Singular perturbation modeling of nonlinear processes with nonexplicit time-scale multiplicity

Kumar, Aditya; Christofides, Panagiotis D.; Daoutidis, Pródromos

doi:10.1016/s0009-2509(98)00006-2

Cited by 83 publications

(52 citation statements)

References 9 publications

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“…Again, we note the strong resemblance of our decomposition approach to other nonlinear model reduction procedures (see e.g., Baldea et al, 2006;Kumar et al, 1998;Sujit et al, 2011;Vora and Daoutidis, 2001). Likewise, this species conservation is at work in systems such as the isomerization reactions of Wei and Prater (1962) and numerous follow-up studies (e.g., Lombardo and Hall, 1971) where the eigenvector associated with a single zero eigenvalue of the reaction rate coefficient array represents the conservation of species A 1 þ A 2 þ A 3 in the three-species equilibrium reaction network of the cited studies.…”

Section: A Simple Deposition Reaction Schemementioning

confidence: 60%

Reaction factorization for the dynamic analysis of atomic layer deposition kinetics

Remmers

Travis

Adomaitis

2015

Chemical Engineering Science

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Section: A Simple Deposition Reaction Schemementioning

confidence: 60%

Reaction factorization for the dynamic analysis of atomic layer deposition kinetics

Remmers

Travis

Adomaitis

2015

Chemical Engineering Science

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“…However, systems without explicit timescale separation (or in non-standard form) can also be treated [9], [10], [11]. Briefly speaking, a systemẋ = F(x, ε) exhibiting slow and fast dynamics can be put into standard form (1) via a change of coordinates which may depend on ε.…”

Section: Definition 2 (Normally Hyperbolic)mentioning

confidence: 99%

“…First, recall that X denotes the vector field (8), and Φ the blow up map (11). LetX denote the blown up vector field, that isX = DΦ −1 • X • Φ, where DΦ denotes the Jacobian of Φ.…”

Section: Next We Have the Most Important Property Of (12)mentioning

confidence: 99%

Model Order Reduction and Composite Control for a Class of Slow-Fast Systems Around a Non-Hyperbolic Point

Jardón-Kojakhmetov

Scherpen

2017

IEEE Control Syst. Lett.

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Model order reduction and composite control for a class of slow-fast systems around a nonhyperbolic point Jardón Kojakhmetov, H.; Scherpen, Jacquelien M.A. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCSYS.2017.2703983, IEEE Control Systems LettersModel order reduction and composite control for a class of slow-fast systems around a non-hyperbolic point H. Jardón-Kojakhmetov 1 and Jacquelien M.A. Scherpen 1Abstract-In this letter we investigate a class of slow-fast systems for which the classical model order reduction technique based on singular perturbations does not apply due to the lack of a Normally Hyperbolic critical manifold. We show, however, that there exists a class of slow-fast systems that after a well-defined change of coordinates have a Normally Hyperbolic critical manifold. This allows the use of model order reduction techniques and to qualitatively describe the dynamics from auxiliary reduced models even in the neighborhood of a non-hyperbolic point. As an important consequence of the model order reduction step, we show that it is possible to design composite controllers that stabilize the (non-hyperbolic) origin.

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“…However, the descriptor form of A/C model cannot be used directly for singular perturbation method as it is not in standard form. Instead, the A/C model is transformed into a specific form, on which the theory also works as proved in [36,37]. Specifically, if the time-factor exists on the right hand side of the system dynamical equations as follow:…”

Section: Model and Controller Order Reductionmentioning

confidence: 99%

Modeling and output feedback control of automotive air conditioning system

Zhang

Canova

2015

International Journal of Refrigeration

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This paper presents an application of robust control theory to an automotive Air Conditioning (A/C) system. A control-oriented model built using movingboundary method is validated against experimental data collected on a vehicle chassis dynamometer, at constant engine speeds as well as on driving cycles.Next, an H ∞ controller is synthesized by formulating an optimization problem whose solution requires appropriate weighting functions selection. Singular perturbation method is utilized to remove states associated with fast dynamics in both model and controller. Both full-order and reduced-order H ∞ controllers are verified by simulation results obtained using the nonlinear A/C system model. It is demonstrated that the designed controller is capable of tracking the reference output trajectories while rejecting disturbances introduced on the boundary conditions of the heat exchangers. Furthermore, a preliminary study is performed to reveal the opportunity of designing a gain-scheduled H ∞ controller for global output tracking.

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Singular perturbation modeling of nonlinear processes with nonexplicit time-scale multiplicity

Cited by 83 publications

References 9 publications

Reaction factorization for the dynamic analysis of atomic layer deposition kinetics

Reaction factorization for the dynamic analysis of atomic layer deposition kinetics

Model Order Reduction and Composite Control for a Class of Slow-Fast Systems Around a Non-Hyperbolic Point

Modeling and output feedback control of automotive air conditioning system

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