Controller parameter self-tuning when control loop mode switching for multi-loop PID control system of chemical process

doi:10.11949/0438-1157.20211473

Abstract

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

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

CLC Number:

TP 273

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.

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.

Figures/Tables 14

Fig.1 Multivariable decoupling control

Fig.2 Multivariate decentralized control

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

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

Fig.5 System control chart

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

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

Fig.8 Computer-aided flowchart

Fig.9 Flowchart of heavy oil fractionator

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

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

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

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

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

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

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

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