0
Research Papers

Internal Model Control–Proportional Integral Derivative–Fractional-Order Filter Controllers Design for Unstable Delay Systems

[+] Author and Article Information
Kahina Titouche

L2CSP Laboratory,
Mouloud Mammeri University,
Tizi-Ouzou 15000, Algeria
e-mail: titouche.kahina@gmail.com

Rachid Mansouri

L2CSP Laboratory,
Mouloud Mammeri University,
Tizi-Ouzou 15000, Algeria
e-mail: rachid_mansouri_ummto@yahoo.fr

Maamar Bettayeb

Center of Excellence in Intelligent
Engineering Systems,
University of Sharjah,
Sharjah, UAE;
Center of Excellence in Intelligent
Engineering Systems,
King Abdulaziz University,
Jaddah, Saudi Arabia
e-mail: maamar@sharjah.ac.ae

Ubaid M. Al-Saggaf

Center of Excellence in Intelligent
Engineering Systems,
King Abdulaziz University,
Jeddah 21146, Saudi Arabia
e-mail: usaggaf@kau.edu.sa

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 15, 2014; final manuscript received November 23, 2015; published online December 23, 2015. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 138(2), 021006 (Dec 23, 2015) (10 pages) Paper No: DS-14-1416; doi: 10.1115/1.4032131 History: Received October 15, 2014; Revised November 23, 2015

