Design of an H(lemniscate) PI controller with given relative stability and its application to the CSTR problem

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Vol 72, No 3
PDF (2,168 kB)
Published: Jun 5, 2018
DOI: https://doi.org/10.2298/HEMIND170529007D
Keywords:
H control, characteristics of H controller, low-order controllers, HPI controller, CSTR

Main Article Content

Ljubiša M. Dubonjić
Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac
Vojislav Ž. Filipović
Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac
Novak N. Nedić
Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac
Vladimir S. Đorđević
Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac

Abstract

H¥ control theory has achieved a very high level, which is not followed by appropriate application in industry. Some reasons are: synthesis of H¥ controllers is complex and based on the numerical Nevanlinna-Pick procedure, high order of controllers (higher than the order of the process) and sensitivity to deviation of controller coefficients (fragile controller). On the other hand, PI (PID) controllers are still dominant in industry, which places the problem of design of fixed structure controllers at the forefront. The mentioned problem is very difficult. This paper proposes a simple interactive procedure for design of H¥ PI controllers with the presence of constraints (given relative stability) based on D-decomposition. The catalogue of responses to references, suppression of disturbances and minimum of H¥ criteria of control is created. The selection of controllers, based on the catalogue, is left to the user. The application of H¥ PI controllers to a CSTR (continuous stirred-tank reactor) is demonstrated.

Article Details

How to Cite
[1]
L. M. Dubonjić, V. Ž. Filipović, N. N. Nedić, and V. S. Đorđević, “Design of an H(lemniscate) PI controller with given relative stability and its application to the CSTR problem”, Hem Ind, vol. 72, no. 3, pp. 115–127, Jun. 2018, doi: 10.2298/HEMIND170529007D.
Issue
Vol. 72 No. 3 (2018)
Section
Chemical Engineering - Simulation and Optimization
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Author Biography

Ljubiša M. Dubonjić, Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac

Katedra za automatsko upravljanje, robotiku i fluidnu tehniku.

How to Cite

[1]
L. M. Dubonjić, V. Ž. Filipović, N. N. Nedić, and V. S. Đorđević, “Design of an H(lemniscate) PI controller with given relative stability and its application to the CSTR problem”, Hem Ind, vol. 72, no. 3, pp. 115–127, Jun. 2018, doi: 10.2298/HEMIND170529007D.
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References

Bode HW. Network Analysis and Feedback Amplifier Design, Van Nostrand, Princeton, 1945.

Horowitz IM. Synthesis of Feedback Systems. Academic Press, London, 1963.

Bellman R. Dynamic Programming. Princeton University Press, Princeton, 1957.

Pontryagin LS, Boltyanski VG, Gamkerelidze RV, Mischenko EF. Mathematical Theory of Optimal Processes. Nauka, Moskow, 1969. (in Russian)

Zhou K, Doyle JC, Glover K. Robust and Optimal Control. Prentice-Hall, New Jersey, 1996.

Boltyanski VG, Poznyak AS. The Robust Maximum Principle. Theory and Applications. Birkhauser, Basel, 2010.

Francis BA. A Course in H Control Theory. Springer, Berlin, 1987.

Doyle JC, Francis BA, Tannenbaum AR. Feedback Control Theory. New York, Macmillan Publishing Company, 1992.

Zhou K, Doyle JC. Essentials of Robust Control. Prentice Hall, New Jersey, 1998.

Duren PL. Theory of Hp Spaces. New York, Academic Press, 1970.

Nevanlinna R. Über beschränkte Funktionen, die in gegebenen punkten vorgescriebene Werte annehmen. Ann Acad Sci Fenn Ser A I Math. 1919; 13(1). (in German)

Pick G. Über Beschrankungen analytischer Funktionen, welche durch vorgegebenen Funktionswerte bewirkt sind. Math Ann 1916; 77: 7-23. (in German)

Yang GH, Guo XG, Che WW, Guan W. Linear Systems: Non-Fragile Control and Filtering. Boca Raton, CRC Pres, 2013.

