Performance preserving controller reduction via additive perturbation of closed loop transfer function

Wang, G.; Sreeram, Victor; Liu, Wanquan

doi:10.1109/acc.1998.694745

Cited by 8 publications

(7 citation statements)

References 16 publications

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“…We ® rst brie¯y mention some points for comparing our reduction method with existing ones, whose aim is also to reduce a controller under a closed loop performance constraint (Lenz et al 1988, Chen et al 1994, Zhou and Chen 1995, Goddard and Glover 1998, Wang et al 1998). Note as a preliminary result that Goddard and Glover (1998) and Wang et al (1998) propose a method, which takes explicitly into account a closed loop H 1 performance constraint, and which consists in performing a classical frequency weighted model reduction, using speci® c choices of the weightings which are known to preserve the H1 constraint:…”

Section: A Brief Comparison With Other Reduction Methodsmentioning

confidence: 99%

“…Note as a preliminary result that Goddard and Glover (1998) and Wang et al (1998) propose a method, which takes explicitly into account a closed loop H 1 performance constraint, and which consists in performing a classical frequency weighted model reduction, using speci® c choices of the weightings which are known to preserve the H1 constraint:…”

Section: A Brief Comparison With Other Reduction Methodsmentioning

confidence: 99%

“…the full and reduced order controllers must both ensure that the H1 norm of a closed loop transfer function remains less than a ® xed value ® . An approximate state-space solution has been especially proposed in Goddard and Glover (1998) and Wang et al (1998) .…”

Section: Introductionmentioning

confidence: 99%

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Controller reduction with closed loop H infinity performance constraints: A QFT perspective

Ferreres¹,

Gorrec²

1999

International Journal of Control

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Controller reduction with closed loop H 1 1 performance constraints: a QFT perspective GILLES FERRERES{{ and YANN LE GORREC{Assume that an initial stabilizing controller K 0 … s † , which satis® es various closed loop frequency domain speci® cations, has been a priori synthesized using, e.g. H1 control, · synthesis techniques or closed loop convex synthesis. Remembering that the order of K 0 … s † is typically at least equal to the order of the plant to be controlled, the aim of this paper is to ® nd a stabilizing reduced order controller, which also satis® es the performance speci® cations and which moreover minimizes the open loop bandwidth. To this aim, the structured singular value · is used to translate at each frequency closed loop frequency domain speci® cations into requirements on the frequency response of the controller. The principle of our reduction method is thus very close to the original idea of the SISO QFT design approach, except that the problem of translating closed loop frequency domain speci® cations into open loop ones is much more complex in the MIMO case. The problem reduces to the issue of ® nding a controller, whose frequency response belongs at each frequency to a template. The convexity of these templates greatly facilitates the practical realization of the controller. As a ® nal point, the method is successfully applied to a standard H1 problem, which is extracted from the · Analysis and Synthesis Toolbox of Matlab, namely the synthesis of an autopilot for the space shuttle.

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Section: A Brief Comparison With Other Reduction Methodsmentioning

confidence: 99%

Section: A Brief Comparison With Other Reduction Methodsmentioning

confidence: 99%

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Controller reduction with closed loop H infinity performance constraints: A QFT perspective

Ferreres¹,

Gorrec²

1999

International Journal of Control

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“…This was further extended to multivariable case by Hung and Glover [11]. The frequency weighted balanced approach to reduce stable coprime factors of the controller has been discussed in several papers [12], [13], [14] whereas controller reduction methods originating from synthesis are developed in [15], [16], [17].…”

Section: Introductionmentioning

confidence: 97%

Controller reduction using optimal Hankel norm approximation with guaranteed closed-loop performance

Kumar

Nagar

Tiwari

2012

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

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The present work deals with the problem of frequency weighted controller reduction using optimal Hankel norm approximation. The advanced controller designs methods like LQG/LTR or based synthesis methods leads to controllers of order comparable to the plant and sometimes unstable controller whereas lower order controller should be sought out to keep the closed-loop stability and system performance within acceptable limit. For unstable controller reduction a controller decomposition algorithm is developed using two stage transformations. The algorithm discussed for computation of balancing transform is based on orthogonal transformation which circumvents the ill-conditioned cases due to numerical errors. Resulting closed-loop system with reduced order controller is guaranteed to preserve the dominant time domain and frequency domain characteristics.

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“…In the frequency weighted reduction scheme, the norm of the difference between two controllers multiplied by some optimal weights is considered to be minimized . An alternative method uses the performance preserving property by reducing the error between the closed‐loop systems with the full and reduced‐order controllers . The discrete‐time version of the fixed‐order controller design problem is introduced in References , which uses a discrete version of the bounded real lemma and the information of full‐order controller simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Direct synthesis of fixed‐order multi‐objective controllers

Abdolahi

Babazadeh

Nobakhti

2020

Optim Control Appl Methods

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This paper introduces a new methodology for the design of fixed-order multi-objective output feedback controllers. The problem comprises a set of linear matrix inequalities and an additional rank constraint. The primary idea is to classify convex subsets of the set of rank constrained matrices in such formulations, based on which two noniterative and relatively fast methods are developed. The proposed methods require solving a convex optimization problem at each step and can be applied with any weighted summation of design objectives such as  2 performance,  ∞ performance, passivity, and regional pole assignment. Several benchmark systems with performance criteria including H ∞ , mixed H 2 ∕H ∞ , and pole placement are used to demonstrate a marked improvement in comparison to the existing methods. K E Y W O R D Sfixed-order control, linear matrix inequality, multi-objective control, rank constraint 1 Optim Control Appl Meth. 2020;41:849-865.wileyonlinelibrary.com/journal/oca

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Performance preserving controller reduction via additive perturbation of closed loop transfer function

Cited by 8 publications

References 16 publications

Controller reduction with closed loop H infinity performance constraints: A QFT perspective

Controller reduction with closed loop H infinity performance constraints: A QFT perspective

Controller reduction using optimal Hankel norm approximation with guaranteed closed-loop performance

Direct synthesis of fixed‐order multi‐objective controllers

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