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Akhilanand Pati Tiwari - One of the best experts on this subject based on the ideXlab platform.
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State Feedback Control Using Pole Placement
Energy Systems in Electrical Engineering, 2017Co-Authors: Ravindra Munje, Balasaheb M. Patre, Akhilanand Pati TiwariAbstract:In this chapter, a state feedback-based control technique is explored for spatial control of Advanced Heavy Water Reactor (AHWR). The AHWR model with 90 state, 18 output, and 5 input variables is decomposed into slow and Fast Subsystems of orders 73 and 17, respectively, by two-stage linear transformation. As the Fast Subsystem is observed to be stable, controller is designed only for the slow Subsystem and then composite controller is derived for the original system. Vectorized nonlinear model of AHWR is simulated with presented composite controller and performance is tested under various transient conditions. It is noticed that xenon oscillations are effectively suppressed and performance is found to be acceptable.
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CCA - Spatial control of advanced heavy water reactor by Fast output sampling technique
2013 IEEE International Conference on Control Applications (CCA), 2013Co-Authors: Ravindra Munje, P. S. Londhe, J. G. Parkhe, Balasaheb M. Patre, Akhilanand Pati TiwariAbstract:In this paper, a spatial control strategy based on Fast Output Sampling (FOS) technique is proposed for Advanced Heavy Water Reactor (AHWR). The non-linear model of AHWR, represented by 90 first order differential equations having 5 inputs and 18 outputs, is linearized to obtain standard state-space representation. Using similarity transformation, the original higher order, ill-conditioned discrete system of AHWR is first decomposed into two comparatively lower order Subsystems, namely, `slow' and `Fast' Subsystem of orders 73 and 17 respectively. Now, state feedback controls are designed separately for slow and Fast Subsystem and then a composite controller is obtained using these individual state feedback controls, which is then realized using FOS feedback gain. Thus, the states of the system are not required for feedback. The efficacy of the controller has been demonstrated by simulation of transient behavior of non-linear model of AHWR. Performance of the controller is found to be satisfactory.
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Direct Block Diagonalization and Composite Control of Three-Time-Scale Systems
Modeling and Control of a Large Nuclear Reactor, 2013Co-Authors: S. R. Shimjith, Akhilanand Pati Tiwari, Bijnan BandyopadhyayAbstract:Singular perturbation methods have successfully been used in control applications to deal with multi-time-scale systems, by which the system is decomposed into a ‘slow’ Subsystem and one or more ‘boundary layer’ or ‘Fast’ Subsystems[56]. A system expressed in explicit singularly perturbed form generally has a small parameter e appearing as a multiplier to the derivative of the ‘Fast’ variables. Here, the system decomposition is achieved by setting e =0 and solving for the ‘Fast’ Subsystem variables in terms of the ‘slow’ ones, and then substituting them in the ‘slow’ Subsystem equations[58].
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Spatial control of a large pressurized heavy water reactor by Fast output sampling technique
IEEE Transactions on Nuclear Science, 2003Co-Authors: G.l. Sharma, Bijnan Bandyopadhyay, Akhilanand Pati TiwariAbstract:In this paper a method is presented to design a controller for discrete two time scale system based on Fast output sampling technique. Using similarity transformation the two time scale system is converted into a block diagonal form which is then partitioned into two Subsystems, namely, a Fast Subsystem and a slow Subsystem. Now state feedback controls are designed separately for the slow Subsystem and the Fast Subsystem. Then a composite state feedback control is obtained from the state feedback controls designed for Subsystems to assign the eigenvalues of the entire system at arbitrary locations. This composite state feedback gain is realized by using Fast output sampling feedback gain. Thus the states of the system are not needed for feedback. But in practice there are two problems in realizing the state feedback gain exactly viz. poor error dynamics and noise sensitivity. So a linear matrix inequality formulation is used to overcome these undesired effects. The method has been applied to a large pressurized heavy water reactor (PHWR) for control of xenon induced spatial oscillations. A particular grouping of the state variables has been considered to decompose the system into the slow Subsystem and the Fast Subsystem. Then Fast output sampling fedback gains have been calculated. The efficacy of the control has been demonstrated by simulation of transient behavior of the nonlinear model of the PHWR.
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Spatial control of a large pressurized heavy water reactor
IEEE Transactions on Nuclear Science, 1996Co-Authors: Akhilanand Pati Tiwari, B. Banyopadhyay, G. GovindarajanAbstract:The paper presents tile design of a near optimal linear regulator for controlling xenon-induced spatial oscillations in a large, pressurized heavy water reactor. The nonlinear mathematical model of the reactor including xenon iodine dynamics is characterized by 56 state variables land 14 inputs. This nonlinear model is linearized over rated power of the reactor and then the singularly perturbed structure of the linear model is exploited to decompose it into a Fast Subsystem of 14th order and a slow Subsystem of 42nd order. The slow Subsystem regulator problem is formulated as a cheap control problem that entails the solving of regulator problems of a 28th-order submodel and a 14th-order submodel. The Fast Subsystem regulator problem is also solved, Separately designed regulators are finally combined to obtain the near-optimal composite control for the original 56th-order model.
