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Two-Phase Flow Dynamics
Published in Neil E. Todreas, Mujid S. Kazimi, Nuclear Systems Volume I, 2021
Neil E. Todreas, Mujid S. Kazimi
For the intermediate case only, as indicated by intersection points 1, 2 and 3, multiple channel flow rates are possible. In this case, however, not all intersections are stable conditions. The criterion for stability can be developed by the following perturbation analysis. The fluid in a heated channel accelerates owing to the difference between the imposed external (or boundary) pressure drop (ΔPex) and the intrinsic (mostly friction) pressure drop (ΔPf), as given by Idm˙dt=ΔPex−ΔPf
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Published in S.P. Bhattacharyya, L.H. Keel, of UNCERTAIN DYNAMIC SYSTEMS, 2020
The stability of a linear time invariant continuous time feedback control system is characterized by the root locations of its characteristic polynomial δ(s) for stability the polynomial δ(s) must be Hurwitz i.e. have all its roots in the open left half of the complex plane. Since control systems operate under large uncertainties it is important to determine if stability is robust, that is, preserved under various perturbations. This type of consideration motivated the development of the celebrated Theorem of Kharitonov which deals with the family of real polynomials δ(s)=δ0+δ1s+δ2s2+⋯+δnsn
Performance Evaluation of Flexible Manufacturing Systems by Coloured Timed Petri Nets and Timed State Space Generation
Published in Javier Campos, Carla Seatzu, Xiaolan Xie, in Manufacturing, 2018
Gasper Mušič, Liana Napalkova, Miquel Àngel Piera
To estimate the system performance from a single simulation run, computer simulation can be combined with perturbation methods that analyse the changes in the system performance as a result of small perturbations in control parameters by tracing the sample-path function. The most well-known perturbation method is infinitesimal perturbation analysis that uses derivatives to provide sensitivity information on performance measures with respect to control parameters [32]. Despite all derivatives can be derived from a single simulation run, which represents a significant advantage in terms of computational efficiency, this approach does not work when the sample-path function is discontinuous in the relevant parameter.
Bifurcation Analysis of Xenon Oscillations in Large Pressurized Heavy Water Reactors with Spatial Control
Published in Nuclear Science and Engineering, 2022
Abhishek Chakraborty, Suneet Singh, M. P. S. Fernando
Since the nature of these spatial power oscillations due to variations of xenon depend on the magnitude of reactivity feedback coefficients, reactor core dimensions, and the extent of flux flattening, stability analysis is required to find out the stable and unstable regimes of operation. Traditionally, linear stability analysis used to be performed by the transfer function technique, time and frequency domain approaches,1 bode plots, etc. Linear stability analysis is particularly valid for “small” perturbations to the system from its equilibrium point,2 and hence, the system behavior for “large” perturbations cannot be predicted using this analysis.
Linear convergence of proximal incremental aggregated gradient method for nonconvex nonsmooth minimization problems
Published in Applicable Analysis, 2022
One can see that the metric subregularity of a set-valued map around is in fact equivalent to the calmness of the inverse map around . They are important tools in the study of perturbation analysis and error bounds of the optimization problems. For a nice survey about this topic, see [24].
A numerical approach to hybrid nonlinear optimal control
Published in International Journal of Control, 2021
Esmaeil Sharifi, Christopher J. Damaren
Since open-loop control is undesirable for practical systems, various approaches have been investigated to generate closed-loop solutions to the HJB equation. One technique is the perturbation method wherein the nonlinear system is assumed to be a perturbation of a linear system. The approximation is then formed by finding a finite number of terms involved in a Taylor series expansion of the value function (Garrard & Jordan, 1977; Nishikawa et al., 1971). Perturbation methods are, however, limited to systems with analytic optimal cost and control which only deviate slightly from a linear system. Another approach is to regularise the cost function so that an analytic expression for the control can be obtained. The basic idea is to consider a cost function consisting of a term chosen such that the HJB equation reduces to a form similar to the Riccati equation (Freeman & Kokotovic, 1995; Lu, 1993). Although this approach results in solutions that stabilise the system, it is difficult to estimate how far the control deviates from the optimal solution. Feedback linearisation is another technique which uses feedback to cancel out the nonlinearities involved in the system (Isidori, 1989; Nijmeijer & van der Schaft, 1990). The drawback associated with feedback linearisation is that the control sometimes cancels out nonlinearities that enhance the stability and performance of the system. Moreover, the control effort used to cancel the nonlinearities can be unreasonably large. Neural networks can be also trained by computing open-loop controls for various points in the state space to approximate the solution of the HJB equation (Abu-Khalaf & Lewis, 2005; Cheng et al., 2007; Liu et al., 2009). Nevertheless, there is no guarantee for the stability of the closed-loop system via this approach. Furthermore, finite difference and finite element techniques have been used to approximate the HJB equation (Bardi & Capuzzo-Dolcetta, 2008; Richardson & Wang, 2006; Wang et al., 2003). These methods, however, suffer from the curse of dimensionality since the computational load and computer memory required for the approximation grow exponentially with the dimension of the state of the system. A survey of research directed toward approximating the HJB equation can be found in (Beard, 1995) and (Beard & McLain, 1998b).