, 2017, 68(7): 2833-2843.
	Xu F, Yuan W W, Luo X L. Cascade control configuration design for non-square multivariable system of chemical processes[J]. CIESC Journal, 2017, 68(7): 2833-2843.
11	许锋, 袁未未, 罗雄麟. 大系统的常规控制系统结构设计[J]. 计算机与应用化学, 2017, 34(9): 661-668.
	Xu F, Yuan W W, Luo X L. Regulatory control configuration design for large-scale systems[J]. Computers and Applied Chemistry, 2017, 34(9): 661-668.
12	Mc Avoy 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.
13	Xu F, Cao P F, Luo X L. Regulator configuration design by means of model predictive control[J]. Journal of Process Control, 2015, 28: 95-103.
14	Xiong Q, Cai W J, He M J. A practical loop pairing criterion for multivariable processes[J]. Journal of Process Control, 2005, 15(7): 741-747.
15	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.
16	He M J, Cai W J, Ni W, et al. RNGA based control system configuration for multivariable processes[J]. Journal of Process Control, 2009, 19(6): 1036-1042.
17	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, 760.
	Ren L H, Liu Y B, Luo X L, et al. Association analysis and variable pairing for multivariable system with time delays[J]. Control and Instruments in Chemical Industry, 2012, 39(6): 743-746, 760.
18	Lee J, Cho W, Edgar T F. Multiloop PI controller tuning for interacting multivariable processes[J]. Computers & Chemical Engineering, 1998, 22(11): 1711-1723.
19	Wang Q G, Hang C C, Zou B. A frequency response approach to autotuning of multivariable controllers[J]. Chemical Engineering Research and Design, 1997, 75(8): 797-806.
20	Kolotilina L Y. On determinantal diagonal dominance conditions[J]. Journal of Mathematical Sciences, 2011, 176(1): 57-67.
21	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.
22	Rosenbrock H H, Owens D H. Computer aided control system design[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1976, 6(11): 794.
23	Rosenbrock H H. Progress in the design of multivariable control systems[J]. Measurement and Control, 1971, 4(1): 9-11.
24	McMorran P D. Extension of the inverse Nyquist method[J]. Electronics Letters, 1970, 6(25): 800-801.
25	McMorran P D. Design of gas-turbine controller using inverse Nyquist method[J]. Proceedings of the Institution of Electrical Engineers, 1970, 117(10): 2050.
26	Ho W K, Lee T H, Xu W, et al. The direct Nyquist array design of PID controllers[J]. IEEE Transactions on Industrial Electronics, 2000, 47(1): 175-185.
27	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.
28	Chen D, Seborg D E. Multiloop PI/PID controller design based on Gershgorin bands[J]. IEE Proceedings-Control Theory and Applications, 2002, 149(1): 68-73.
29	Luyben W L. Simple method for tuning SISO controllers in multivariable systems[J]. Industrial & Engineering Chemistry Process Design and Development, 1986, 25(3): 654-660.
30	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.
31	Lee J, Kim D H, Edgar T F. Static decouplers for control of multivariable processes[J]. AIChE Journal, 2005, 51(10): 2712-2720.
32	He M J, Cai W J, Wu B F, et al. Simple decentralized PID controller design method based on dynamic relative interaction analysis[J]. Industrial & Engineering Chemistry Research, 2005, 44(22): 8334-8344.
33	Garelli F, Mantz R J, De Battista H. Limiting interactions in decentralized control of MIMO systems[J]. Journal of Process Control, 2006, 16(5): 473-483.
34	Carrier J F, Stephanopoulos G. Wavelet-based modulation in control-relevant process identification[J]. AIChE Journal, 1998, 44(2):341-360.
35	Van Den Hof P M J, Schrama R J P. Identification and control—closed-loop issues[J]. Automatica, 1995, 31(12): 1751-1770.
36	Prett D M, Garcia C E. Fundamental Process Control [M]. Boston: Butterworths-Heinemann, 1988.

[1]	曹跃, 余冲, 李智, 杨明磊. 工业数据驱动的加氢裂化装置多工况切换过渡状态检测[J]. 化工学报, 2023, 74(9): 3841-3854.
[2]	康飞, 吕伟光, 巨锋, 孙峙. 废锂离子电池放电路径与评价研究[J]. 化工学报, 2023, 74(9): 3903-3911.
[3]	苏晓丹, 朱干宇, 李会泉, 郑光明, 孟子衡, 李防, 杨云瑞, 习本军, 崔玉. 湿法磷酸半水工艺考察与石膏结晶过程研究[J]. 化工学报, 2023, 74(4): 1805-1817.
[4]	张江淮, 赵众. 碳三加氢装置鲁棒最小协方差约束控制及应用[J]. 化工学报, 2023, 74(3): 1216-1227.
[5]	张中秋, 李宏光, 石逸林. 基于人工预测调控策略的复杂化工过程多任务学习方法[J]. 化工学报, 2023, 74(3): 1195-1204.
[6]	赵涛岩, 曹江涛, 李平, 冯琳, 商瑀. 区间二型模糊免疫PID在环己烷无催化氧化温度控制系统中的应用[J]. 化工学报, 2022, 73(7): 3166-3173.
[7]	王琨, 侍洪波, 谭帅, 宋冰, 陶阳. 局部时差约束邻域保持嵌入算法在故障检测中的应用[J]. 化工学报, 2022, 73(7): 3109-3119.
[8]	周乐, 沈程凯, 吴超, 侯北平, 宋执环. 深度融合特征提取网络及其在化工过程软测量中的应用[J]. 化工学报, 2022, 73(7): 3156-3165.
[9]	张兴硕, 罗雄麟, 许锋. 催化裂化装置反再系统动态模拟精细化与控制系统“工艺优先”配对设计[J]. 化工学报, 2022, 73(2): 747-758.
[10]	张成, 潘立志, 李元. 基于加权统计特征KICA的故障检测与诊断方法[J]. 化工学报, 2022, 73(2): 827-837.
[11]	卢道铭, 唐钊艇, 范怡平, 卢春喜. 大差异颗粒分级再生设备的性能研究[J]. 化工学报, 2021, 72(8): 4184-4195.
[12]	李元, 杨东昇, 赵丽颖, 张成. 层次变分高斯混合模型与主多项式分析的故障检测策略[J]. 化工学报, 2021, 72(3): 1616-1626.
[13]	谢苗苗, 张浪文, 谢巍. 复杂非线性系统的子系统分解方法[J]. 化工学报, 2021, 72(3): 1557-1566.
[14]	任超,孙琳,罗雄麟. 换热器因应结垢慢时变的控制系统重构分析[J]. 化工学报, 2021, 72(10): 5273-5283.
[15]	冯思琦, 罗雄麟. 模式切换类经济预测控制切换时间在线估计[J]. 化工学报, 2020, 71(S2): 225-240.