Feedback stabilization of fluids using reduced-order models for control and compensator design

Borggaard, Jeff; Gugercin, Serkan; Zietsman, Lizette

doi:10.1109/cdc.2016.7799440

Cited by 3 publications

(7 citation statements)

References 37 publications

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“…In the context of nonlinear flow control, the problem of linearization errors and compensation by reduced-order controllers has been considered in [14]. There it is mentioned that linearization errors in (19) from (18) result in additive disturbances on the transfer function, which can be handled as disturbances in the coprime factorization. In fact, the coprime factorization can be explicitly written down.…”

Section: As Ode Systemmentioning

confidence: 99%

“…The practical construction of a reduced-order controller for (18) follows, in principle, the different steps mentioned in this paper so far with some additional numerical tricks. For simplicity, we give a final summary of the performed steps in the following:…”

Section: Computation Of Low-rank Controllersmentioning

confidence: 99%

“…Step 2. Construction of the reduced-order model: Now, the full-order system (18) needs to be reduced by Algorithm 1. Therefore, we use the final low-rank solution factors Z k and Z k of the projected algebraic Riccati equations (23a) and (23b), respectively, from the previous computation of the robustness margin in Step 1 corresponding to the computed such that…”

Section: Computation Of Low-rank Controllersmentioning

confidence: 99%

“…As second example, we borrow the numerical setup from [18] of the wake with two cylinders in two dimensions; see Fig. 3.…”

Section: Test Case: Double Cylindermentioning

confidence: 99%

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Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

2022

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Output-based controllers are known to be fragile with respect to model uncertainties. The standard $$\mathcal {H}_{\infty }$$ H ∞ -control theory provides a general approach to robust controller design based on the solution of the $$\mathcal {H}_{\infty }$$ H ∞ -Riccati equations. In view of stabilizing incompressible flows in simulations, two major challenges have to be addressed: the high-dimensional nature of the spatially discretized model and the differential-algebraic structure that comes with the incompressibility constraint. This work demonstrates the synthesis of low-dimensional robust controllers with guaranteed robustness margins for the stabilization of incompressible flow problems. The performance and the robustness of the reduced-order controller with respect to linearization and model reduction errors are investigated and illustrated in numerical examples.

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Section: As Ode Systemmentioning

confidence: 99%

Section: Computation Of Low-rank Controllersmentioning

confidence: 99%

Section: Computation Of Low-rank Controllersmentioning

confidence: 99%

“…As second example, we borrow the numerical setup from [18] of the wake with two cylinders in two dimensions; see Fig. 3.…”

Section: Test Case: Double Cylindermentioning

confidence: 99%

See 2 more Smart Citations

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

2022

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“…that maps v(t) into the kernel of J along the orthogonal complement (in the inner product induced by the mass matrix E) of J T . Making use of Π and the identities ΠE = EΠ T -which holds for symmetric E -and Π T v δ = v δ , we can eliminate the discrete pressure p and the algebraic constraint 0 = Jv δ and rewrite (17) as an ODE…”

Section: Semi-discretization and Linearization Of Nsementioning

confidence: 99%

Robust output-feedback stabilization for incompressible flows using low-dimensional $\mathcal{H}_{\infty}$-controllers

Benner,

Heiland,

Werner

2021

Preprint

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Output-based controllers are known to be fragile with respect to model uncertainties. The standard H ∞ -control theory provides a general approach to robust controller design based on the solution of the H ∞ -Riccati equations. In view of stabilizing incompressible flows in simulations, two major challenges have to be addressed: the high-dimensional nature of the spatially discretized model and the differential-algebraic structure that comes with the incompressibility constraint. This work demonstrates the synthesis of low-dimensional robust controllers with guaranteed robustness margins for the stabilization of incompressible flow problems. The performance and the robustness of the reduced-order controller with respect to linearization and model reduction errors are investigated and illustrated in numerical examples.

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Nonlinear feedback stabilization of incompressible flows via updated Riccati-based gains

Benner

Heiland

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Feedback stabilization of fluids using reduced-order models for control and compensator design

Cited by 3 publications

References 37 publications

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

Robust output-feedback stabilization for incompressible flows using low-dimensional $\mathcal{H}_{\infty}$-controllers

Nonlinear feedback stabilization of incompressible flows via updated Riccati-based gains

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