scholarly journals Input–output measures for model reduction and closed-loop control: application to global modes

2011 ◽  
Vol 685 ◽  
pp. 23-53 ◽  
Author(s):  
Alexandre Barbagallo ◽  
Denis Sipp ◽  
Peter J. Schmid
Keyword(s):  
Feedback Control ◽  
Model Reduction ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Reduction Process ◽  
Open Loop ◽  
Input Output ◽  
Control Applications ◽  
Reduced Order ◽  
Global Modes

AbstractFeedback control applications for flows with a large number of degrees of freedom require the reduction of the full flow model to a system with significantly fewer degrees of freedom. This model-reduction process is accomplished by Galerkin projections using a reduction basis composed of modal structures that ideally preserve the input–output behaviour between actuators and sensors and ultimately result in a stabilized compensated system. In this study, global modes are critically assessed as to their suitability as a reduction basis, and the globally unstable, two-dimensional flow over an open cavity is used as a test case. Four criteria are introduced to select from the global spectrum the modes that are included in the reduction basis. Based on these criteria, four reduced-order models are tested by computing open-loop (transfer function) and closed-loop (stability) characteristics. Even though weak global instabilities can be suppressed, the concept of reduced-order compensators based on global modes does not demonstrate sufficient robustness to be recommended as a suitable choice for model reduction in feedback control applications. The investigation also reveals a compelling link between frequency-restricted input–output measures of open-loop behaviour and closed-loop performance, which suggests the departure from mathematically motivated ${\mathscr{H}}_{\infty } $-measures for model reduction toward more physically based norms; a particular frequency-restricted input–output measure is proposed in this study which more accurately predicts the closed-loop behaviour of the reduced-order model and yields a stable compensated system with a markedly reduced number of degrees of freedom.

scholarly journals Closed-loop control of an open cavity flow using reduced-order models

2009 ◽  
Vol 641 ◽  
pp. 1-50 ◽  
Author(s):  
ALEXANDRE BARBAGALLO ◽  
DENIS SIPP ◽  
PETER J. SCHMID
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Transfer Functions ◽  
Reynolds Numbers ◽  
Open Loop ◽  
Reduced Order Models ◽  
Loop Control ◽  
Reduced Order ◽  
Global Modes ◽  
Proper Orthogonal

The control of separated fluid flow by reduced-order models is studied using the two-dimensional incompressible flow over an open square cavity at Reynolds numbers where instabilities are present. Actuation and measurement locations are taken on the upstream and downstream edge of the cavity. A bi-orthogonal projection is introduced to arrive at reduced-order models for the compensated problem. Global modes, proper orthogonal decomposition (POD) modes and balanced modes are used as expansion bases for the model reduction. The open-loop behaviour of the full and the reduced systems is analysed by comparing the respective transfer functions. This analysis shows that global modes are inadequate to sufficiently represent the input–output behaviour whereas POD and balanced modes are capable of properly approximating the exact transfer function. Balanced modes are far more efficient in this process, but POD modes show superior robustness. The performance of the closed-loop system corroborates this finding: while reduced-order models based on POD are able to render the compensated system stable, balanced modes accomplish the same with far fewer degrees of freedom.

Empirical pseudo-balanced model reduction and feedback control of weakly nonlinear convection patterns

2010 ◽  
Vol 662 ◽  
pp. 36-65 ◽  
Author(s):  
A. C. OR ◽  
J. L. SPEYER
Keyword(s):  
Feedback Control ◽  
Model Reduction ◽  
Large Scale ◽  
Open Loop ◽  
Nonlinear Convection ◽  
Weakly Nonlinear ◽  
Reduced Order ◽  
Convection Patterns ◽  
Balanced Model ◽  
Convection Rolls

An empirical model reduction method is performed on nonlinear transient convection patterns near the threshold, using a pseudo-inverse-based projective method called the pseudo-balanced proper orthogonal decomposition (PBPOD). These transient patterns are large-scale amplitude/phase modulations in convection rolls, obtained by prescribing selected spatial input-shape functions. For the nonlinear convection patterns modelled, PBPOD appears to be very effective. Using the nonlinear front example, PBPOD is compared with other existing methods, such as POD and linearized BPOD. The limitations of the methods are discussed. Using a complex prescribed input, complex disturbances are generated and the outputs of the open-loop responses are compared between the original and the reduced-order models. The agreement is good. A feedback-control study is performed using the nonlinear front example. The controller is built by the pseudo-balanced reduced-order model, with a low-order nonlinear estimator. Closed-loop simulations show that the nonlinear travelling fronts can be effectively damped out by the feedback-control actions.

