Abstract: Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.
Abstract: In this paper, we propose a new modular approach called neuroglial consisting of two neural networks slow and fast which emulates a biological reality recently discovered. The implementation is based on complex multi-time scale systems; validation is performed on the model of the asynchronous machine. We applied the geometric approach based on the Gerschgorin circles for the decoupling of fast and slow variables, and the method of singular perturbations for the development of reductions models.
This new architecture allows for smaller networks with less complexity and better performance in terms of mean square error and convergence than the single network model.
Abstract: An analysis of a synchronous generator in a bond
graph approach is proposed. This bond graph allows to determine the
simplified models of the system by using singular perturbations.
Firstly, the nonlinear bond graph of the generator is linearized. Then,
the slow and fast state equations by applying singular perturbations
are obtained. Also, a bond graph to get the quasi-steady state of the
slow dynamic is proposed. In order to verify the effectiveness of the
singularly perturbed models, simulation results of the complete
system and reduced models are shown.
Abstract: This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.
Abstract: The three-time-scale plant model of a wind power
generator, including a wind turbine, a flexible vertical shaft, a Variable
Inertia Flywheel (VIF) module, an Active Magnetic Bearing (AMB)
unit and the applied wind sequence, is constructed. In order to make
the wind power generator be still able to operate as the spindle speed
exceeds its rated speed, the VIF is equipped so that the spindle speed
can be appropriately slowed down once any stronger wind field is
exerted. To prevent any potential damage due to collision by shaft
against conventional bearings, the AMB unit is proposed to regulate
the shaft position deviation. By singular perturbation order-reduction
technique, a lower-order plant model can be established for the
synthesis of feedback controller. Two major system parameter
uncertainties, an additive uncertainty and a multiplicative uncertainty,
are constituted by the wind turbine and the VIF respectively.
Frequency Shaping Sliding Mode Control (FSSMC) loop is proposed
to account for these uncertainties and suppress the unmodeled
higher-order plant dynamics. At last, the efficacy of the FSSMC is
verified by intensive computer and experimental simulations for
regulation on position deviation of the shaft and counter-balance of
unpredictable wind disturbance.
Abstract: Iterative learning control aims to achieve zero tracking
error of a specific command. This is accomplished by iteratively
adjusting the command given to a feedback control system, based on
the tracking error observed in the previous iteration. One would like
the iterations to converge to zero tracking error in spite of any error
present in the model used to design the learning law. First, this need
for stability robustness is discussed, and then the need for robustness
of the property that the transients are well behaved. Methods of
producing the needed robustness to parameter variations and to
singular perturbations are presented. Then a method involving
reverse time runs is given that lets the world behavior produce the
ILC gains in such a way as to eliminate the need for a mathematical
model. Since the real world is producing the gains, there is no issue
of model error. Provided the world behaves linearly, the approach
gives an ILC law with both stability robustness and good transient
robustness, without the need to generate a model.
Abstract: In this work, we analyze the deformation of surface
waves in shallow flows conditions, propagating in a channel of
slowly varying cross-section. Based on a singular perturbation
technique, the main purpose is to predict the motion of waves by
using a dimensionless formulation of the governing equations,
considering that the longitudinal variation of the transversal section
obey a power-law distribution. We show that the spatial distribution
of the waves in the varying cross-section is a function of a kinematic
parameter,κ , and two geometrical parameters εh
and w ε . The above
spatial behavior of the surface elevation is modeled by an ordinary
differential equation. The use of single formulas to model the varying
cross sections or transitions considered in this work can be a useful
approximation to natural or artificial geometrical configurations.