Implicit Quasi-Steady-State Approximation and Application to a Power Plant Evaporator

2006 ◽  
Vol 129 (1) ◽  
pp. 66-71 ◽  
Author(s):  
Eduard Eitelberg ◽  
Edward Boje
Keyword(s):  
Steady State ◽  
Power Plant ◽  
Nonlinear Models ◽  
Low Frequency ◽  
Perturbation Parameter ◽  
Perturbation Approach ◽  
Quasi Steady State ◽  
Reduced Order ◽  
First Order ◽  
Time Scale Separation

Construction of reduced order models using the conventional quasi-steady-state (QSS) or singular perturbation approach may not yield good low frequency approximations, especially if there is not a distinct time scale separation into slow and fast subsystems. An implicit QSS technique is proposed for general nonlinear models. The resulting reduced order model is accurate to first order in the perturbation parameter and its linearization is accurate to first order in frequency. An example is included showing the application of the proposed method to model reduction on a power plant evaporator.

Kinetics of NO2 air space absorption in isolated rat lungs

1992 ◽  
Vol 73 (5) ◽  
pp. 1939-1945 ◽  
Author(s):  
E. M. Postlethwait ◽  
S. D. Langford ◽  
A. Bidani
Keyword(s):  
Steady State ◽  
Tidal Volume ◽  
Gas Phase ◽  
Initial Rate ◽  
Quasi Steady State ◽  
Closed Chamber ◽  
First Order ◽  
First Order Kinetics ◽  
Rat Lungs ◽  
Kinetics Of

We previously showed, during quasi-steady-state exposures, that the rate of inhaled NO2 uptake displays reaction-mediated characteristics (J. Appl. Physiol. 68: 594–603, 1990). In vitro kinetic studies of pulmonary epithelial lining fluid (ELF) demonstrated that NO2 interfacial transfer into ELF exhibits first-order kinetics with respect to NO2, attains [NO2]-dependent rate saturation, and is aqueous substrate dependent (J. Appl. Physiol. 71: 1502–1510, 1991). We have extended these observations by evaluating the kinetics of NO2 gas phase disappearance in isolated ventilating rat lungs. Transient exposures (2–3/lung at 25 degrees C) employed rebreathing (NO2-air) from a non-compliant continuously stirred closed chamber. We observed that 1) NO2 uptake rate is independent of exposure period, 2) NO2 gas phase disappearance exhibited first-order kinetics [initial rate (r*) saturation occurred when [NO2] > 11 ppm], 3) the mean effective rate constant (k*) for NO2 gas phase disappearance ([NO2] < or = 11 ppm, tidal volume = 2.3 ml, functional residual capacity = 4 ml, ventilation frequency = 50/min) was 83 +/- 5 ml/min, 4) with [NO2] < or = 11 ppm, k* and r* were proportional to tidal volume, and 5) NO2 fractional uptakes were constant across [NO2] (< or = 11 ppm) and tidal volumes but exceeded quasi-steady-state observations. Preliminary data indicate that this divergence may be related to the inspired PCO2. These results suggest that NO2 reactive uptake within rebreathing isolated lungs follows first-order kinetics and displays initial rate saturation, similar to isolated ELF.(ABSTRACT TRUNCATED AT 250 WORDS)

Application of Quasi-Steady-State Methods to Nonlinear Models of Intracellular Transport by Molecular Motors

2017 ◽  
Vol 79 (9) ◽  
pp. 1923-1978 ◽  
Author(s):  
Cole Zmurchok ◽  
Tim Small ◽  
Michael J. Ward ◽  
Leah Edelstein-Keshet
Keyword(s):  
Steady State ◽  
Molecular Motors ◽  
Intracellular Transport ◽  
Nonlinear Models ◽  
Quasi Steady State

scholarly journals New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Heonjong Yoo ◽  
Zoran Gajic
Keyword(s):  
Perturbation Parameter ◽  
Fast Time ◽  
Feedback Controllers ◽  
Two Stage ◽  
Scale Separation ◽  
Reduced Order ◽  
Time Scale Separation ◽  
Reduced Order Observer ◽  
Ill Conditioning ◽  
Perturbed Linear Systems

The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ) only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III)–(V), they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.

Reduced-order unsteady aerodynamic models at low Reynolds numbers

2013 ◽  
Vol 724 ◽  
pp. 203-233 ◽  
Author(s):  
Steven L. Brunton ◽  
Clarence W. Rowley ◽  
David R. Williams
Keyword(s):  
Steady State ◽  
Wind Tunnel ◽  
Active Flow Control ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Low Frequency ◽  
Leading Edge ◽  
Low Frequencies ◽  
Reduced Order ◽  
Unsteady Fluid Dynamics

AbstractIn this paper we develop reduced-order models for the unsteady lift on a pitching and plunging aerofoil over a range of angles of attack. In particular, we analyse the pitching and plunging dynamics for two cases: a two-dimensional flat plate at $\mathit{Re}= 100$ using high-fidelity direct numerical simulations and a three-dimensional NACA 0006 aerofoil at $\mathit{Re}= 65\hspace{0.167em} 000$ using wind-tunnel measurements. Models are obtained at various angles of attack and they are verified against measurements using frequency response plots and large-amplitude manoeuvres. These models provide a low-dimensional balanced representation of the relevant unsteady fluid dynamics. In simulations, flow structures are visualized using finite-time Lyapunov exponents. A number of phenomenological trends are observed, both in the data and in the models. As the base angle of attack increases, the boundary layer begins to separate, resulting in a decreased quasi-steady lift coefficient slope and a delayed relaxation to steady state at low frequencies. This extends the low-frequency range of motions that excite unsteady effects, meaning that the quasi-steady approximation is not valid until lower frequencies than are predicted by Theodorsen’s classical inviscid model. In addition, at small angles of attack, the lift coefficient rises to the steady-state value after a step in angle, while at larger angles of attack, the lift coefficient relaxes down to the steady-state after an initially high lift state. Flow visualization indicates that this coincides with the formation and convection of vortices at the leading edge and trailing edge. As the angle of attack approaches the critical angle for vortex shedding, the poles and zeros of the model approach the imaginary axis in the complex plane, and some zeros cross into the right half plane. This has significant implications for active flow control, which are discussed. These trends are observed in both simulations and wind-tunnel data.

Network reconstruction based on steady-state data

2008 ◽  
Vol 45 ◽  
pp. 161-176 ◽  
Author(s):  
Eduardo D. Sontag
Keyword(s):  
Steady State ◽  
Reverse Engineering ◽  
Theoretical Method ◽  
Network Reconstruction ◽  
Quasi Steady State ◽  
State Data

This paper discusses a theoretical method for the “reverse engineering” of networks based solely on steady-state (and quasi-steady-state) data.

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