Averaging Method

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Ali Emadi - One of the best experts on this subject based on the ideXlab platform.

  • modeling of power electronic loads in ac distribution systems using the generalized state space Averaging Method
    IEEE Transactions on Industrial Electronics, 2004
    Co-Authors: Ali Emadi
    Abstract:

    Most of the loads in ac distribution systems have positive incremental impedance characteristic. However, power electronic loads, when tightly regulated, sink constant power from the system. Therefore, they have negative incremental impedance characteristic. This can cause negative impedance instability. Power electronic loads usually have a controlled or uncontrolled rectifier at the front end. In this paper, these loads are modeled using the generalized state-space Averaging Method. An assessment of their effects in ac distribution systems is also presented. Experimental results are presented to verify the proposed analysis.

  • modeling and analysis of multiconverter dc power electronic systems using the generalized state space Averaging Method
    IEEE Transactions on Industrial Electronics, 2004
    Co-Authors: Ali Emadi
    Abstract:

    This paper presents a modular approach for the modeling and simulation of multiconverter DC power electronic systems based on the generalized state-space Averaging Method. These systems may consist of many individual converters connected together to form large and complex systems. In addition to simplifying the analysis procedure, by using the proposed Method, the time step for analysis of the system can be increased. Therefore, the required computation time and computer memory for complex systems can be reduced considerably. In this paper, after introducing the proposed approach, results of applying the Method to a representative system are presented.

  • Application of state space Averaging Method to sliding mode control of PWM DC/DC converters
    IAS '97. Conference Record of the 1997 IEEE Industry Applications Conference Thirty-Second IAS Annual Meeting, 1997
    Co-Authors: Jafar Mahdavi, Ali Emadi, Hamid A. Toliyat
    Abstract:

    A novel approach for the analysis and design of sliding mode controllers for PWM DC/DC power converters is presented. The main advantage of this nonlinear controller is that there is no restriction on the size of the signal variations around the operating point. Small as well as large signal variations around the operating point are considered. Sliding mode controllers for buck, boost, buck-boost, and Cuk power converters have been designed and discussed. These controllers have been simulated on a digital computer and their dynamic performances have been shown to be satisfactory. Finally, Lyapunov's second theorem has been used to verify the stability of the designed sliding mode controller for the Cuk power converter

Lin Xiao - One of the best experts on this subject based on the ideXlab platform.

  • dual Averaging Methods for regularized stochastic learning and online optimization
    Journal of Machine Learning Research, 2010
    Co-Authors: Lin Xiao
    Abstract:

    We consider regularized stochastic learning and online optimization problems, where the objective function is the sum of two convex terms: one is the loss function of the learning task, and the other is a simple regularization term such as l1-norm for promoting sparsity. We develop extensions of Nesterov's dual Averaging Method, that can exploit the regularization structure in an online setting. At each iteration of these Methods, the learning variables are adjusted by solving a simple minimization problem that involves the running average of all past subgradients of the loss function and the whole regularization term, not just its subgradient. In the case of l1-regularization, our Method is particularly effective in obtaining sparse solutions. We show that these Methods achieve the optimal convergence rates or regret bounds that are standard in the literature on stochastic and online convex optimization. For stochastic learning problems in which the loss functions have Lipschitz continuous gradients, we also present an accelerated version of the dual Averaging Method.

  • dual Averaging Method for regularized stochastic learning and online optimization
    Neural Information Processing Systems, 2009
    Co-Authors: Lin Xiao
    Abstract:

    We consider regularized stochastic learning and online optimization problems, where the objective function is the sum of two convex terms: one is the loss function of the learning task, and the other is a simple regularization term such as l1-norm for promoting sparsity. We develop a new online algorithm, the regularized dual Averaging (RDA) Method, that can explicitly exploit the regularization structure in an online setting. In particular, at each iteration, the learning variables are adjusted by solving a simple optimization problem that involves the running average of all past subgradients of the loss functions and the whole regularization term, not just its subgradient. Computational experiments show that the RDA Method can be very effective for sparse online learning with l1-regularization.

  • dual Averaging Method for regularized stochastic learning and online optimization
    Neural Information Processing Systems, 2009
    Co-Authors: Lin Xiao
    Abstract:

    We consider regularized stochastic learning and online optimization problems, where the objective function is the sum of two convex terms: one is the loss function of the learning task, and the other is a simple regularization term such as l1-norm for promoting sparsity. We develop extensions of Nesterov's dual Averaging Method, that can exploit the regularization structure in an online setting. At each iteration of these Methods, the learning variables are adjusted by solving a simple minimization problem that involves the running average of all past subgradients of the loss function and the whole regularization term, not just its subgradient. In the case of l1-regularization, our Method is particularly effective in obtaining sparse solutions. We show that these Methods achieve the optimal convergence rates or regret bounds that are standard in the literature on stochastic and online convex optimization. For stochastic learning problems in which the loss functions have Lipschitz continuous gradients, we also present an accelerated version of the dual Averaging Method.