Panagopoulos H, Astrom KJ,. PID control design and H loop shaping. Int J Robust Nonlin Control 2000; 10: 1249-1261.

Vinnicombe G. Uncertainty and Feedback-H loop shaping and the ν-gap metric. London, Imperial College Press, 2001.

Tsakalis KS, Dash S. Approximate H loop shaping in PID parameter adaption. Int J Adapt Control Signal Process. 2013; 27: 136-152.

Mercader P, Astrom KJ, Banos A, Hagglund T. Robust PID design based on QFT and convex-concave optimization. IEEE Trans Control Syst Technol 2017; 25: 441-452.

Horowitz IM. Some ideas for QFT research. Int J Robust Nonlin Control 2003; 13: 599-605.

Yaniv O, Nagurka M. Automatic loop shaping of structured controllers satisfying QFT performance. J Dyn Syst Meas Control 2005; 127: 472-477.

Boyd S, Vandenberghe L. Convex Optimization. Cambridge, Cambridge University Press, 2004.

Neimark YI. (1948) Search for the parameter values that make automatic control system stable. Automatica i Telemekhanika. 1948; 9(3):190–203 (in Russian).

Mitrović D. Graphical analysis and synthesis of feedback control systems. I-Theory and analysis, II-Synthesis, III-Sampled-data feedback control systems, IEEE Trans Ind Appl 1959; 77: 476–496.

Šiljak D. Analysis and synthesis of feedback control systems in the parameter plane. I-Linear continuous systems, II-Sampled-data systems, IEEE Trans Ind Appl 1964; 83: 449–466.

Dubonjić LJ, Nedić N, Filipović V, Pršić D. Design of PI controllers for hydraulic control systems. Math Probl Eng 2013; 2013: 1–10.

Prodanović S, Nedić N, Filipović V, Dubonjić LJ. Modified approach to distillation column control. Hem Ind 2017; 71(3):183-193.

Bhattacharyya SP, Datta A, Keel LH. Linear Control Theory: Structure, Robustness and Optimality. Boca Raton, CRC Press, Taylor & Francis Group, 2009.

Kiselev ON, Polyak BT. Design of law order controllers with H or maximal robustness performance index. Autom Remote Control 1999; 34: 393-402.

Stephanopulos G. Chemical Process Control: An Introduction to Theory and Practice. New Jersey, Prentice-Hall, 1984.

Henson MA, Seborg DE. Input-output line optimization of general nonlinear processes. AIChE J 1990; 36: 1753-1757.

Huang CT, Chon CJ, Wang JL. Tuning of PID controllers based on the second-order model by calculation. J Chin Inst Chem Eng 1996; 27: 107–120.

Ghaffari V, Naghavi VS, Safavi AA. Robust model predictive control of a class of uncertain nonlinear systems with application to typical CSTR problems, J Proc Control 2013; 23: 493-499.

Zhang B, Mao Z. Robust adaptive control of Hammerstein nonlinear systems and its application to typical CSTR problems. Int J Adapt Control Signal Process 2017; 31: 163-190.

Filipović V. Industrial Controllers, Kraljevo, University of Kragujevac, 2016. (in Serbian).

Schmidt LD. The Engineering of Chemical Reactions. Oxford, Oxford University Press, 1998.

Bequette BW. Process Dynamics Modeling, Analysis and Simulation. New Jersey, Prentice-Hall, 1998.

Jana AK. Nonlinear state estimation and model control of a continuous stirred tank reactor. IJCRE 2007; 5: 1-15.

Makila PM, Partington JR. Laguerre and Kautz shift approximation of delay systems. Int J Control 1999; 72: 932-946.

Normey-Rico JE, Camacho EF. Control of Dead-Time Processes. Berlin, Springer, 2007.

Landau ID, Zito G. Digital Control System, Design, Identification and Implementation. Berlin, Springer, 2006.

Astrom KJ. Limitations on control systems performance. Eur J Control 2000; 6: 2-20.

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