A Physics-Based Dynamic Model for Boilers: Part 2 — Model Reduction in a Cogeneration Application

2017 ◽  
Author(s):  
Matthew J. Blom ◽  
Michael J. Brear ◽  
Chris G. Manzie ◽  
Ashley P. Wiese
Keyword(s):  
Model Reduction ◽  
Gas Turbine ◽  
Dynamic Model ◽  
Reduction Process ◽  
Singular Perturbation Theory ◽  
Reduced Order Models ◽  
Reduced Order ◽  
One Dimensional ◽  
Time Scale Separation ◽  
Modelling Framework

This paper is the second part of a two part study that develops, validates and integrates a one-dimensional, physics-based, dynamic boiler model. Part 1 of this study [1] extended and validated a particular modelling framework to boilers. This paper uses this framework to first present a higher order model of a gas turbine based cogeneration plant. The significant dynamics of the cogeneration system are then identified, corresponding to states in the gas path, the steam path, the gas turbine shaft, gas turbine wall temperatures and boiler wall temperatures. A model reduction process based on time scale separation and singular perturbation theory is then demonstrated. Three candidate reduced order models are identified using this model reduction process, and the simplest, acceptable dynamic model of this integrated plant is found to require retention of both the gas turbine and boiler wall temperature dynamics. Subsequent analysis of computation times for the original physics-based one-dimensional model and the candidate, reduced order models demonstrates that significantly faster than real time simulation is possible in all cases. Furthermore, with systematic replacement of the algebraic states with feedforward maps in the reduced order models, further computational savings of up to one order of magnitude can be achieved. This combination of model fidelity and computational tractability suggest suggests that the resulting reduced order models may be suitable for use in model based control of cogeneration plants.

Multi-Stage System Identification of a Gas Turbine

2017 ◽  
Author(s):  
Amit Pandey ◽  
Maurício de Oliveira ◽  
Chad M. Holcomb
Keyword(s):  
Gas Turbine ◽  
Closed Loop ◽  
Open Loop ◽  
Loop System ◽  
Closed Loop Control ◽  
Input Output ◽  
Open Loop System ◽  
Loop Control ◽  
Multi Stage ◽  
Identification Techniques

Several techniques have recently been proposed to identify open-loop system models from input-output data obtained while the plant is operating under closed-loop control. So called multi-stage identification techniques are particularly useful in industrial applications where obtaining input-output information in the absence of closed-loop control is often difficult. These open-loop system models can then be employed in the design of more sophisticated closed-loop controllers. This paper introduces a methodology to identify linear open-loop models of gas turbine engines using a multi-stage identification procedure. The procedure utilizes closed-loop data to identify a closed-loop sensitivity function in the first stage and extracts the open-loop plant model in the second stage. The closed-loop data can be obtained by any sufficiently informative experiment from a plant in operation or simulation. We present simulation results here. This is the logical process to follow since using experimentation is often prohibitively expensive and unpractical. Both identification stages use standard open-loop identification techniques. We then propose a series of techniques to validate the accuracy of the identified models against first principles simulations in both the time and frequency domains. Finally, the potential to use these models for control design is discussed.

Passive optimal feedback control of an articulated flexible arm

2020 ◽  
pp. 107754632095676
Author(s):  
Raja Tebbikh ◽  
Hicham Tebbikh ◽  
Sihem Kechida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Closed Loop ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Convolution Operators ◽  
High Frequencies ◽  
Zero Initial Condition ◽  
Flexible Arm ◽  
Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

Error-Controlled Model Reduction in Flexible Multibody Dynamics

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Jörg Fehr ◽  
Peter Eberhard
Keyword(s):  
Model Reduction ◽  
Error Bounds ◽  
Degrees Of Freedom ◽  
A Priori ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Scanning Tunneling ◽  
Error Estimator ◽  
Gramian Matrix ◽  
Flexible Multibody

One important issue for the simulation of flexible multibody systems is the quality controlled reduction in the flexible bodies degrees of freedom. In this work, the procedure is based on knowledge about the error induced by model reduction. For modal reduction, no error bound is available. For Gramian matrix based reduction methods, analytical error bounds can be developed. However, due to numerical reasons, the dominant eigenvectors of the Gramian matrix have to be approximated. Within this paper, two different methods are presented for this purpose. For moment matching methods, the development of a priori error bounds is still an active field of research. In this paper, an error estimator based on a new second order adaptive global Arnoldi algorithm is introduced and further assists the user in the reduction process. We evaluate and compare those methods by reducing the flexible degrees of freedom of a rack used for active vibration damping of a scanning tunneling microscope.

scholarly journals Closed-loop feedback control for microfluidic systems through automated capacitive fluid height sensing

2017 ◽  
Author(s):  
L. R. Soenksen ◽  
T. Kassis ◽  
M. Noh ◽  
L.G. Griffith ◽  
D.L. Trumper
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Cost Effective ◽  
Capacitive Sensor ◽  
Open Loop ◽  
Small Scale ◽  
Microfluidic Systems ◽  
Wide Range ◽  
Loop Feedback ◽  
Closed Loop Feedback

