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Parametric Synthesis of a Robust Controller for Maximising the Response of an Interval Control System


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DOI: https://doi.org/10.15866/ireaco.v15i2.20560

Abstract


This paper presents a solution to the problem of the parametric synthesis of a robust controller that ensures maximum control response. Since the stability of a linear system determines its response time, the root approach and the criterion of the maximum stability degree are put forward to solve the above-mentioned task. As a method for the parametric synthesis of a controller, the coefficient method that uses interval coefficients of a characteristic polynomial of a system is chosen. Based on obtained sufficient conditions, the methodology of the parametric synthesis of a linear controller is developed. The designed controller can provide the quasi-maximum robust stability degree in the system subject to certain constraints on its oscillativity and minimum acceptable quality factor. The main contribution of this paper is to develop systems of inequalities for third-order interval control systems with a PI-controller for various constraints. The graphical solution to these inequalities allows finding optimal parameterizations of the controller. To validate the obtained theoretical result, the parametric synthesis of a robust PI-controller for third-order control systems at different limits is performed.Parametric Synthesis of a Robust Controller for Maximisingthe Response of an Interval Control System
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Keywords


Parametric Synthesis; Maximum Stability Degree; Coefficient Method; Robust Controller; Interval Characteristic Polynomial; Interval Control Systems

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References


B.N. Petrov, N.I. Sokolov, A.V. Lipatov, Automated control systems for objects with uncertain parameters: Engineering methods of analysis and synthesis (Mashinostroyeniye, 1986).

J. Ackermann, Parameter space design of robust control systems, IEEE Transactions on Automatic Control, Vol. 25 (Issue 6):1058-1072, December 1980.
https://doi.org/10.1109/TAC.1980.1102505

N.P. Petrov, B.T. Polyak, Robust D-partition, Automation and Remote Control, Vol. 11: 41-53, November 1991.

D.S. Bernstein, W.M. Haddad, Robust controller synthesis using Kharitonov's theorem, IEEE Transactions on Automatic Control, Vol. 37(Issue 1): 129 - 132, January 1992.
https://doi.org/10.1109/9.109648

B. Shafai, M. Monaco, M. Milanese, Robust control synthesis using generalized Kharitonov's theorem, 31st Conference on Decision and Control, pp. 659-661, Tucson, Arizona, December 1992.

Y. Tong, N.K. Sinha, A computational technique for the robust root locus, IEEE Transactions on Industrial Electronics, Vol. 41(Issue 1): 79 - 85, February 1994.
https://doi.org/10.1109/41.281611

C.-T. Chen, M.-D. Wang, Robust controller design for interval process systems, Computers and Chemical Engineering, Vol. 21(Issue 7): 739-750, 1997.
https://doi.org/10.1016/S0098-1354(96)00302-X

S. Malan, M. Milanese, M. Taragna, Robust Analysis and Design of Control Systems Using Interval Arithmetic, Automatica, Vol. 33(Issue 7):1363-1372, July 1997.
https://doi.org/10.1016/S0005-1098(97)00028-9

T.S. Cho, S.W. Choi, Y.C. Kim, Robust design of PID controller for interval plants, SICE Annual Conference, pp. 933-936, Morioka, Japan, July 1999.

A.A. Nesenchuk, Parameter synthesis of interval control systems using root loci of Kharitonov's polynomials, European Control Conference, pp. 182-187, Karlsruhe, Germany, August 1999.
https://doi.org/10.23919/ECC.1999.7099296

Ye. Smagina, I. Brewer, Using interval arithmetic for robust state feedback design, Systems and Control Letters, Vol.46(Issue 3):187-194, July 2002.
https://doi.org/10.1016/S0167-6911(02)00132-9

Y. Wang, T. Schmitt-Hartmann, K.J. Hunt, PID and PID-like controller design by pole assignment within D-stable regions, Asian Journal of Control, Vol. 4(Issue 4): 423-432, December 2002.
https://doi.org/10.1111/j.1934-6093.2002.tb00083.x

C. Hwang, S. Yang, Plotting robust root locus for polynomial families of multilinear parameter dependence based on zero inclusion/exclusion tests, Asian Journal of Control, Vol. 5(Issue 2): 293-300, June 2003.
https://doi.org/10.1111/j.1934-6093.2003.tb00120.x

O.S. Vadutov, S.A. Gaivoronski, Solving the problem of allocation of poles of a system using the D-partition method, Journal of Computer and Systems Sciences International, Vol. 43(Issue 5): 681-685, September 2004.

