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Resonant Oscillations of the Coupled controlled System near Equilibrium 15

Resonant Oscillations of the Coupled Controlled System near ...

引用

15th International Conference on Stability and Oscillations of nonlinear control Systems (Pyatnitskiy's Conference), STAB 2020

作者： Barabanov, Ivan Tkhai, Valentin V. A. Trapeznikov Institute of Control Sciences of Ras Laboratory of Dynamics of Nonlinear Control Processes Moscow Russia

ISBN: (纸本)9781728167053

We consider a nonlinear autonomous coupled system of a general type in the vicinity of equilibrium. It is assumed that the linear approximation matrix has a pair of purely imaginary eigenvalues;other eigenvalues are not multiples of the specified ones and are different from zero. We study the oscillations under the action of a periodic controls with a small regulator gain. The existence of a resonant oscillation of the controlled system is established, the oscillation amplitudes are estimated in terms of the value of regulator gain, the stability of the oscillation is analyzed. Previously, the result was known for the Lyapunov system. © 2020 IEEE.

关键词： Eigenvalues and eigenfunctions

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Spatial Oscillations of a Physical Pendulum 16

Spatial Oscillations of a Physical Pendulum

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16th International Conference on Stability and Oscillations of nonlinear control Systems (Pyatnitskiy's Conference), STAB 2022

作者： Tkhai, Valentin N. V.A. Trapeznikov Institute of Control Sciences of RAS E.S. Pyatnitskiy Laboratory of Dynamics of Nonlinear Control Processes Moscow Russia

ISBN: (纸本)9781665465861

The motions of a heavy rigid body with one fixed point and a center of gravity located in the main plane of the energy ellipsoid are investigated. The body admits the motions of a physical pendulum containing a family of pendulum oscillations. The existence of the second spatial family of pendulum oscillations is proved, which, together with Mlodzievskiis pendulum oscillations, proceed from the lower equilibrium and adjoin the upper equilibrium of the body. The Euler-Poisson equations are used. © 2022 IEEE.

关键词： Pendulums

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control of the Predator-Prey System Based on the Expansion of the State Space 16

Control of the Predator-Prey System Based on the Expansion o...

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16th International Conference Management of Large-Scale System Development, MLSD 2023

作者： Tkacheva, Olga Utkin, Victor V.A. Trapeznikov Institute of Control Sciences of Ras Laboratory of Nonlinear Dynamical Systems Moscow Russia V.A. Trapeznikov Institute of Control Sciences of Ras Laboratory of Dynamics of Nonlinear Control Processes Moscow Russia

The article discusses the two-dimensional modified Lotka-Volterra model. An approach based on expanding the state space is used in order to stabilize the number of preys. The observer recovers unmeasured variables and... 详细信息

ISBN: (纸本)9798350337907

关键词： Predator prey systems

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Autonomous control of the Rotational Speed of a Synchronous Generator by Voltage on the Excitation Winding 16

Autonomous Control of the Rotational Speed of a Synchronous ...

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16th International Conference on Stability and Oscillations of nonlinear control Systems (Pyatnitskiy's Conference), STAB 2022

作者： Utkin, Victor Gulyukina, Svetlana V.A. Trapeznikov Institute of Control Sciences of RAS E. S. Pyatnitsky Laboratory of Dynamics of Nonlinear Control Processes Moscow Russia V.A. Trapeznikov Institute of Control Sciences of RAS Laboratory of Systems with Discontinuous Controls Moscow Russia

ISBN: (纸本)9781665465861

The problem of stabilization of the angular frequency of rotation of a synchronous generator by regulating the voltage on the excitation winding is considered. A feature of the proposed approach is the consideration of restrictions on the components of the state vector and control by introducing a nonlinear change of variables in the form of linear functions with saturation (sat-functions). © 2022 IEEE.

关键词： Synchronous generators

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Synthesis of Invariant Systems under Uncoordinated Disturbances Based on the Theory of Sliding Modes 14

Synthesis of Invariant Systems under Uncoordinated Disturban...

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14th International Conference Management of Large-Scale System Development, MLSD 2021

作者： Gulyukina, Svetlana Utkin, Victor Laboratory of Information Process Analysis and Modeling V.A. Trapeznikov Institute of Control Sciences of RAS Moscow Russia Laboratory of Dynamics of Nonlinear Control Processes by E. S. Pyatnitsky V.A. Trapeznikov Institute of Control Sciences of RAS Moscow Russia

ISBN: (纸本)9781665412308

This paper proposes a new philosophy for the synthesis of sliding modes using the method of expanding the state space and the block approach in control. An important feature of the developed algorithms for the synthesis of invariant systems, in contrast to systems with deep feedbacks, is the modulus constraint of controls and state vector coordinates. © 2021 IEEE.

关键词： Invariance

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Synthesis of Invariant Systems of a Given Accuracy Based on the Sliding Modes Theory

Synthesis of Invariant Systems of a Given Accuracy Based on ...

引用

2021 International Russian Automation Conference, RusAutoCon 2021

作者： Utkin, Victor Gulyukina, Svetlana Pyatnitsky V.A. Trapeznikov Institute of Control Sciences of Ras Laboratory of Dynamics of Nonlinear Control Processes by E. S. Moscow Russia V.A. Trapeznikov Institute of Control Sciences of Ras Laboratory of Information Process Analysis and Modeling Moscow Russia

ISBN: (纸本)9780738131566

In this paper, we propose original methods for the synthesis of invariant systems considering the constraints on the components of the state vector and control. A two-step procedure for the synthesis of the problem of ensuring invariance with a given accuracy is developed by expanding the space of states. We used discontinuous functions at the input of integrators, which generate sliding motions in each of the subsystems over a finite time span to solve the stabilization problem. The synchronous generator is considered as an example of application;the numerical simulation results obtained in Matlab showed the high efficiency of the proposed approach. © 2021 IEEE.

