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Jun Zhou - One of the best experts on this subject based on the ideXlab platform.
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contraposition 2 regularized Nyquist stability criteria for linear continuous time periodic systems
IFAC Proceedings Volumes, 2013Co-Authors: Jun ZhouAbstract:Abstract By employing the 2-regularized determinant technique about Hilbert-Schmidt operators and creating what we call the contraposition return difference relationship for finite-dimensional linear continuous-time periodic (FDLCP) feedback systems, a contraposition 2-regularized Nyquist stability Criterion is developed for asymptotic stability analysis in this study. The stability conditions of the contraposition 2-regularized Nyquist stability Criterion are necessary and sufficient, which can be implemented graphically in a way similar to what we do in linear time-invariant cases but without involving open-loop poles distribution and encircling orientation counting of the Nyquist loci. A numeric implementation algorithm for the contraposition 2-regularized Nyquist Criterion is also proposed via truncating the harmonic transfer operator of the FDLCP systems.
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2 regularized Nyquist Criterion in linear continuous time periodic systems and its implementation
Siam Journal on Control and Optimization, 2005Co-Authors: Jun Zhou, T. HagiwaraAbstract:First, by using the 2-regularized determinant technique for Hilbert--Schmidt operators, the computation formula, infinite-product convergence, and analyticity of the 2-regularized determinant of the modified harmonic state operator in finite-dimensional linear continuous-time periodic (FDLCP) systems are derived in this paper. Second, based on these results, a 2-regularized Nyquist Criterion is established for asymptotic stability analysis of a class of FDLCP systems for the first time. Third, a numeric implementation algorithm for the 2-regularized Nyquist Criterion is also proposed via the staircase truncation on the harmonic transfer operator of the FDLCP system concerned. Finally, to illustrate the results of this paper, asymptotic stability of the lossy Mathieu differential equation is investigated.
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generalized Nyquist Criterion of continuous time periodic systems and its implementation ii numerical computations and convergence
Society of Instrument and Control Engineers of Japan, 2002Co-Authors: Jun Zhou, T. HagiwaraAbstract:For Part I see ibid. p.1700 (2002). In this second part, we consider the numerical implementation problem of the generalized Nyquist stability Criterion described in Part I, derived by means of the 2-regularized determinants about the harmonic return difference operators of finite-dimensional linear continuous-time periodic systems. Numerical implementation of this generalized Nyquist Criterion is developed through the staircase truncation on the harmonic return difference operator. To illustrate the results of the second part, the asymptotic stability of the lossy Mathieu differential equation is investigated.
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Generalized Nyquist Criterion of continuous-time periodic systems and its implementation (I): theoretic results
Proceedings of the 41st SICE Annual Conference. SICE 2002., 2002Co-Authors: Jun Zhou, T. HagiwaraAbstract:This paper is divided into two parts. In the first part, we establish a generalized Nyquist stability Criterion to finite-dimensional linear continuous-time periodic systems by means of the 2-regularized determinants about the harmonic transfer operator, which is a Hilbert-Schmidt operator. The generalized Nyquist stability Criterion can apply to most practical periodically time-varying continuous-time systems with standard assumptions about the system matrices.
J Jugo - One of the best experts on this subject based on the ideXlab platform.
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on the stability of time delay systems using Nyquist Criterion
European Control Conference, 2001Co-Authors: J JugoAbstract:This work presents different results on the stability of linear time-delay systems by a simple method derived from the Nyquist Criterion. The main characteristic is the simplicity of the stability tests, maintaining analysis rigour. Based on this simple stability test, delay-independent and delay-dependent stability criteria are derived, being possible the statement of those criteria as numerically treatable problems. Although the presented study concerns systems with different point delays, the extension to systems with distributed delays is possible.
T. Hagiwara - One of the best experts on this subject based on the ideXlab platform.
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2 regularized Nyquist Criterion in linear continuous time periodic systems and its implementation
Siam Journal on Control and Optimization, 2005Co-Authors: Jun Zhou, T. HagiwaraAbstract:First, by using the 2-regularized determinant technique for Hilbert--Schmidt operators, the computation formula, infinite-product convergence, and analyticity of the 2-regularized determinant of the modified harmonic state operator in finite-dimensional linear continuous-time periodic (FDLCP) systems are derived in this paper. Second, based on these results, a 2-regularized Nyquist Criterion is established for asymptotic stability analysis of a class of FDLCP systems for the first time. Third, a numeric implementation algorithm for the 2-regularized Nyquist Criterion is also proposed via the staircase truncation on the harmonic transfer operator of the FDLCP system concerned. Finally, to illustrate the results of this paper, asymptotic stability of the lossy Mathieu differential equation is investigated.
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generalized Nyquist Criterion of continuous time periodic systems and its implementation ii numerical computations and convergence
Society of Instrument and Control Engineers of Japan, 2002Co-Authors: Jun Zhou, T. HagiwaraAbstract:For Part I see ibid. p.1700 (2002). In this second part, we consider the numerical implementation problem of the generalized Nyquist stability Criterion described in Part I, derived by means of the 2-regularized determinants about the harmonic return difference operators of finite-dimensional linear continuous-time periodic systems. Numerical implementation of this generalized Nyquist Criterion is developed through the staircase truncation on the harmonic return difference operator. To illustrate the results of the second part, the asymptotic stability of the lossy Mathieu differential equation is investigated.