M. Pernarowski - One of the best experts on this subject based on the ideXlab platform.
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Fast Subsystem bifurcations in strongly coupled heterogeneous collections of excitable cells
Bulletin of Mathematical Biology, 2000Co-Authors: M. PernarowskiAbstract:A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations. A procedure for finding asymptotic estimates of the thresholds between these (synchronous) behaviors in the cellular aggregates is described for the heterogeneous case where the coupling strength is strong. This procedure is tested on a model of a strongly coupled heterogeneous collection of bursting and beating cells. Since isolated pancreatic β -cells have been observed to both burst and beat, this test of the spatial averaging techniques provides a possible explanation to measured discrepancies between the electrical activities of isolated β -cells and coupled collections (islets) of β -cells.
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Fast Subsystem bifurcations in a slowly varying lie nard system exhibiting bursting
Siam Journal on Applied Mathematics, 1994Co-Authors: M. PernarowskiAbstract:A perturbed Lienard differential system is examined using local stability and Hopf bifurcation analyses, asymptotic techniques, and Melnikov's method. The results of these analyses are applied to a simple cubic model that exhibits a variety of different oscillatory behaviors for different parameter values. For a bounded region in (Fast) parameter space, the model exhibits square-wave bursting patterns analogous to the bursting electrical activity observed in pancreatic ,$\beta $-cells. Under certain hypotheses, solutions of the cubic model are known to have square-wave patterns. By using the theory developed for the more general Lienard system, each hypothesis is shown to correspond to a curve in parameter space. Together, the curves bound a region in which the model exhibits square-wave bursting patterns. Since the model is simple, the curves that bound this region can all be determined analytically.
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Fast Subsystem bifurcations in a slowly varying Lie´nard system exhibiting bursting
SIAM Journal on Applied Mathematics, 1994Co-Authors: M. PernarowskiAbstract:A perturbed Lienard differential system is examined using local stability and Hopf bifurcation analyses, asymptotic techniques, and Melnikov's method. The results of these analyses are applied to a simple cubic model that exhibits a variety of different oscillatory behaviors for different parameter values. For a bounded region in (Fast) parameter space, the model exhibits square-wave bursting patterns analogous to the bursting electrical activity observed in pancreatic ,$\beta $-cells. Under certain hypotheses, solutions of the cubic model are known to have square-wave patterns. By using the theory developed for the more general Lienard system, each hypothesis is shown to correspond to a curve in parameter space. Together, the curves bound a region in which the model exhibits square-wave bursting patterns. Since the model is simple, the curves that bound this region can all be determined analytically.
Sebastian Walcher - One of the best experts on this subject based on the ideXlab platform.
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Tikhonov–Fenichel Reduction for Parameterized Critical Manifolds with Applications to Chemical Reaction Networks
Journal of Nonlinear Science, 2020Co-Authors: Elisenda Feliu, Niclas Kruff, Sebastian WalcherAbstract:We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and Fast variables are made, or necessary. We apply the theoretical results to chemical reaction networks with mass action kinetics admitting slow and Fast reactions. For some relevant classes of such systems, there exist canonical parameterizations of the variety of stationary points; hence, the theory is applicable in a natural manner. In particular, we obtain a closed form expression for the reduced system when the Fast Subsystem admits complex-balanced steady states.
Elisenda Feliu - One of the best experts on this subject based on the ideXlab platform.
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Tikhonov–Fenichel Reduction for Parameterized Critical Manifolds with Applications to Chemical Reaction Networks
Journal of Nonlinear Science, 2020Co-Authors: Elisenda Feliu, Niclas Kruff, Sebastian WalcherAbstract:We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and Fast variables are made, or necessary. We apply the theoretical results to chemical reaction networks with mass action kinetics admitting slow and Fast reactions. For some relevant classes of such systems, there exist canonical parameterizations of the variety of stationary points; hence, the theory is applicable in a natural manner. In particular, we obtain a closed form expression for the reduced system when the Fast Subsystem admits complex-balanced steady states.
Tong Heng Lee - One of the best experts on this subject based on the ideXlab platform.
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Singular perturbation control for vibration rejection in HDDS using the PZT active suspension as Fast Subsystem observer
IEEE Transactions on Industrial Electronics, 2007Co-Authors: Chee Khiang Pang, S.s. Ge, Frank L. Lewis, Ben M. Chen, Xiao Guo, Tong Heng LeeAbstract:Currently, position sensors other than the read/write head are not embedded into current hard disk drives (HDDs) due to signal-to-noise ratio and nanometer resolution issues. Moreover, a noncollocated sensor fusion creates nonminimum phase zero dynamics which degrades the tracking performance. In this paper, the singular perturbation theory is applied to decompose the voice coil motor's (VCM's) and induced PZT active suspension's dynamics into Fast and slow Subsystems, respectively. The control system is decomposed into Fast and slow time scales for controller designs, and control effectiveness is increased to tackle more degrees-of-freedom via an inner loop vibration suppression with measured high-frequency VCM's and PZT active suspension's dynamics from the piezoelectric elements in the suspension. Experimental results on a commercial HDD with a laser doppler vibrometer show the effective suppression of the VCM and PZT active suspension's flexible resonant modes, as well as an improvement of 39.9% in 3 sigma position error signal during track following when compared to conventional notch-based servos.