An analytical design for proportional integral derivative (PID) controller cascaded with a fractional-order filter is proposed for first-order unstable processes with time delay. The design algorithm is based on the internal model control (IMC) paradigm. A two degrees-of-freedom (2DOF) control structure is used to improve the performance of the closed-loop system. In the 2DOF control structure, an integer order controller is used to stabilize the inner-loop, and a fractional-order controller for the stabilized system is employed to improve the performance of the closed-loop system. The Walton–Marshall's method, which is applicable to quasi-polynomials, is then used to establish the internal stability condition of the closed-loop system (the fractional part of the controller in particular) and to seek the set of stabilizing proportional (P) or proportional-derivative (PD) controller parameters.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Agrawal, P. , and Lim, H. C. , 1984, “ Analyses of Various Control Schemes for Continuous Bioreactors,” Bioprocess Parameter Control (Advances in Biochemical Engineering/Biotechnology), Vol. 30, Springer, Berlin, pp. 61–90.
Uppal, A. , Ray, W. H. , and Poore, A. B. , 1974, “ On the Dynamic Behavior of Continuous Stirred Tank Reactors,” Chem. Eng. Sci., 29(4), pp. 967–985. [CrossRef]
Lee, Y. K. , and Watkins, J. M. , 2011, “ Determination of all Stabilizing Fractional-Order PID Controllers,” American Control Conference (ACC), San Francisco, CA, June 29–July 1, pp. 5007–5012.
Luo, Y. , and Chen, Y. , 2012, “ Stabilizing and Robust Fractional Order PI Controller Synthesis for First Order Plus Time Delay Systems,” Automatica, 48(9), pp. 2159–2167. [CrossRef]
Zulfiqar, A. , and Ahmed, N. , 2013, “ Stability Regions of Fractional-Order PIαDβ Controllers With Dead-Time Plant,” 2013 IEEE 9th International Conference on Emerging Technology (ICET), Islamabad, Dec. 9–10, pp. 1–5.
Chen, Y. , and Moore, K. L. , 2002, “ Analytical Stability Bound for a Class of Delayed Fractional-Order Dynamic Systems,” Nonlinear Dyn., 29(1), pp. 191–200. [CrossRef]
Hamamci, S. E. , and Koksal, M. , 2010, “ Calculation of all Stabilizing Fractional-Order PD Controllers for Integrating Time Delay Systems,” Comput. Math. Appl., 59(5), pp. 1621–1629. [CrossRef]
Gao, Z. , Yan, M. , and Wei, J. , 2014, “ Robust Stabilizing Regions of Fractional-Order PDμ Controllers of Time-Delay Fractional-Order Systems,” J. Process Control, 24(1), pp. 37–47. [CrossRef]
Hwang, C. , and Cheng, Y. C. , 2006, “ A Numerical Algorithm for Stability Testing of Fractional Delay Systems,” Automatica, 42(5), pp. 825–831. [CrossRef]
Hamamci, S. E. , 2007, “ An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers,” IEEE Trans. Autom. Control, 52(10), pp. 1964–1969. [CrossRef]
Merrikh-Bayat, F. , and Karimi-Ghartemani, M. , 2009, “ An Efficient Numerical Algorithm for Stability Testing of Fractional-Delay Systems,” ISA Trans., 48(1), pp. 32–37. [CrossRef] [PubMed]
Cheng, Y. C. , and Hwang, C. , 2006, “ Stabilization of Unstable First-Order Time-Delay Systems Using Fractional-Order PD Controllers,” J. Chin. Inst. Eng., 29(2), pp. 241–249. [CrossRef]
Bonnet, C. , and Partington, J. R. , 2007, “ Stabilization of Some Fractional Delay Systems of Neutral Type,” Automatica, 43(12), pp. 2047–2053. [CrossRef]
Tavazoei, M. S. , and Haeri, M. , 2008, “ Stabilization of Unstable Fixed Points of Chaotic Fractional Order Systems by a State Fractional PI Controller,” Eur. J. Control, 14(3), pp. 247–257. [CrossRef]
Kheirizad, I. , Jalali, A. A. , and Khandani, K. , 2013, “ Stabilization of All-Pole Unstable Delay Systems by Fractional-Order [PI] and [PD] Controllers,” Trans. Inst. Meas. Control, 35(3), pp. 257–266. [CrossRef]
Muresan, C. I. , Ionescu, C. , Folea, S. , and De Keyser, R. , 2014, “ Fractional Order Control of Unstable Processes: The Magnetic Levitation Study Case,” Nonlinear Dyn., 80(4), pp. 1761–1772. [CrossRef]
Huang, H. P. , and Chen, C. C. , 1997, “ Control-System Synthesis for Open-Loop Unstable Process With Time Delay,” IEE Proc. Control Theory Appl., 144(4), pp. 334–346. [CrossRef]
Youla, D. C. , Bongiorno, J. J., Jr. , and Jabr, H. , 1976, “ Modern Wiener–Hopf Design of Optimal Controllers—Part I: The Single-Input-Output Case,” IEEE Trans. Autom. Control, 21(1), pp. 3–13. [CrossRef]
Freudenberg, J. S. , and Looze, D. P. , 1985, “ Right Half Plane Poles and Zeros and Design Trade-offs in Feedback Systems,” IEEE Trans. Autom. Control, 30(6), pp. 555–565. [CrossRef]
Freudenberg, J. , and Looze, D. P. , 1987, “ A Sensitivity Tradeoff for Plants With Time Delay,” IEEE Trans. Autom. Control, 32(2), pp. 99–104. [CrossRef]
Looze, D. P. , and Freudenberg, J. S. , 1991, “ Limitations of Feedback Properties Imposed by Open-Loop Right Half Plane Poles,” IEEE Trans. Autom. Control, 36(6), pp. 736–739. [CrossRef]
Xiang, C. , Wang, Q. G. , Lu, X. , Nguyen, L. A. , and Lee, T. H. , 2007, “ Stabilization of Second-Order Unstable Delay Processes by Simple Controllers,” J. Process Control, 17(8), pp. 675–682. [CrossRef]
Dambrine, M. , and Richard, J. P. , 1993, “ Stability Analysis of Time-Delay Systems,” Dyn. Syst. Appl., 2(3), pp. 405–414.
Walton, K. , and Marshall, J. E. , 1987, “ Direct Method for TDS Stability Analysis,” IEE Proc. Control Theory Appl., 134(2), pp. 101–107. [CrossRef]
Silva, G. J. , Datta, A. , and Bhattacharyya, S. P. , 2005, PID Controllers for Time-Delay Systems, Birkhauser, Boston, MA.
Garcia, C. E. , and Morari, M. , 1982, “ Internal Model Control. A Unifying Review and Some New Results,” Ind. Eng. Chem. Process Des. Dev., 21(2), pp. 308–323. [CrossRef]
Rivera, D. E. , Morari, M. , and Skogestad, S. , 1986, “ Internal Model Control: PID Controller Design,” Ind. Eng. Chem. Process Des. Dev., 25(1), pp. 252–265. [CrossRef]
Morari, M. , and Zafiriou, E. , 1991, Robust Process Control, Prentice-Hall, Englewood Cliffs, NJ.
Vilanova, R. , 2008, “ IMC Based Robust PID Design: Tuning Guidelines and Automatic Tuning,” J. Process Control, 18(1), pp. 61–70. [CrossRef]
Bettayeb, M. , and Mansouri, R. , 2014, “ Fractional IMC-PID-Filter Controllers Design for Non-Integer Order Systems,” J. Process Control, 24(4), pp. 261–271. [CrossRef]
Bettayeb, M. , and Mansouri, R. , 2014, “ IMC-PID-Fractional-Order-Filter Controllers Design for Integer Order Systems,” ISA Trans., 53(5), pp. 1620–1628. [CrossRef] [PubMed]
Huang, H. P. , and Chen, C. C. , 1999, “ Auto-Tuning of PID Controllers for Second Order Unstable Process Having Dead Time,” J. Chem. Eng. Jpn., 32(4), pp. 486–497. [CrossRef]
Rotstein, G. E. , and Lewin, D. R. , 1991, “ Simple PI and PID Tuning for Open-Loop Unstable Systems,” Ind. Eng. Chem. Res., 30(8), pp. 1864–1869. [CrossRef]
Shamsuzzoha, M. , and Lee, M. , 2008, “ Analytical Design of Enhanced PID Filter Controller for Integrating and First Order Unstable Processes With Time Delay,” Chem. Eng. Sci., 63(10), pp. 2717–2731. [CrossRef]
Lee, Y. , Lee, J. , and Park, S. , 2000, “ PID Controller Tuning for Integrating and Unstable Processes With Time Delay,” Chem. Eng. Sci., 55(17), pp. 3481–3493. [CrossRef]
Lee, Y. , Park, S. , Lee, M. , and Brosilow, C. , 1998, “ PID Controller Tuning for Desired Closed-Loop Responses for SI/SO Systems,” AIChE J., 44(1), pp. 106–115. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