B.M. Patre, P.J. Deore, Robust PI controller design for an uncertain recycle system, Systems Science, Vol.31 (Issue 4): 2386 - 2390, 2005.

F. Morilla, F. Ázquez, R Hernández, PID control design with guaranteed stability, IFAC-PapersOnline, Vol. 7 (Issue 1): 13-18, 2006.
https://doi.org/10.3182/20060621-3-ES-2905.00004

S.A.Gayvoronskiy, I.V. Khozhaev, T.A. Ezangina, Motion control system for a remotely operated vehicle with interval parameters, International Journal of Mechanical Engineering and Robotics Research, Vol. 6 (Issue 5): 378-384, September 2017.
https://doi.org/10.18178/ijmerr.6.5.378-384

A.A. Nesenchuk, S.M. Fedorovich, Parametric synthesis method of integral systems on the basis of root locus curves of Kharitonov polynomials, Automation and Remote Control, Vol. 69 (Issue 7): 1133-1141, July 2008.
https://doi.org/10.1134/S0005117908070047

E.N. Gryazina, B.T. Polyak, A.A., Tremba. D-decomposition technique state-of-the-art, Automation, and Remote Control, Vol.69 (Issue 12): 1991-2026, December 2008.
https://doi.org/10.1134/S0005117908120011

C. Hwang, L.F. Hwang, J.H. Hwang, Robust D-partition, Journal of the Chinese Institute of Engineers, Vol.33 (Issue 6): 811-821, 2010.
https://doi.org/10.1080/02533839.2010.9671671

M.G. Zotov, An approach to robust control design, Automation and Remote Control, Vol.71(Issue 11): 2395-2404, November 2010.
https://doi.org/10.1134/S0005117910110111

A.A. Nesenchuk, The root-locus method of synthesis of stable polynomials by adjustment of all coefficients, Automation and Remote Control, Vol. 71(Issue 8): 1515-1525, August 2010.
https://doi.org/10.1134/S0005117910080023

S. Gayvoronskiy, T. Ezangina, I. Khozhaev, Analysis and synthesis of dual mode control systems of a tethered descent undersea vehicle, OCEANS 2016 - Shanghai, article number 7485341, Shanghai, China, April 2016.
https://doi.org/10.1109/OCEANSAP.2016.7485341

S.A. Gayvoronskiy, I.V. Khozhaev, T.A. Ezangina, Method of interval system poles allocation based on domination principle, 2017 International Conference on Mechanical, System and Control Engineering (ICMSC 2017), pp. 245-249, St. Petersburg, Russian Federation, May 2017.
https://doi.org/10.1109/ICMSC.2017.7959480

M. Kwon, H.-J. Chang, Extended root-locus technique applied to pole-placement for PI controller design, UKACC International Conference on Control (UKACC Control), article number 7737535, Queen's University Belfast, United Kingdom, November 2016.
https://doi.org/10.1109/CONTROL.2016.7737535

M. Kwon, H.-J. Chang, PI controller design method by an extension of root-locus technique, Journal of Institute of Control, Robotics and Systems, Vol. 22(Issue 2): 126-132, January 2016.
https://doi.org/10.5302/J.ICROS.2016.15.0178

A. Doria-Cerezo, M. Bodson, Design of Controllers for Electrical Power Systems Using a Complex Root Locus Method, IEEE Transactions on Industrial Electronics, Vol. 63(Issue 6): 3706-3716, June 2016.
https://doi.org/10.1109/TIE.2016.2521599

S.P. Bhattacharyya, Robust control under parametric uncertainty: Overview and recent results, Annual Reviews in Control, vol.44:45-77, 2017.
https://doi.org/10.1016/j.arcontrol.2017.05.001

