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On the Problem of Robust Assignment of Dynamic System Poles

Nikita Dobroskok(1*), Victor Vtorov(2)

(1) Saint-Petersburg Electrotechnical University “LETI”, Russian Federation
(2) Saint-Petersburg Electrotechnical University “LETI”, Russian Federation
(*) Corresponding author


DOI: https://doi.org/10.15866/ireaco.v14i4.20904

Abstract


For a linear time-invariant single-input system with a linear inertia-free state feedback, a problem of such assignment of poles, in which bounded parametric perturbations do not bring these poles outside a certain region is considered. A generalization of the well-known solution to this problem, based on Rouche's theorem and assuming that the structure of system and the input matrices meet the consistency conditions, to linear control systems with matrices of an arbitrary form is proposed. A special parameter is introduced, on the value of which the fulfilment of the conditions of Rouche's theorem, the shape of the pole scatter region, its "volume" and the minimum attainable root measures of the dynamics performance depend. The relationship between the width of parametric uncertainty intervals and the minimum required value of the geometric mean root of the characteristic polynomial of a system with a modal controller is revealed. An example of application of the proposed technique and a computer program developed on its basis in the MATLAB language for the synthesis of a modal controller for an electromechanical system is given.
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Keywords


Modal Control; Parametric Uncertainty; Robust Pole Assignment; Rouché's Theorem; Standard Polynomials; Pole Scatter Region

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References


D. N. Gerasimov and V. O. Nikiforov. Simple adaptive output control of linear systems, 2014 IEEE International Symposium on Intelligent Control (ISIC), Juan Les Pins, France, 2014, pp. 566-571.
https://doi.org/10.1109/ISIC.2014.6967606

B. Sayyarrodsari, J. P. How and A. Carrier. Robust adaptive control of linear systems with constant uncertain parameters, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), Albuquerque, NM, USA, 1997, pp. 2376-2378 vol.4.
https://doi.org/10.1109/ACC.1997.609111

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

Chursin, Y., Sonkin, D., Sukhodoev, M., Nurmuhametov, R., Pavlichev, V., Control System for an Object with Interval-Given Parameters: Quality Analysis Based on Leading Coefficients of Characteristic Polynomials, (2018) International Review of Automatic Control (IREACO), 11 (4), pp. 203-207.
https://doi.org/10.15866/ireaco.v11i4.15727

Hedayati, M., Bashi, S., Mariun, N., Hizam, H., A Short Review of Different Optimal H∞ Robust FACTS Controller Designs, (2018) International Journal on Engineering Applications (IREA), 6 (6), pp. 187-195.
https://doi.org/10.15866/irea.v6i6.16996

Mekki, I., Bouhamida, M., Saad, M., Robust Control of a Chemical Multivariable System in the Presence of Strong Uncertainties in the Model Parameters, (2018) International Review of Automatic Control (IREACO), 11 (4), pp. 166-173.
https://doi.org/10.15866/ireaco.v11i4.13886

H. Khallouk and F. Mesquine, Regional Pole Assignment for Constrained Input Uncertain Systems, 2018 7th International Conference on Systems and Control (ICSC), 2018, pp. 294-299.
https://doi.org/10.1109/ICoSC.2018.8587782

B. T. Polyak, M. V. Khlebnikov, P. S. Shcherbakov. An LMI approach to structured sparse feedback design in linear control systems, 2013 European Control Conference (ECC), 2013, pp. 833-838.
https://doi.org/10.23919/ECC.2013.6669578

G. G. Koch, C. R. D. Osório, H. Pinheiro, R. C. L. F. Oliveira and V. F. Montagner, Design Procedure Combining Linear Matrix Inequalities and Genetic Algorithm for Robust Control of Grid-Connected Converters, IEEE Transactions on Industry Applications, vol. 56, no. 2, pp. 1896-1906, March-April 2020.
https://doi.org/10.1109/TIA.2019.2959604

A. N. Parshukov. Synthesis method of modal regulator for control object with interval uncertainty of coefficients, Vestnik Tomskogo Gosudarstvennogo Universiteta - Upravlenie, Vychislitel'naya Tekhnika i Informatika [Tomsk State University Journal of Control and Computer Science], Vol 49, pp 14 - 22, 2019.
https://doi.org/10.17223/19988605/49/2

