Stability of Nonstationary Automatic-Control Systems of Variable Structure in Forced Motion

Matviichuk, K. S.

doi:10.1023/b:inam.0000010376.69311.6d

Cited by 5 publications

(7 citation statements)

References 8 publications

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“…При этом, параметры гиперплоскости переключения остаются постоянными. Предложенный подход изучения технической устойчивости заданных систем с переменной структурой не связывается с условиями существования скользящего режима на границе переключений в фазовом пространстве [1,3,5,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Построены условия технической неустойчивости по мере заданного процесса автоматического фильтрованного управления с использованием свойств систем сравнения снизу [5,10,15, 17-21, 23,].…”

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Conditions of technical stability on non-stationary processes of automatic control of variable structure with correlative forming and filtering systems of control signals.

Matviychuk¹

2012

Mechanics - Proceedings of National Academy of Sciences of Armenia

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Ключевые слова: техническая устойчивость и неустойчивость систем, нестационарные системы автоматического управления с переменной структурой, коммутируемые фильтры сигналов, метод дифференциальных неравенств, нормированные функции Ляпунова, системы сравнения. Key words: technical stability and instability of the systems, non-stationary control systems with variable structure, switched filters of the signals, method of differential inequalities, Lyapunov's normalized functions, systems of comparison. Մատվիյչուկ Կ.Ս. Փոփոխական կառուցվածքով ավտոմատ ղեկավարման փոխկապակցված ձևավորող և ֆիլտրող ղեկավարող ազդանշանների ենթահամակարգերով ոչ ստացիոնար համակարգերի դինամիկ վիճակների տեխնիկական կայունության պայմանները Հետազոտվում են փոփոխական կառուցվածքով ավտոմատ ղեկավարման ոչ ստացիոնար համակարգերի դինամիկ վիճակների ըստ չափի տեխնիկական կայունության հատկությունները ղեկավարող ազդանշանների ֆիլտրացիայի առկայությամբ: Համապատասխան դիֆերենցիալ հավասարումները պարունակում են թռիչքաձև փոփոխվող գործակիցներ: Փոփոխական կառուցվածքով ավտոմատ ղեկավարման ոչ ստացիոնար համակարգերի տարբեր տիպի ըստ չափի տեխնիկական կայունության հայտանիշները ստացված են դիֆերենցիալ անհավասարությունների մեթոդի և որոշակի դրական ֆունկցիաների դասի հատկությունների զուգորդմամբ Matviychuk K.S. Conditions of Technical Stability on Non-Stationary Processes of Automatic Control of Variable Structure with Correlative Forming and Filtering Systems of Control Signals The conditions of technical stability by measure of the dynamical states of the non-stationary control systems with variable structure are investigated in presence of filtration process of the control signals. The suitable systems of the differential equations have the changing coefficients, which are altering in time and by jumplike together with jumplike changing of the control function of the process and with simultaneous jumplike changing at the direction of the suitable phase velocity vector of the process. The criteria of technical stability by measure on finite and infinite intervals of time, asymptotical technical stability by measure, and also the criterion of the technical instability by measure of given, inwardly dependent on quality of filtering of control signals of non-stationary dynamical systems with variable structure are determiner under base of the differential inequalities method at combination with properties of the class of the absolutely positive functions, for all feasible initial disturbances from the pre-assigned by measure set of initial states of the process. Исследуются свойства технической устойчивости по мере динамических состояний нестационарных систем автоматического управления с переменной структурой при наличии процессов фильтрации управляющих сигналов. Соответствующие системы дифференциальных уравнений содержат переменные коэффициенты, изменяющиеся во времени и скачкообразно совместно со скачкообразным изменением функции управления процесса и с одновременным скачкообразным изменением направления соответствующего вектора фазовой скорости этого процесса. Критерии технической устойчивос...

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Conditions of technical stability on non-stationary processes of automatic control of variable structure with correlative forming and filtering systems of control signals.

