Input-Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows

Bagheri, Shervin; Henningson, Dan S.; Hœpffner, Jérôme; Schmid, Peter J.

doi:10.1115/1.3077635

Cited by 154 publications

(257 citation statements)

References 86 publications

(23 reference statements)

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“…easily recover the original characterization of the problem (Bagheri et al 2009b). In the present contribution, the dual algorithm is referred to as adjoint of adjoint-direct (AAD).…”

Section: Aim Of the Investigationmentioning

confidence: 99%

“…Lewis & Syrmos 1995;Zhou, Doyle & Glover 2002;Bagheri et al 2009b); the aim of this section is to introduce the main relations in a concise way, as these will be needed in § 4.…”

Section: Optimal Control and Estimation: A Brief Reviewmentioning

confidence: 99%

“…Note that the unknown of the Riccati equation (3.11) is the expected energy of the estimation error e(t) (Lewis & Syrmos 1995;Bagheri et al 2009b). By analogy with the control problem, it is interesting to note that the optimal gain matrix L can be computed by introducing the dual fictitious adjoint system 12) where the 'feedback law' is now represented byỹ(t) = L H p(t).…”

mentioning

confidence: 99%

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Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

et al. 2013

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The control of Tollmien-Schlichting (TS) in a 2D boundary layer is analysed by using numerical simulation. Full-dimensional optimal controllers are used in combination with a set-up of spatially localised inputs (actuators and disturbance) and outputs (sensors). The Adjoint of the Direct-Adjoint (ADA) algorithm, recently proposed by Pralits & Luchini (2010), is used to efficiently compute the Linear Quadratic Regulator (LQR) controller; the method is iterative and allows to by-pass the solution of the corresponding Riccati equation, unfeasible for high-dimensional systems. We show that an analogous iteration can be cast for the estimation problem; the dual algorithm is referred to as Adjoint of the Adjoint-Direct (AAD). By combining the solutions of the estimation and control problem, a full dimensional, model-free, Linear Gaussian Quadratic (LQG) controllers are obtained and used for the attenuation of the disturbances arising in the boundary layer flow. Model-free, full dimensional controllers turn out to be an excellent benchmark for evaluating the performance of the optimal control/estimation design based on open-loop model reduction. We show the conditions under which the two strategies are in perfect agreement by focusing on the issues arising when feedback configurations are considered. An analysis of the finite amplitude cases is also carried out addressing the limitations of the optimal controllers, the role of the estimation and the robustness to the nonlinearities arising in the flow of the control design

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“…easily recover the original characterization of the problem (Bagheri et al 2009b). In the present contribution, the dual algorithm is referred to as adjoint of adjoint-direct (AAD).…”

Section: Aim Of the Investigationmentioning

confidence: 99%

“…Lewis & Syrmos 1995;Zhou, Doyle & Glover 2002;Bagheri et al 2009b); the aim of this section is to introduce the main relations in a concise way, as these will be needed in § 4.…”

Section: Optimal Control and Estimation: A Brief Reviewmentioning

confidence: 99%

mentioning

confidence: 99%

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Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

et al. 2013

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“…Indeed, using the HSV, it is possible to evaluate a priori the theoretical error bounds when exact balanced truncation is performed (see Skogestad & Postlethwaite 2005). By assuming that the theoretical bounds of the exact balanced truncation are valid also for the approximate case when the converged modes are considered (see Bagheri et al 2009b), we kept an error bound of order O(10 −4 ) for all of the models used in this work. Transition delay in a boundary layer flow using active control…”

Section: Appendix Control Designmentioning

confidence: 99%

“…For a complete derivation of the LQG solution, we refer to Lewis & Syrmos (1995), Dullerud & Paganini (1999) and Bagheri et al (2009b). First, the controller is computed by assuming full knowledge of the state and solving the associated algebraic Riccati equation 0 = A H r X + XA r − XB 2r R −1 B H 2r X + C H 1r C 1r .…”

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confidence: 99%

Transition delay in a boundary layer flow using active control

et al. 2013

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Active linear control is applied to delay the onset of laminar-turbulent transition in the boundary layer over a flat plate. The analysis is carried out by numerical simulations of the nonlinear, transitional regime. A three-dimensional, localized initial condition triggering Tollmien-Schlichting waves of finite amplitude is used to numerically simulate the transition to turbulence. Linear quadratic Gaussian controllers based on reduced-order models of the linearized Navier-Stokes equations are designed, where the wall sensors and the actuators are localized in space. A parametric analysis is carried out in the nonlinear regime, for different disturbance amplitudes, by investigating the effects of the actuation on the flow due to different distributions of the localized actuators along the spanwise direction, different sizes of the actuators and the effort of the controllers. We identify the range of parameters where the controllers are effective and highlight the limits of the device for high amplitudes and strong control action. Despite the fully linear control approach, it is shown that the device is effective in delaying the onset of laminar-turbulent transition in the presence of packets characterized by amplitudes a ≈ 1 % of the free stream velocity at the actuator location. Up to these amplitudes, it is found that a proper choice of the actuators positively affects the performance of the controller. For a transitional case, a ≈ 0.20 %, we show a transition delay of ∆Re x = 3.0 × 10 5 .

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Stabilization of linear time‐varying reduced‐order models: A feedback controller approach

Mojgani

Balajewicz

2020

Numerical Meth Engineering

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Summary Many of the commonly used methods in model‐order reduction do not guarantee stability of the reduced‐order model. This article extends the eigenvalue reassignment method of stabilization of linear time‐invariant ROMs, to the more general case of linear time‐varying systems. Through a postprocessing step, the ROM is controlled to ensure the stability while enhancing/maintaining its accuracy using a constrained nonlinear lease‐square minimization problem. The controller and the input signals are defined at the algebraic level, using left and right singular vectors of the reduced system matrices. The choice provides a control on the upper bound of the growth of the energy of the reduced system. The optimization problem is applied to several time‐invariant, time‐periodic, and time‐varying problems, and the reproductive and predictive capabilities of the proposed method, with respect to novel inputs and the system parameters, are evaluated.

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Input-Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows

Cited by 154 publications

References 86 publications

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

Transition delay in a boundary layer flow using active control

Stabilization of linear time‐varying reduced‐order models: A feedback controller approach

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