关键词： Invariance

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Stabilization of State Constrained Delayed Systems Using control-Lyapunov and control-Barrier Functions 16

Stabilization of State Constrained Delayed Systems Using Con...

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16th International Conference on Stability and Oscillations of nonlinear control Systems (Pyatnitskiy's Conference), STAB 2022

作者： Sedova, Natalia Druzhinina, Olga Ulyanovsk State University Faculty of Mathematics Information and Aviation Technologies Ulyanovsk Russia V.A. Trapeznikov Institute of Control Sciences of RAS E.S. Pyatnitskiy Laboratory of Dynamics of Nonlinear Control Processes Moscow Russia

ISBN: (纸本)9781665465861

One of the modern control design methods for stabilization of affine nonlinear systems is the so-called control Lyapunov function method which is used to design universal formulas for control law like Sontags formula. It is known that the latter cannot be directly extended to delay systems using Lyapunov-Razumikhin *** this paper, we use modified conditions for the derivative of a Lyapunov function to solve the stabilization problem for nonlinear affine time-variant delay systems under state constraints. The assumptions introduced make it possible to provide the Sontag-based solution for the problem using a Razumikhin-type control Lyapunov function (CLRF). A stabilizing feedback law is proposed in terms of CLRF whose derivative can change sign under the Razumikhin condition. State constraints are taken into account in the form of an unsafe set, and in order to ensure the safety objective, we use a Razumikhin-type control barrier function (CBRF). Furthermore, for time-invariant systems the suggested CLRF and CBRF are combined to achieve the stabilization and safety objectives simultaneously. © 2022 IEEE.

关键词： Stabilization

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Stabilization of Constrained nonlinear Triangular Delay Systems Using Convex Optimization 15

Stabilization of Constrained Nonlinear Triangular Delay Syst...

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15th International Conference on Stability and Oscillations of nonlinear control Systems (Pyatnitskiy's Conference), STAB 2020

作者： Sedova, Natalia Druzhinina, Olga Ulyanovsk State University Faculty of Mathematics Information and Aviation Technologies Ulyanovsk Russia V.A. Trapeznikov Institute of Control Sciences of Ras E.S. Pyatnitskiy Laboratory of Dynamics of Nonlinear Control Processes Moscow Russia

ISBN: (纸本)9781728167053

The possibility is studied of reducing the stabilization problem for delay differential nonlinear system to optimization problems with known numerical procedures for solving. Assuming a triangular structure of the system, algorithms are proposed for constructing a stabilizing control. The description of the subsystems in the form of Takagi-Sugeno models is used. Given the state and control constraints, as well as the properties of weight functions, the stabilization problem is reduced to some optimization problems, including LMIs. The obtained controls retain stabilizing properties for non-stationary weight functions, as well as for perturbed systems. Chances of numerical implementation of algorithms based on standard procedures of computational software are considered. © 2020 IEEE.

关键词： nonlinear systems

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Static Output Feedback Stabilization: Cascade Delayed control Design for Chains of Integrators 5

Static Output Feedback Stabilization: Cascade Delayed Contro...

引用

5th Scientific School on dynamics of Complex Networks and their Applications, DCNA 2021

作者： Sedova, Natalia Druzhinina, Olga Faculty of Mathematics Information and Aviation Technologies Ulyanovsk State University Ulyanovsk Russia E.S. Pyatnitskiy Laboratory of Dynamics of Nonlinear Control Processes V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences Moscow Russia

ISBN: (纸本)9781665442824

In the paper, a delayed control for an even-order chain of integrators is proposed. It is known that for many differential models, in particular, for models of mechanical systems, the control problem is reduced to the stabilization of chain of integrators. The proposed method use a simple inductive design and cascade systems’ asymptotic stability property. For any order of the integrator the control is a linear combination of delayed state coordinates with odd indices, and it depends on three numerical parameters. The parameters are selected from the stability region of a second-order linear delayed system and they can vary within a wide range. The result obtained can be applied to the stabilization problem for systems with incomplete measurements. In particular, for some class of mechanical systems, the proposed control can be a derivative-free alternative of stabilizing control. © 2021 IEEE

关键词： Stabilization

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Resonant Oscillations of the Coupled controlled System Near Equilibrium

Resonant Oscillations of the Coupled Controlled System Near ...

引用

International Conference on Stability and Oscillations of nonlinear control Systems (Pyatnitskiy's Conference)

作者： Ivan Barabanov Valentin Tkhai Laboratory of Dynamics of Nonlinear Control Processes V. A. Trapeznikov Institute of Control Sciences of RAS Moscow Russia

ISBN: (数字)9781728167053

ISBN: (纸本)9781728167060

We consider a nonlinear autonomous coupled system of a general type in the vicinity of equilibrium. It is assumed that the linear approximation matrix has a pair of purely imaginary eigenvalues; other eigenvalues are not multiples of the specified ones and are different from zero. We study the oscillations under the action of a periodic controls with a small regulator gain. The existence of a resonant oscillation of the controlled system is established, the oscillation amplitudes are estimated in terms of the value of regulator gain, the stability of the oscillation is analyzed. Previously, the result was known for the Lyapunov system.

关键词： Oscillators control systems Resonant frequency Eigenvalues and eigenfunctions nonlinear dynamical systems Autonomous systems Linear approximation

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