Matviychuk¹

2012

Mechanics - Proceedings of National Academy of Sciences of Armenia

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“…The approach proposed here for the stability analysis of such variable-structure systems is based on the existence conditions for the sliding mode at the switching boundary in the phase space [1][2][3][4]. Error gain is used for stabilization purposes [5,17]. The established stability criteria are applied to a nonstationary filtered-control system of variable structure of the third order.…”

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confidence: 99%

“…The established stability criteria are applied to a nonstationary filtered-control system of variable structure of the third order. The study is based on the results from [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

mentioning

confidence: 99%

“…Condition (5), on the one hand, leads to closed-form equations of motion in the form (1), (2) [5,17,18] and, on the other hand, is one of the possible approximations for a linear combination of the external action function f and its derivatives of finite order in the form of a linear combination of the function g (controller input) and its derivatives up to the nth order [1,8,20].…”

mentioning

confidence: 99%

“…At fixed C and m -1 , arbitrary time intervals T h , h ³ 0, are defined as in [16][17][18], where T T 0 = for h = 0 and T I ¥ = as h = +¥. The notation that will not be explained below is the same as in [16][17][18].…”

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confidence: 99%

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Stability in sliding mode of nonstationary automatic-control systems of variable structure with switched filters

Matviichuk

2006

Int Appl Mech

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Stability conditions for a nonstationary automatic-control system of variable structure in sliding mode are established. The controller of the system has feedback-switched filters functioning together with the shaper and actuator. The nonstationary parameters of the system vary within given ranges, at a finite rate, under appropriate control laws, with adjustment for the error signal, its derivatives of finite order, and all variable parameters of the filter. The parameters of the switching hyperplane remain constant. This approach to stability analysis is based on the existence conditions for the sliding mode at the switching boundary in the phase space. The general stability and instability criteria are applied to nonstationary automatic filtered-control systems of variable structure of the third order Keywords: nonstationary automatic-control systems of variable structure, switched filters, sliding mode, stability and instability, error gain, nonstationary filtered-control system of variable structure of the third order Introduction. Filtered-control systems of variable structure are important, in particular, for solving practical problems in flight automation and automatic control of surface and subsurface ships, in various nonstationary filtration of program automatic control signals to reject artificial or natural interference, and in dynamic elastic processes and objects that should be controlled taking the time-dependence of their parameters into account [5, 10, 11, etc.]. The nonstationary parameters of the variable-structure system under consideration vary within given ranges, at a finite rate, under appropriate control laws, and with adjustment for the error signal, its derivatives of finite order, and all independent variable parameters of the filter [5,9,13], the parameters of the switching hyperplane remaining constant.The present paper addresses the stability of dynamic states of nonstationary automatic-control systems with variable structure in sliding modes. The controller in such systems includes control filters functionally commuted with the shaper and actuator. The approach proposed here for the stability analysis of such variable-structure systems is based on the existence conditions for the sliding mode at the switching boundary in the phase space [1][2][3][4]. Error gain is used for stabilization purposes [5,17]. The established stability criteria are applied to a nonstationary filtered-control system of variable structure of the third order. The study is based on the results from [1-20].1. Problem Formulation. Consider a nonstationary automatic-control system of variable structure that functionally includes filters of control signals [1,13]. The dynamic states of the system are described by the following equations [5,[18][19][20]:

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Technical Stability of Forced Motion in Nonstationary Automatic-Control Systems of Variable Structure

Matviichuk

2004

International Applied Mechanics

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Stability of Nonstationary Automatic-Control Systems of Variable Structure in Forced Motion

Cited by 5 publications

References 8 publications

Conditions of technical stability on non-stationary processes of automatic control of variable structure with correlative forming and filtering systems of control signals.

Conditions of technical stability on non-stationary processes of automatic control of variable structure with correlative forming and filtering systems of control signals.

Stability in sliding mode of nonstationary automatic-control systems of variable structure with switched filters

Technical Stability of Forced Motion in Nonstationary Automatic-Control Systems of Variable Structure

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