Z. Gao, L.-R. Zhai, Y.-D. Liu, Robust stabilizing regions of fractional-order PIλ controllers for fractional-order systems with time-delays, International Journal of Automation and Computing, Vol. 14(Issue 3): 340-349, June 2017.
https://doi.org/10.1007/s11633-015-0941-7

Y.-C.Si, C.-K. Xie, N. Zhao, Boundary control for a class of reaction-diffusion systems, International Journal of Automation and Computing, Vol. 15(Issue 1): 94-102, February 2018.
https://doi.org/10.1007/s11633-016-1012-4

M. Yagoubi, A Linear Quadratic Controller Design Incorporating a Parametric Sensitivity Constraint, International Journal of Automation and Computing, Vol. 16(Issue 4): 553-562, August 2019.
https://doi.org/10.1007/s11633-016-1048-5

A.N. Volkov, Y.V. Zagashvili, A method of synthesis of automatic control systems with maximum stability degree under constraints, Journal of Computer and Systems Sciences International, Vol.36(Issue 3): 338-345, 1997.

A.M. Shubladze, S.V. Gulyaev, T.I. Shchokina, High-speed PI and PID control systems with the maximum level of stability, Instruments and Systems: Monitoring, Control, and Diagnostics, Vol. 3: 16-18, 2001.

Y.V. Zagashvili, Account for requirements on performance indices in synthesizing control systems with a maximum degree of stability, Journal of Computer and Systems Sciences International, Vol. 41(Issue 2): 191-194, March 2002.

D.P. Kim, A condition for boundary stability and synthesis of control systems with the maximal stability degree, Journal of Computer and Systems Sciences International, Vol.42(Issue 4): 499-502, July 2003.

D.P. Kim, Synthesis of systems with maximum robust degree of stability, Journal of Computer and Systems Sciences International, Vol.46(Issue 5): 721-725, October 2007.
https://doi.org/10.1134/S106423070705005X

I. Fiodorov, Synthesis algorithms of controllers for automatic control systems with maximum stability degree, Annals of the University of Craiova, Electrical Engineering series, Vol.37:139-143, 2013.

I. Fiodorov, B. Izvoreanu, I. Cojuhari, Synthesis of robust PID controller by the maximum stability degree criterion, 20th International Conference on Control Systems and Computer Science (CSCS), pp. 57-64, Bucharest, Romania, July 2015.
https://doi.org/10.1109/CSCS.2015.68

I. Fiodorov, I. Cojuhari, B. Izvoreanu, D. Moraru, S. Botnaru, R. Melnic, The experimental method for tuning of PID controller based on the maximum stability degree criterion, 14th International Conference on Development and Application Systems (DAS), pp. 47-52, Suceava, Romania, June 2018.
https://doi.org/10.1109/DAAS.2018.8396069

M. A. Aizerman, Theory of Automatic Control (Elsevier, 1963).

A. Petrovas, R. Rinkevičienė, Automatic Control Theory I, II: A Laboratory Manual (Technika, 2012).
https://doi.org/10.3846/1335-S

Dobroskok, N., Vtorov, V., On the Problem of Robust Assignment of Dynamic System Poles, (2021) International Review of Automatic Control (IREACO), 14 (4), pp. 179-190.
https://doi.org/10.15866/ireaco.v14i4.20904

Varghese, E., Dasgupta, S., Savier, J., Robust Fractional Order Attitude Controller for Launch Vehicle with Flexible Dynamics, (2021) International Review of Automatic Control (IREACO), 14 (2), pp. 85-92.
https://doi.org/10.15866/ireaco.v14i2.20565

Gayvoronskiy, S., Ezangina, T., Pushkarev, M., Khozhaev, I., Parametrical Synthesis of Linear Controllers in Aperiodical Systems on Basis of Decomposition Approach, (2019) International Review of Automatic Control (IREACO), 12 (4), pp. 192-199.
https://doi.org/10.15866/ireaco.v12i4.16401


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