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Constructing quasi-invariant control systems based on the Lyapunov function method for nonlinear plants with an incomplete mathematical model

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Abstract

The problem of constructing feedback control systems for one-dimensional plants with incomplete mathematical models and known structures is studied. A quadratic form decomposable into linear multipliers used as the Lyapunov function helps decompose the control into two components viz. the Utkin-Drazhenovich equivalent control and the stabilizing control. A condition used to find the stabilizing control is given. An equation involving the observation error is obtained. The equation is used to derive the estimation formula for the nonlinearity and external perturbation. The high estimation accuracy and the feasible unlimited increase of the gain coefficients of the controller and observer without breaking the system’s stability ensure the high performance and tracking accuracy of the reference trajectory. Model stabilization problems are solved in Matlab/Simulink.

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Authors and Affiliations

  1. Azerbaijan Technical University, pr. G. Dzhavida 25, Baku, Az-1073, Azerbaijan

    G. A. Rustamov

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  1. G. A. Rustamov
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Correspondence to G. A. Rustamov.

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Original Russian Text © G.A. Rustamov, 2012, published in Avtomatika i Vychislitel’naya Tekhnika, 2012, No. 3, pp. 5–14.

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Rustamov, G.A. Constructing quasi-invariant control systems based on the Lyapunov function method for nonlinear plants with an incomplete mathematical model. Aut. Conrol Comp. Sci. 46, 95–102 (2012). https://doi.org/10.3103/S0146411612030078

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  • DOI: https://doi.org/10.3103/S0146411612030078

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