AbstractPrecise fluid height sensing in open-channel microfluidics has long been a desirable feature for a wide range of applications. However, performing accurate measurements of the fluid level in small-scale reservoirs (<1mL) has proven to be an elusive goal, especially if direct fluid-sensor contact needs to be avoided. In particular, gravity-driven systems used in several microfluidic applications to establish pressure gradients and impose flow remain open-loop and largely unmonitored due to these sensing limitations. Here we present an optimized self-shielded coplanar capacitive sensor design and automated control system to provide submillimeter fluid-height resolution (~250 μm) and control of small-scale open reservoirs without the need for direct fluid contact. Results from testing and validation of our optimized sensor and system also suggest that accurate fluid height information can be used to robustly characterize, calibrate and dynamically control a range of microfluidic systems with complex pumping mechanisms, even in cell culture conditions. Capacitive sensing technology provides a scalable and cost-effective way to enable continuous monitoring and closed-loop feedback control of fluid volumes in small-scale gravity-dominated wells in a variety of microfluidic applications.

Academic Blade Geometries for Baseline Comparisons of Industry-Specific Forced Response Predictions

2017 ◽  
Author(s):  
James H. Little ◽  
Jeffrey L. Kauffman ◽  
Matthias Huels
Keyword(s):  
Model Reduction ◽  
Turbine Blades ◽  
Reduction Process ◽  
Forced Response ◽  
Vibration Characteristics ◽  
Contact Dynamics ◽  
Qualitative Behavior ◽  
Friction Damper ◽  
Blade Vibration ◽  
Reduced Order

Predicting the energy dissipation associated with contact of underplatform dampers remains a critical challenge in turbomachinery blade and friction damper design. Typical turbomachinery blade forced vibration response analyses rely on reduced order models and simplified nonlinear codes to predict blade vibration characteristics in a computationally tractable manner. Recent research has focused on both the model reduction process and simulation of the contact dynamics. This paper proposes two academic turbine blade geometries with coupled underplatform dampers as vehicles by which these model reduction and forced response simulation techniques may be compared. The blades correspond to two types of freestanding turbine blades and demonstrate the same qualitative behavior as more complex industry geometries. The blade geometries are fully described here and analyzed using the same procedure as used for an industry-specific blade. Standard results are presented in terms of resonance frequency, amplitude, and damping across a range of aerodynamic excitation. In addition, the predicted blade vibration characteristics are examined under variations in the contact interface: friction coefficient, damper / platform surface roughness, and damper mass, with relative sensitivities to each term generated. Finally, the effect of the number of modes retained in the reduced order model is studied to uncover patterns of convergence as well as to provide additional sets of standard data for comparison with other model reduction and forced response simulation methods.

Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach

2010 ◽  
Vol 63 (3) ◽  
Author(s):  
Denis Sipp ◽  
Olivier Marquet ◽  
Philippe Meliga ◽  
Alexandre Barbagallo
Keyword(s):  
Closed Loop ◽  
Selection Process ◽  
Open Loop ◽  
Base Flow ◽  
Closed Loop Control ◽  
Mean Flow ◽  
Loop Control ◽  
Dynamics And Control ◽  
Global Modes ◽  
And Control

This review article addresses the dynamics and control of low-frequency unsteadiness, as observed in some aerodynamic applications. It presents a coherent and rigorous linearized approach, which enables both to describe the dynamics of commonly encountered open-flows and to design open-loop and closed-loop control strategies, in view of suppressing or delaying instabilities. The approach is global in the sense that both cross-stream and streamwise directions are discretized in the evolution operator. New light will therefore be shed on the streamwise properties of open-flows. In the case of oscillator flows, the unsteadiness is due to the existence of unstable global modes, i.e., unstable eigenfunctions of the linearized Navier–Stokes operator. The influence of nonlinearities on the dynamics is studied by deriving nonlinear amplitude equations, which accurately describe the dynamics of the flow in the vicinity of the bifurcation threshold. These equations also enable us to analyze the mean flow induced by the nonlinearities as well as the stability properties of this flow. The open-loop control of unsteadiness is then studied by a sensitivity analysis of the eigenvalues with respect to base-flow modifications. With this approach, we manage to a priori identify regions of the flow where a small control cylinder suppresses unsteadiness. Then, a closed-loop control approach was implemented for the case of an unstable open-cavity flow. We have combined model reduction techniques and optimal control theory to stabilize the unstable eigenvalues. Various reduced-order-models based on global modes, proper orthogonal decomposition modes, and balanced modes were tested and evaluated according to their ability to reproduce the input-output behavior between the actuator and the sensor. Finally, we consider the case of noise-amplifiers, such as boundary-layer flows and jets, which are stable when viewed in a global framework. The importance of the singular value decomposition of the global resolvent will be highlighted in order to understand the frequency selection process in such flows.

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