Nonconservative QFT bounds for tracking error specifications

Elso, Jorge; Gil-Martínez, Montserrat; García-Sanz, Mario

doi:10.1002/rnc.1804

Cited by 11 publications

(18 citation statements)

References 13 publications

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“…The advantage of this approach is that the tracking error problem can be tackled with existing techniques, such as or . Both and lead to bounds on

l_{ii 0} MathClass-rel= g_{ii} {\overset{p}{true}}_{ii 0}^{i}

.…”

Section: Derivation Of Siso Equivalent Problemsmentioning

confidence: 99%

“…An equivalent way to express , more suitable for computer‐based design , is

(||, \frac{T_{u}}{T_{v}}) ⩽ \frac{B}{A} MathClass-punc, MathClass-rel\forall q_{u} MathClass-punc, q_{v} MathClass-rel\in scriptQ MathClass-punc,

where T u and T v are two complementary sensitivity functions based on plants within the uncertainty set. For the SISO tracking error problem , the necessary and sufficient condition is derived in by means of a graphical analysis and takes the form

(||, \frac{T_{u}}{T_{v}}) ⩽ \frac{MathClass-rel| M MathClass-rel| normalcos β MathClass-bin+ \sqrt{B^{2} MathClass-bin- MathClass-rel| M {MathClass-rel|}^{2} {normalsin}^{2} β}}{MathClass-rel| M MathClass-rel| normalcos β MathClass-bin- \sqrt{B^{2} MathClass-bin- MathClass-rel| M {MathClass-rel|}^{2} {normalsin}^{2} β}} MathClass-punc, with β MathClass-rel= \frac{1}{2} MathClass-rel| ∠ T_{u} MathClass-bin- ∠ T_{v} MathClass-rel| MathClass-punc, MathClass-rel\forall q_{u} MathClass-punc, q_{v} MathClass-rel\in scriptQ MathClass-punc.

…”

Section: Qft Bounds For the Equivalent Siso Tracking Error Problemmentioning

confidence: 99%

“…The case of is that of a tracking error specification imposed on the system depicted in Figure , namely,

(||, M MathClass-bin- \frac{PGF MathClass-bin- C}{1 MathClass-bin+ PG}) ⩽ B

where C comprises the f kj and m kj terms. The presence of an uncertain plant C in the feedforward path makes it very difficult for the graphical approach undertaken in .…”

Section: Qft Bounds For the Equivalent Siso Tracking Error Problemmentioning

confidence: 99%

“…This expression constitutes an improvement with respect to (9), because it reduces the demand for feedback. Once (12) is fulfilled, the prefilter is designed either by applying F D F 0 D M=T 0 , which requires appropriate choice of M to avoid high order or improper controllers, or by building bounds in the F plane for acceptable deviations from F 0 at each frequency [4].…”

Section: Previous Approachesmentioning

confidence: 99%

“…The problem of tracking error, also called model matching, has drawn considerable attention from the quantitative feedback theory (QFT) community [1][2][3][4][5][6][7][8][9]. Common motivations for this interest refer to (i) the ability of such specifications to capture phase information and (ii) the potential reduction of overdesign that it entails in comparison with the classical approaches.…”

Section: Introductionmentioning

confidence: 99%

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A quantitative feedback solution to the multivariable tracking error problem

Elso

Gil-Martínez

García-Sanz

2013

Int. J. Robust. Nonlinear Control

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SUMMARYThis paper introduces a novel solution for the multi‐input multi‐output (MIMO) quantitative feedback theory control design problem with tracking error specifications. Looking for a minimum controller overdesign, the technique finds new controller quantitative feedback theory bounds based on necessary and sufficient conditions for the existence of suitable associated prefilter matrix elements. It improves previous approaches to the subject and includes (i) the possibility of a free selection of the nominal plant, (ii) a less conservative application of the Schwartz inequality to decisively reduce the potential controller overdesign, (iii) a methodology to design independently the elements of the prefilter matrix, and (iv) a scope of application to both sequential and nonsequential MIMO controller design methods. The benefits of the new control design technique are illustrated by means of two examples. The first one, a standard 2 × 2 MIMO problem, is provided for comparison purposes with previous approaches. The second example, included as a major control challenge, deals with a well‐known demanding distillation column benchmark problem. Copyright © 2013 John Wiley & Sons, Ltd.

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“…The advantage of this approach is that the tracking error problem can be tackled with existing techniques, such as or . Both and lead to bounds on

l_{ii 0} MathClass-rel= g_{ii} {\overset{p}{true}}_{ii 0}^{i}

.…”

Section: Derivation Of Siso Equivalent Problemsmentioning

confidence: 99%

“…An equivalent way to express , more suitable for computer‐based design , is

(||, \frac{T_{u}}{T_{v}}) ⩽ \frac{B}{A} MathClass-punc, MathClass-rel\forall q_{u} MathClass-punc, q_{v} MathClass-rel\in scriptQ MathClass-punc,

(||, \frac{T_{u}}{T_{v}}) ⩽ \frac{MathClass-rel| M MathClass-rel| normalcos β MathClass-bin+ \sqrt{B^{2} MathClass-bin- MathClass-rel| M {MathClass-rel|}^{2} {normalsin}^{2} β}}{MathClass-rel| M MathClass-rel| normalcos β MathClass-bin- \sqrt{B^{2} MathClass-bin- MathClass-rel| M {MathClass-rel|}^{2} {normalsin}^{2} β}} MathClass-punc, with β MathClass-rel= \frac{1}{2} MathClass-rel| ∠ T_{u} MathClass-bin- ∠ T_{v} MathClass-rel| MathClass-punc, MathClass-rel\forall q_{u} MathClass-punc, q_{v} MathClass-rel\in scriptQ MathClass-punc.

…”

Section: Qft Bounds For the Equivalent Siso Tracking Error Problemmentioning

confidence: 99%

“…The case of is that of a tracking error specification imposed on the system depicted in Figure , namely,

(||, M MathClass-bin- \frac{PGF MathClass-bin- C}{1 MathClass-bin+ PG}) ⩽ B

where C comprises the f kj and m kj terms. The presence of an uncertain plant C in the feedforward path makes it very difficult for the graphical approach undertaken in .…”

Section: Qft Bounds For the Equivalent Siso Tracking Error Problemmentioning

confidence: 99%

Section: Previous Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A quantitative feedback solution to the multivariable tracking error problem

Elso

Gil-Martínez

García-Sanz

2013

Int. J. Robust. Nonlinear Control

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Quantitative feedback control for multivariable model matching and disturbance rejection

Elso

Gil-Martínez

García-Sanz

2016

Int. J. Robust. Nonlinear Control

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SUMMARYThis article extends two recent contributions in the field of quantitative feedback theory to the multivariable case. They concern the model matching and the measured disturbance rejection problems. The model matching problem is a tracking control problem with specifications given as acceptable deviations from an ideal response. The measured disturbance rejection problem balances feedback and feedforward actions to reject disturbances. Both perspectives present advantages over classical quantitative feedback theory techniques in certain situations. This paper develops the necessary tools to solve both control problems in the case of multi-input multi-output plants. In particular, it shows how to derive nonconservative controller bounds for each of the single-input single-output control problems in which the overall multivariable problem is divided. The result is a systematic controller design methodology for multi-input multi-output plants with structured uncertainty. The application of the technique to the well-known quadruple-tank process illustrates the benefits of the method.

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