Normalized H/sub ∞/ controller reduction with a priori error bounds

El-Zobaidi, H.; Jaimoukha, Imad M.; Limebeer, D.J.N.

doi:10.1109/9.948481

Cited by 9 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In (9.2) and (9.3) the weights have usually special forms to enforce either closed-loop stability [AL89,LAL90] or to preserve the closed-loop performance bounds for H ∞ controllers [GG98,Gu95,WSL01,EJL01]. The main appeal of coprime factorization based techniques is that in many cases (e.g., feedback controllers resulting from LQG, H 2 or H ∞ designs) fractional representations of the controller can be obtained practically without any computation from the underlying synthesis approach.…”

Section: Controller Reduction Approachesmentioning

confidence: 99%

“…This method has been also considered in [EJL01] for the case of normalized coprime factor H ∞ controller reduction.…”

Section: Relative Error Coprime Factors Reductionmentioning

confidence: 99%

“…However, to be useful, the low order controller resulting in this way must provide an acceptable performance degradation of the closed loop behavior. This led to methods which try to enforce also the preservation of closed-loop performance [AL89,GG98,Gu95,WSL01,EJL01].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dimension Reduction of Large-Scale Systems

Benner

Mehrmann

2005

Lecture Notes in Computational Science and Engineering

247

View full text Add to dashboard Cite

Preface VII and algorithmic tools with the ability to tackle challenging problems in scientific computing ranging from control of nonlinear PDEs to the DC analysis of future generation VLSI chips.An equally important aspect to this workshop is the collection and distribution of an extensive set of test problems and application specific benchmarks. This should make it much easier to develop relevant methods and to systematically test them.

show abstract

Section: Controller Reduction Approachesmentioning

confidence: 99%

“…This method has been also considered in [EJL01] for the case of normalized coprime factor H ∞ controller reduction.…”

Section: Relative Error Coprime Factors Reductionmentioning

confidence: 99%

See 1 more Smart Citation

Dimension Reduction of Large-Scale Systems

Benner

Mehrmann

2005

Lecture Notes in Computational Science and Engineering

247

View full text Add to dashboard Cite

show abstract

“…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)

View full text Add to dashboard Cite

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.

show abstract

Controller Reduction Using Accuracy-Enhancing Methods

Varga

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

Summary. The efficient solution of several classes of controller approximation problems by using frequency-weighted balancing related model reduction approaches is considered. For certain categories of performance and stability enforcing frequencyweights, the computation of the frequency-weighted controllability and observability Gramians can be achieved by solving reduced order Lyapunov equations. All discussed approaches can be used in conjunction with square-root and balancing-free accuracy enhancing techniques. For a selected class of methods robust numerical software is available. IntroductionThe design of low order controllers for high order plants is a challenging problem both theoretically as well as from a computational point of view. The advanced controller design methods like the LQG/LTR loop-shaping, H ∞ -synthesis, µ and linear matrix inequalities based synthesis methods produce typically controllers with orders comparable with the order of the plant. Therefore, the orders of these controllers tend often to be too high for practical use, where simple controllers are preferred over complex ones. To allow the practical applicability of advanced controller design methods for high order systems, the model reduction methods capable to address controller reduction problems are of primary importance. Comprehensive presentations of controller reduction methods and the reasons behind different approaches can be found in the textbook [ZDG96] and in the monograph [OA00].The goal of controller reduction is to determine a low order controller starting from a high order one to ensure that the closed loop system formed from the original (high order) plant and low order controller behaves like the original plant with the original high order controller. Thus a basic requirement for controller reduction is preserving the closed-loop stability and many controller

show abstract

Normalized H/sub ∞/ controller reduction with a priori error bounds

Cited by 9 publications

References 16 publications

Dimension Reduction of Large-Scale Systems

Dimension Reduction of Large-Scale Systems

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

Controller Reduction Using Accuracy-Enhancing Methods

Contact Info

Product

Resources

About