NONUNIFORM GRIDS FOR REDUCED BASIS DESIGN OF LOW ORDER FEEDBACK CONTROLLERS FOR NONLINEAR CONTINUOUS SYSTEMS

In this paper, we discuss the use of nonuniform grids in reduced basis design for developing low order nonlinear feedback controllers for hybrid distributed parameter systems. The reduced basis approach was presented in an earlier paper by Burns and King; therein, all approximations were based upon uniform grids. In this paper, we explore the effect on control design of using nonuniform grids in the fundamental step of approximating the functional controller gains. We illustrate the process using a weakly nonlinear distributed parameter system.

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A Reduced Basis Approach to the Design of Low-Order Feedback Controllers for Nonlinear Continuous Systems

Journal of Vibration and Control ◽

10.1177/107754639800400305 ◽

1998 ◽

Vol 4 (3) ◽

pp. 297-323 ◽

Cited By ~ 60

Author(s):

John A. Burns ◽

Belinda B. King

Keyword(s):

Continuous Systems ◽

Reduced Basis ◽

Feedback Controllers ◽

Low Order

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On the Convexity Preservation of a Quasi C3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids

Mathematics ◽

10.3390/math9040310 ◽

2021 ◽

Vol 9 (4) ◽

pp. 310 ◽

Cited By ~ 1

Author(s):

Pedro Ortiz ◽

Juan Carlos Trillo

Keyword(s):

Initial Data ◽

Numerical Experiments ◽

Approximation Order ◽

Piecewise Polynomial ◽

Nonuniform Grids ◽

Uniform Grids ◽

Reconstruction Operator ◽

Convexity Properties ◽

Second Degree

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.

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Arbitrary pole placement via low order dynamic output feedback controllers: a solution in closed form

Proceedings of 1995 34th IEEE Conference on Decision and Control ◽

10.1109/cdc.1995.478527 ◽

2002 ◽

Cited By ~ 1

Author(s):

J. Leventides ◽

N. Karcanias

Keyword(s):

Closed Form ◽

Output Feedback ◽

Pole Placement ◽

Dynamic Output Feedback ◽

Feedback Controllers ◽

Dynamic Output ◽

Low Order

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Analytical approximation of weakly nonlinear continuous systems using renormalization group method

Applied Mathematical Modelling ◽

10.1016/j.apm.2012.05.011 ◽

2013 ◽

Vol 37 (4) ◽

pp. 2102-2114 ◽

Cited By ~ 7

Author(s):

S.A.A. Hosseini

Keyword(s):

Renormalization Group ◽

Analytical Approximation ◽

Group Method ◽

Continuous Systems ◽

Renormalization Group Method ◽

Weakly Nonlinear

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Convex optimization of nonlinear feedback controllers via occupation measures

The International Journal of Robotics Research ◽

10.1177/0278364914528059 ◽

2014 ◽

Vol 33 (9) ◽

pp. 1209-1230 ◽

Cited By ~ 44

Author(s):

Anirudha Majumdar ◽

Ram Vasudevan ◽

Mark M. Tobenkin ◽

Russ Tedrake

Keyword(s):

Convex Optimization ◽

Nonlinear Feedback ◽

Feedback Controllers ◽

Occupation Measures

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Set point boundary control for a nonlinear distributed parameter system

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) ◽

10.1109/cdc.2003.1272579 ◽

2004 ◽

Author(s):

C.I. Bymes ◽

D.S. Gilliam ◽

A. Isidori ◽

V.I. Shubov

Keyword(s):

Boundary Control ◽

Distributed Parameter ◽

Distributed Parameter System ◽

Point Boundary ◽

Parameter System ◽

Set Point ◽

Nonlinear Distributed Parameter System

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Predicting Thermoacoustic Instability in an Industrial Gas Turbine Combustor: Combining a Low Order Network Model With Flame LES

Volume 4A: Combustion, Fuels and Emissions ◽

10.1115/gt2017-63247 ◽

2017 ◽

Cited By ~ 2

Author(s):

Y. Xia ◽

A. S. Morgans ◽

W. P. Jones ◽

J. Rogerson ◽

G. Bulat ◽

...

Keyword(s):

Gas Turbine ◽

Acoustic Waves ◽

Gas Turbine Combustor ◽

Network Modelling ◽

Weakly Nonlinear ◽

Thermoacoustic Instability ◽

Reduced Chemistry ◽

Flame Describing Function ◽

Industrial Gas Turbine ◽

Low Order

The thermoacoustic modes of a full scale industrial gas turbine combustor have been predicted numerically. The predictive approach combines low order network modelling of the acoustic waves in a simplified geometry, with a weakly nonlinear flame describing function, obtained from incompressible large eddy simulations of the flame region under upstream forced velocity perturbations, incorporating reduced chemistry mechanisms. Two incompressible solvers, each employing different numbers of reduced chemistry mechanism steps, are used to simulate the turbulent reacting flowfield to predict the flame describing functions. The predictions differ slightly between reduced chemistry approximations, indicating the need for more involved chemistry. These are then incorporated into a low order thermoacoustic solver to predict thermoacoustic modes. For the combustor operating at two different pressures, most thermoacoustic modes are predicted to be stable, in agreement with the experiments. The predicted modal frequencies are in good agreement with the measurements, although some mismatches in the predicted modal growth rates and hence modal stabilities are observed. Overall, these findings lend confidence in this coupled approach for real industrial gas turbine combustors.

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