Б. О. Джолдошева из Института автоматики и информационных технологий нан кр, г. Бишкек; «Cинтез кибернетических автоматических систем с использованием эталонной модели»
THE ANALYSIS OF ROBUST STABILITY OF CONTROL SYSTEMS
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| THE ANALYSIS OF ROBUST STABILITY OF CONTROL SYSTEMS
BASED ON METHOD OF FUNCTION A.M. LYAPUNOV L.G. Abdrakhmanova L.N. Gumilyov Eurasian national university E-mail: leila2186@mail.ru The analysis of stability of the systems of control with the presence of uncertainty in the parameter spaces (robust theory) is completely important and urgent direction in the theory of control [1, 2]. The general formulation of investigating the system for the robust stability consists of the indication of limitations to a change in the parameters of control system, with which remains the stability. Is proposed the procedure of a study of robust stability based on the geometric interpretation of the direct method of Lyapunov and gradient nature of dynamic systems with respect to a certain potential function of dynamic system [3] assigned in space of states. Assume that control system is assigned by equation of state (1) Regulator is described by the equation: Let us assume that , and then we can represent equations (1) in the expanded form: (2) From a geometric point of view the stability analysis according to the second method of Lyapunov is reduced to the construction of the family of the closed surfaces, which surround the beginning of coordinates and possessing themes to properties, that the integral curves can intersect each of these surfaces, then by this will be immediately established the stability of the undisturbed motion [4, 5]. Let us assume that there is a positively determined Lyapunov’s function , for which the ant gradient it is assigned by velocity vector (vector by the function of right side) the equation of state of system i.e. (3) Complete time derivative of Lyapunov's vector function it is defined as the scalar product of the gradient of the Lyapunov functions, to the velocity vector i.e. (4) Lyapunov's vector function is represented in the form: (5) The obtained results make it possible to obtain the condition of the over stability of the matrix of closed system (1), for example for the system of the second order: A radius of the robust stability of the system of the second order is determined on the basis of the obtained results, if the parameters of system have uncertainties. Literature: [1] Siljak D.D. Parameter space methods for robust control design: a guided tour // IEEE Tr. On Autom. Control. 1989. 34. № 7. P. 674-688. [2] Polyak B.T., Shcherbakov P.S. Robust stability and control. M.: Science, 2002. 303 p. [3] Gilmore R. The theory of the catastrophes. M.: World, Vol.1, 1981. 344 p. [4] Malkin I.G. Theory of stability of motion. M.: Science, 1966. 540 p. [5] Barbashin E.A. Introduction into the theory of the stability. M.: Science, 1967. 225 p. жүктеу/скачать 28,25 Mb. Достарыңызбен бөлісу:
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