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

S. A. Gayvoronskiy, T. Ezangina, I. Khozhaev. Robust Controllers Synthesis and Order Reduction of Unmanned Underwater Vehicle Submerging Control System with Interval Parametric Uncertainty, IFAC-PapersOnLine, Volume 52, Issue 21, 2019, Pages 224-229.
https://doi.org/10.1016/j.ifacol.2019.12.311

E. Dincel, M. T. Söylemez. Robust PID controller design via dominant pole assignment for systems with parametric uncertainties, Asian Journal of Control, 2020, pp. 1-11.
https://doi.org/10.1002/asjc.2484

Q. Wang, ZG Wu. Robust Output Feedback Control for Input-Saturated Systems Based on a Sliding Mode Observer. Circuits Syst Signal Process 40, 2267-2281 (2021).
https://doi.org/10.1007/s00034-020-01584-7

I. Korobiichuk, O. Lobok, B. Goncharenko, N. Savitskaya, M. Sych, L. Vihrova. (2020) Using Linear Matrix Inequalities for Synthesis of Modal Control of Multidimensional Linear Systems. Mechatronics 2019: Recent Advances Towards Industry 4.0. MECHATRONICS 2019. Advances in Intelligent Systems and Computing, vol 1044. Springer, Cham.
https://doi.org/10.1007/978-3-030-29993-4_3

A. A. Anisimov, Method of Robust Control for Mechatronic Systems with Digital State Controllers and Observers, 2018 X International Conference on Electrical Power Drive Systems (ICEPDS), 2018, pp. 1-5.
https://doi.org/10.1109/ICEPDS.2018.8571592

A. A. Anisimov, S. V. Tararykin, Peculiarities of synthesis of parametrically robust modal control system with state observers. J. Comput. Syst. Sci. Int. 51, 617-627 (2012).
https://doi.org/10.1134/S1064230712040028

S. V. Tararykin, A. A. Anisimov and A. A. Gerasimov, Synthesizing Parametrically Robust Control Systems with State Controllers and Observers Based on Gramian Method. Int. J. Control Autom. Syst. 17, 2490-2499 (2019).
https://doi.org/10.1007/s12555-018-0382-5

M. Ait Rami, S. El Faiz, A. Benzaouia and F. Tadeo, Robust Exact Pole Placement via an LMI-Based Algorithm, IEEE Transactions on Automatic Control, vol. 54 (Issue. 2), pp. 394-398, Feb. 2009.
https://doi.org/10.1109/TAC.2008.2008358

A. Varga, Robust pole assignment techniques via state feedback, Proceedings of the 39th IEEE Conference on Decision and Control, 2000, pp. 4655-4660 vol.5.

N. T. Kuzovkov, Modal control and observing devices (Mashinostroenie, 1976).

R.C. Dorf, R.H. Bishop, Modern Control Systems (Basic Knowledge Laboratory, 2002)

G. Garcia and J. Bernussou, Pole assignment for uncertain systems in a specified disk by state feedback, IEEE Transactions on Automatic Control, vol. 40 (Issue. 1), pp. 184-190, Jan. 1995.
https://doi.org/10.1109/9.362872

A. W. Olbrot, Arbitrary robust eigenvalue placement by a static state feedback, IEEE Transactions on Automatic Control, Vol. 41 (Issue 8). 1214-1215, August 1996
https://doi.org/10.1109/9.533688

V.B. Vtorov, Ch. Xiao, On the problem of robust assignment of poles of a dynamical system, Izvestia 'LETI', Automation and control series, Vol. 1, 29-35, June 2004.

B.R. Andrievsky, A.A. Bobtsov, A.L. Fradkov, Methods of Analysis and Synthesis of Nonlinear Control Systems (Institute for Computer Research, 2018).

Nikita Dobroskok (2021). Robust assignment of dynamic system poles (example)MATLAB Central File Exchange. Retrieved May 26, 2021.
(https://www.mathworks.com/matlabcentral/fileexchange/92995-robust-assignment-of-dynamic-system-poles-example)

El Hansali, H., Bennani, M., H-Infinity Control of a Six-Legged Robot in Lifting Mode, (2021) International Review of Electrical Engineering (IREE), 16 (2), pp. 174-182.
https://doi.org/10.15866/iree.v16i2.18690

Kahouli, A., Guesmi, T., Hadj Abdallah, H., Abderrazak, O., Fuzzy Control Approach for Monomachine Power Systems, (2019) International Journal on Engineering Applications (IREA), 7 (5), pp. 179-187.
https://doi.org/10.15866/irea.v7i5.18408


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