Abstract
This paper solves the robust control problem of a plant with distributed delay using a reference model. The plant is subjected to bounded exogenous disturbances and the parameters of its mathematical model appear unknown. The author suggests a control algorithm for compensating the a priori parametric uncertainty and the bounded exogenous disturbances with a desired accuracy. A numerical example with corresponding simulation results is provided.
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Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Kharitonov, V.L., Asymptotic Stability of an Equilibrium Position of a Family of Systems of Linear Differential Equations, Differ. Uravn., 1978, vol. 14, no. 11, pp. 2086–2088.
Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B A., State-Space Solution to Standard H 2 and H ∞ Control Problems, IEEE Trans. Automat. Control, 1989, vol. 34, no. 8, pp. 831–847.
Nazin, S.A., Polyak, B.T., and Topunov, M.V., Rejection of Bounded Exogenous Disturbances by the Method of Invariant Ellipsoids, Autom. Remote Control, 2007, vol. 68, no. 3, pp. 467–486.
Polyak, B.T. and Topunov, M.V., Suppression of Bounded Exogenous Disturbances: Output Feedback, Autom. Remote Control, 2008, vol. 69, no. 5, pp. 801–818.
Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Synthesis of Control Laws Based on Linear Matrix Inequalities), Moscow: Fizmatlit, 2007.
Khlebnikov, M.V., Suppression of Bounded Exogenous Disturbances: A Linear Dynamic Output Controller, Autom. Remote Control, 2011, vol. 72, no. 4, pp. 699–712.
Balandin, D.V. and Kogan, M.M., Synthesis of a Suboptimal Controller by Output for Dampening Limited Disturbances, Autom. Remote Control, 2011, vol. 72, no. 4, pp. 677–683.
Park, P., A Delay-Dependent Stability for Systems with Uncertain Time-Invariant Delays, IEEE Trans. Automat. Control, 1999, vol. 44, pp. 876–887.
Zhang, W., Allgover, F., and Liu, T., Controller Parameterization for SISO and MIMO Plants with Delay, J. Process Control, 2006, vol. 55, no. 10, pp. 794–802.
Gao, H., Chen, T., and Lam, J., A New Delay System Approach to Network Based Control, Automatica, 2008, vol. 44, no. 1, pp. 38–52.
Ivanescu, D., Niculescu, S.I., Dugard, L., Dion, J.M., and Verriest, E.I., On Delay Dependent Stability of Neutral Systems, Automatica, 2003, vol. 39, no. 2, pp. 255–261.
Mishiels, W., Engelbarghs, K., Roose, D., and Dochain, D., Sensitivity to Infinitesimal Delays in Neutral Equations, SIAM J. Control Optim., 2002, vol. 40, no. 4, pp. 1134–1158.
Li, X.G., Zhu, X.J., Cela, A., and Reama, A., Stability Analysis of Neutral Systems with Mixed Delays, Automatica, 2008, vol. 44, no. 11, pp. 2698–2772.
Tsykunov, A.M., Robust Control Algorithms with Compensation of Bounded Perturbations, Autom. Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224.
Tsykunov, A.M., Adaptivnoe i robastnoe upravlenie dinamicheskimi ob”ektami po vykhodu (Adaptive and Robust Output Control for Dynamic Objects), Moscow: Fizmatlit, 2009.
Kolmanovskii, V.B. and Nosov, V.R., Ustoichivost’ i periodicheskie rezhimy reguliruemykh sistem s posledeistviem (Stability and Periodic Modes of the Controlled Systems with Aftereffect), Moscow: Nauka, 1981.
Khalil, H.K., Nonlinear Systems, New York: Prentice Hall, 1996, 2nd ed.
Brusin, V.A., On a Class of Singularly Perturbed Adaptive Systems, Autom. Remote Control, 1995, no. 4, part 2, pp. 552–559.
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Original Russian Text © A.M. Tsykunov, 2013, published in Problemy Upravleniya, 2013, No. 3, pp. 2–8.
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Tsykunov, A.M. Robust control of a plant with distributed delay. Autom Remote Control 76, 721–731 (2015). https://doi.org/10.1134/S0005117915040153
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DOI: https://doi.org/10.1134/S0005117915040153