Volume 13 Number 6
December 2016
Article Contents
Zhuo-Yun Nie, Rui-Juan Liu, Fu-Jiang Jin and Lai-Cheng Yan. Analysis and Design of Scaling Optimal GPM-PID Control with Application to Liquid Level Control. International Journal of Automation and Computing, vol. 13, no. 6, pp. 624-633, 2016. doi: 10.1007/s11633-016-0998-y
Cite as: Zhuo-Yun Nie, Rui-Juan Liu, Fu-Jiang Jin and Lai-Cheng Yan. Analysis and Design of Scaling Optimal GPM-PID Control with Application to Liquid Level Control. International Journal of Automation and Computing, vol. 13, no. 6, pp. 624-633, 2016.

# Analysis and Design of Scaling Optimal GPM-PID Control with Application to Liquid Level Control

Author Biography:
• Rui-Juan Liu,received the B. Sc. and M. Sc degrees in mathematics from Changsha University of Science and Technology, China in 2004 and 2007, respectively, and Ph. D. degree in control theory and control engineering from Central South University, China in 2014. She is currently a lecturer in the School of Applied Mathematics, Xiamen University of Technology, China.
Her research interests include robust control, nonlinear control, and fractional-order system.
E-mail:liuruijuan0313@163.com

Fu-Jiang Jin, received the M. Sc. and Ph. D. degree in control theory and control engineering from Zhejiang University, China in 1998 and 2002, respectively. He is currently a professor in the School of Information Engineering, Huaqiao University, China.
His research interests include process modeling and control.
E-mail:jinfujiang@163.com

Lai-Cheng Yan,received the B. Sc. and M. Sc degrees in electrical engineering from Chongqing Communication Institute and Chongqing University, China in 2004 and 2007, respectively. He is currently a lecturer in the School of Information Engineering, Huaqiao University, China.
His research interests include robot modeling and control.
E-mail:ylaicheng@126.com

• Corresponding author: Zhuo-Yun Nie received the B. Sc. degree in automation from Central South University, China in 2006, and Ph.D. degree in control theory and control engineering from Central South University, China in 2012. He is currently a lecturer in the School of Information Engineering, Huaqiao University, China.
research interests include robust control, nonlinear control, and financial forecasting.
E-mail: yezhuyun2004@sina.com ;
ORCID iD: 0000-0002-5980-3268
• Accepted: 2015-07-17
• Published Online: 2016-06-20
Fund Project:

This work was supported by National Natural Science Foundation of China 61403149 and 61273069

Natural Science Foundation of Fujian Province 2015J01261

• In this paper,a new analysis and design method for proportional-integrative-derivative (PID) tuning is proposed based on controller scaling analysis.Integral of time absolute error (ITAE) index is minimized for specified gain and phase margins (GPM) constraints,so that the transient performance and robustness are both satisfied.The requirements on gain and phase margins are ingeniously formulated by real part constraints (RPC) and imaginary part constraints (IPC).This set of new constraints is simply related with three parameters and decoupling of the remaining four unknowns,including three controller parameters and the gain margin,in the nonlinear and coupled characteristic equation simultaneously.The formulas of the optimal GPM-PID are derived based on controller scaling analysis.Finally,this method is applied to liquid level control of coke fractionation tower,which demonstrate that the proposed method provides better disturbance rejection and robust tracking performance than some commonly used PID tuning methods.
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###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

Figures (20)  / Tables (4)

## Analysis and Design of Scaling Optimal GPM-PID Control with Application to Liquid Level Control

• ###### Corresponding author:Zhuo-Yun Nie received the B. Sc. degree in automation from Central South University, China in 2006, and Ph.D. degree in control theory and control engineering from Central South University, China in 2012. He is currently a lecturer in the School of Information Engineering, Huaqiao University, China. research interests include robust control, nonlinear control, and financial forecasting. E-mail: yezhuyun2004@sina.com ;ORCID iD: 0000-0002-5980-3268
Fund Project:

This work was supported by National Natural Science Foundation of China 61403149 and 61273069

Natural Science Foundation of Fujian Province 2015J01261

Abstract: In this paper,a new analysis and design method for proportional-integrative-derivative (PID) tuning is proposed based on controller scaling analysis.Integral of time absolute error (ITAE) index is minimized for specified gain and phase margins (GPM) constraints,so that the transient performance and robustness are both satisfied.The requirements on gain and phase margins are ingeniously formulated by real part constraints (RPC) and imaginary part constraints (IPC).This set of new constraints is simply related with three parameters and decoupling of the remaining four unknowns,including three controller parameters and the gain margin,in the nonlinear and coupled characteristic equation simultaneously.The formulas of the optimal GPM-PID are derived based on controller scaling analysis.Finally,this method is applied to liquid level control of coke fractionation tower,which demonstrate that the proposed method provides better disturbance rejection and robust tracking performance than some commonly used PID tuning methods.

Zhuo-Yun Nie, Rui-Juan Liu, Fu-Jiang Jin and Lai-Cheng Yan. Analysis and Design of Scaling Optimal GPM-PID Control with Application to Liquid Level Control. International Journal of Automation and Computing, vol. 13, no. 6, pp. 624-633, 2016. doi: 10.1007/s11633-016-0998-y
 Citation: Zhuo-Yun Nie, Rui-Juan Liu, Fu-Jiang Jin and Lai-Cheng Yan. Analysis and Design of Scaling Optimal GPM-PID Control with Application to Liquid Level Control. International Journal of Automation and Computing, vol. 13, no. 6, pp. 624-633, 2016.
Reference (26)

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