H. Grotstollen - One of the best experts on this subject based on the ideXlab platform.

  • Symbolic analysis Methods for averaged modeling of switching power converters
    IEEE Transactions on Power Electronics, 1997
    Co-Authors: H. Grotstollen
    Abstract:

    Symbolic analysis Methods for the averaged modeling of switching power converters are presented in this paper. A general Averaging Method suitable for computer-aided modeling is discussed first. Then, a symbolic analysis package that uses this Averaging Method to automatically generate an analytical averaged model for a switching power converter is described. The package is implemented using the computer algebra system Mathematica and can be used for modeling DC/DC power converters employing different switching techniques, including hard-switching pulse-width modulation (PWM), quasi-resonant soft switching, and soft transition. Several examples are provided to demonstrate the applications of the package. Further applications of symbolic analysis Methods in power electronics are also discussed.

  • Symbolic analysis of switching power converters based on a general Averaging Method
    PESC Record. 27th Annual IEEE Power Electronics Specialists Conference, 1996
    Co-Authors: H. Grotstollen
    Abstract:

    Symbolic analysis Methods for averaged modeling of switching power converters are discussed in this paper. A general Averaging Method suitable for computer-aided analysis is discussed first. A symbolic analysis package which uses this Averaging Method to automatically generate an analytical averaged model for a switching power converter is then described. The package is implemented using the computer algebra system Mathematica and can be applied to DC/DC power converters using different switching techniques, including hard switching PWM, quasi-resonant soft switching, and soft transition. Several examples are provided to demonstrate the applications of the package. Possible further applications of symbolic analysis Methods in power electronics are also discussed.

W Q Zhu - One of the best experts on this subject based on the ideXlab platform.

  • a stochastic Averaging Method for analyzing vibro impact systems under gaussian white noise excitations
    Journal of Sound and Vibration, 2014
    Co-Authors: W Q Zhu
    Abstract:

    Abstract A new stochastic Averaging Method for predicting the response of vibro-impact (VI) systems to random perturbations is proposed. First, the free VI system (without damping and random perturbation) is analyzed. The impact condition for the displacement is transformed to that for the system energy. Thus, the motion of the free VI systems is divided into periodic motion without impact and quasi-periodic motion with impact according to the level of system energy. The energy loss during each impact is found to be related to the restitution factor and the energy level before impact. Under the assumption of lightly damping and weakly random perturbation, the system energy is a slowly varying process and an averaged Ito stochastic differential equation for system energy can be derived. The drift and diffusion coefficients of the averaged Ito equation for system energy without impact are the functions of the damping and the random excitations, and those for system energy with impact are the functions of the damping, the random excitations and the impact energy loss. Finally, the averaged Fokker–Plank–Kolmogorov (FPK) equation associated with the averaged Ito equation is derived and solved to yield the stationary probability density of system energy. Numerical results for a nonlinear VI oscillator are obtained to illustrate the proposed stochastic Averaging Method. Monte-Carlo simulation (MCS) is also conducted to show that the proposed stochastic Averaging Method is quite effective.

  • stochastic Averaging of quasi integrable and non resonant hamiltonian systems under combined gaussian and poisson white noise excitations
    Nonlinear Dynamics, 2014
    Co-Authors: Wantao Jia, W Q Zhu
    Abstract:

    A stochastic Averaging Method for predicting the response of quasi-integrable and non-resonant Hamiltonian systems to combined Gaussian and Poisson white noise excitations is proposed. First, the motion equations of a quasi-integrable and non-resonant Hamiltonian system subject to combined Gaussian and Poisson white noise excitations is transformed into stochastic integro-differential equations (SIDEs). Then $$n$$ -dimensional averaged SIDEs and generalized Fokker–Plank–Kolmogrov (GFPK) equations for the transition probability densities of $$n$$ action variables and $$n$$ - independent integrals of motion are derived by using stochastic jump–diffusion chain rule and stochastic Averaging principle. The probability density of the stationary response is obtained by solving the averaged GFPK equation using the perturbation Method. Finally, as an example, two coupled non-linear damping oscillators under both external and parametric excitations of combined Gaussian and Poisson white noises are worked out in detail to illustrate the application and validity of the proposed stochastic Averaging Method.

M Ehsani - One of the best experts on this subject based on the ideXlab platform.

  • analysis of power electronic converters using the generalized state space Averaging approach
    IEEE Transactions on Circuits and Systems I-regular Papers, 1997
    Co-Authors: J Mahdavi, A Emaadi, M D Bellar, M Ehsani
    Abstract:

    Power electronic converters are periodic time-variant systems, because of their switching operation. The generalized state-space Averaging Method is a way to model them as time independent systems, defined by a unified set of differential equations, capable of representing circuit waveforms. Therefore, it can be a convenient approach for designing controllers to he applied to switched converters. This brief shows that the generalized state-space Averaging Method works well only within specific converter topologies and parametric limits, where the model approximation order is not defined by the topology number of components. This point is illustrated with detailed examples from several basic dc/dc converter topologies.