IMC and conventional feedback control structures

Grahic Jump Location
Fig. 2

Two degrees-of-freedom control structure

Grahic Jump Location
Fig. 3

KM and Km of UFOPTD with G0 = 1 and T = 1

Grahic Jump Location
Fig. 4

b̂ of UFOPTD with G0 = 1 and T = 1

Grahic Jump Location
Fig. 7

Closed-loop step response for θ=1.2 and τc=3, with disturbance

Grahic Jump Location
Fig. 8

Closed-loop step response for θ=1.2 and τc=3, with white noise added to the output signal

Grahic Jump Location
Fig. 9

Closed-loop step response with 10% loop-gain variation for θ=1.2 and τc=3

Grahic Jump Location
Fig. 10

Closed-loop step response with 10% time constant variation for θ=1.2 and τc=3

Grahic Jump Location
Fig. 11

Closed-loop step response with 10% dead time variation for θ=1.2 and τc=3

Grahic Jump Location
Fig. 14

Closed-loop step responses with loop-gain variation: proposed method

Grahic Jump Location
Fig. 15

Closed-loop step responses with loop-gain variation: method proposed in Ref. [35]

Grahic Jump Location
Fig. 16

Closed-loop step responses with loop-gain variation: method proposed in Ref. [34]

Grahic Jump Location
Fig. 17

Closed-loop step responses with time constant variation: proposed method

Grahic Jump Location
Fig. 18

Closed-loop step responses with time constant variation: method proposed in Ref. [35]

Grahic Jump Location
Fig. 19

Closed-loop step responses with time constant variation: method proposed in Ref. [34]

Grahic Jump Location
Fig. 20

Closed-loop step responses with dead time variation: proposed method

Grahic Jump Location
Fig. 21

Closed-loop step responses with dead time variation: method proposed in Ref. [35]

Grahic Jump Location
Fig. 22

Closed-loop step responses with dead time variation: method proposed in Ref. [34]

Grahic Jump Location
Fig. 13

Closed-loop step responses with noise where θ=0.4 and τc=1

Grahic Jump Location
Fig. 12

Closed-loop step responses with θ=0.4 and τc=1

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In