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Generalized Nyquist Criterion of continuous-time periodic systems and its implementation (I): theoretic results
Proceedings of the 41st SICE Annual Conference. SICE 2002., 2002Co-Authors: Jun Zhou, T. HagiwaraAbstract:This paper is divided into two parts. In the first part, we establish a generalized Nyquist stability Criterion to finite-dimensional linear continuous-time periodic systems by means of the 2-regularized determinants about the harmonic transfer operator, which is a Hilbert-Schmidt operator. The generalized Nyquist stability Criterion can apply to most practical periodically time-varying continuous-time systems with standard assumptions about the system matrices.
Pericle Zanchetta - One of the best experts on this subject based on the ideXlab platform.
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experimental validation of harmonic impedance measurement and ltp Nyquist Criterion for stability analysis in power converter networks
IEEE Transactions on Power Electronics, 2019Co-Authors: Valerio Salis, Alessandro Costabeber, Stephen M Cox, Francesco Tardelli, Pericle ZanchettaAbstract:This paper presents the first experimental validation of the stability analysis based on the online measurement of harmonic impedances exploiting the linear time-periodic (LTP) approach applied to ac networks of power converters. Previous studies have provided the theoretical framework for the method, enabling the stability assessment of an unknown system adopting a black-box approach, relying only on injected perturbations and local measurements. The experimental case study considered in this paper comprises two single-phase converters, one acting as source subsystem and the other as load subsystem . A third converter, the stability measurement unit , is controlled to inject small current perturbations at the point of common coupling (PCC). From the measured small-signal perturbations of PCC voltage, source current, and load current, the harmonic impedances of source and load subsystems are calculated. The LTP Nyquist Criterion is then applied to the ratio of the two harmonic impedances in order to assess the stability of the whole system. Theoretical and experimental results from a 5-kW laboratory prototype are provided and confirm the effectiveness of the method. In addition, the measurements do not require sophisticated equipment or control boards and can be easily performed from data sampled by commercial micro-controllers.
Alain Oustaloup - One of the best experts on this subject based on the ideXlab platform.
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A Nyquist Criterion for time-varying periodic systems, with application to a hydraulic test bench
2020Co-Authors: Valérie Pommier, Jocelyn Sabatier, Aitor Garcia Iturricha, Alain OustaloupAbstract:Abstract: In this paper, stability results dedicated to sampled periodic systems are applied to a mechanical system whose stiffness exhibits quick variations: a hydraulic test bench used to achieve mechanical test on complex structures. To carry out this application, time-varying w transformation representation of sampled periodic systems are first introduced. An extension of the Nyquist Criterion to sampled periodic systems is then given. Finally, this theorem is applied to evaluate the stability degree of the hydraulic test bench controlled using CRONE control methodology. Key words: Time-varying system, Periodic systems, CRONE Control, stability degree, hydraulic actuator In this paper, extensions of Nyquist Criterion developed in [Garcia 01] is applied to the analysis of the stability degree of a testing bench constituted of a hydraulic actuator used to achieve mechanical deformations on complex structures. Given parametric variations of the parameters of the structure and given quick variations of the structure stiffness during the test, the testing bench whose velocity is controlled using a robust CRONE controller, behaves as a sampled time-varying system with parametric uncertainties. Given that the velocity of the actuator is controlled on a finite time interval, this time-varying system can be artificially considered as a sampled periodic system. The paper is organized as follows. Section 2 deals with the representation of continuous time-varying systems using TVWTs and TVPFRs. Section 3 is dedicated to the stability analysis of sampled time-varying systems with periodic coefficients. Section 4 first gives a presentation of the testing bench and of its control using CRONE control methodology. Then this section presents the stability degree analysis of the testing bench using the extension of Nyquist Criterion given in section 3. -Introduction -Continuous-time periodic systems -Definitions and hypothesis A linear time-varying continuous-time system with periodic coefficients, also called periodic continuous-time system, is described by the state variable equation: where A(t), B(t), C(t) and D(t) are supposed to be A(t), B(t), C(t) and D(t) and their first derivatives are also supposed to be respectively continuous and piecewise continuous on [0, T]. They can thus be developed in uniformly convergent Fourier series of the form
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a Nyquist Criterion for time varying periodic systems with application to a hydraulic test bench
International Conference on Control Applications, 2002Co-Authors: V Pommieer, Jocelyn Sabatier, Aitor Garcia Iturricha, Alain OustaloupAbstract:In this paper, stability results dedicated to sampled periodic systems are applied to a mechanical system the stiffness of which exhibits quick variations: an hydraulic test bench used for mechanical testing of complex structures. To achieve this application, a time-varying w transformation representation of sampled periodic systems is introduced. An extension of the Nyquist Criterion to sampled periodic systems is then given. Finally, this theorem is applied to evaluate the stability degree of the hydraulic test bench controlled using CRONE control methodology.