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

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

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