New dominance concepts for multivariable control systems design

Yeung, L.F.; Bryant, G.F.

doi:10.1080/00207179208934267

Cited by 21 publications

(7 citation statements)

References 10 publications

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“…Theorem 3.1: Let I + G(s)K(s) have a regular splittingI + G(s)K(s) = R(s) + Q∆(s), where G(s) andḠ(s) have p0 unstable poles. The closed-loop system is asymptotically stable if [5], [7], [12], [14], C1): K(s) stabilizes the nominal systemḠ(s), and C2):…”

Section: System Decomposition Consider a Linear Feedback Systemmentioning

confidence: 99%

Large scale system decentralized controller design based on locally imposed decomposition constraints

Yeung

Nobakhti

et al. 2007

2007 American Control Conference

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This paper proposes a new method for the design of decentralized controllers for large scale systems. The controllers are designed in two steps. In the first step, a powerful assignment algorithm is used to pair the system's inputs and outputs and to identity clusters of strongly interacting subsystems. Then, a decomposition condition is derived which allows for the controller of each of these subsystems to be designed separately. Thus the original problem of designing the decentralized controller becomes that of solving several smaller local problems subject to the satisfaction of a local condition. Consequently each sub-controller can be designed and tuned separately, which is a useful feature in process control applications where decentralized structure is important. It is shown that both the local controller design and the satisfaction of the local decomposition condition can be combined together into a single convex optimization problem which can be solved by linear matrix inequalities.

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Section: System Decomposition Consider a Linear Feedback Systemmentioning

confidence: 99%

Large scale system decentralized controller design based on locally imposed decomposition constraints

Yeung

Nobakhti

et al. 2007

2007 American Control Conference

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“…Condition (17) is related to well-known quasi-block-diagonal dominance conditions [13,14]. The latter have been traditionally formulated, in the hypothesis that uncertainties are linear and time invariant, such that blocks D ij can be described by their transfer function matrix D ij ðsÞ; as…”

Section: Remarkmentioning

confidence: 99%

Necessary and sufficient conditions for robust perfect tracking under variable structure control

Balluchi¹,

Bicchi

2002

Intl J Robust & Nonlinear

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“…The above definitions follow Limebeer [26] and Yeung and Bryant [29] who present stability theorems for dominant systems. 'Dominant' will be used when the type of dominance is clear from the context.…”

Section: Definitionmentioning

confidence: 99%

“…As was shown by Rosenbrock [4,5], any controller can be decomposed as a product of a permutation matrix, a unimodular matrix (a matrix with unity determinant formed from elementary operations) and a diagonal matrix. Yeung and Bryant [29] have used Gauss elimination for stability analysis and design. For the design approach discussed in this section, Equation (3) can be written as, T Y=R ¼ ðI þ PKG D Þ À1 PKG D F. Assume that the permutation has been achieved by correct coupling of inputs and outputs from physical plant considerations, and that the plant is regular so that ðPKÞ À1 ¼ # K K # P P. The diagonal matrix is G D and the unimodular matrix is K, with inverse made up of components,…”

Section: Series Connection}gauss-elimination Approach To Design Of Kðsþmentioning

confidence: 99%

Non‐diagonal controllers in MIMO quantitative feedback design

Boje¹

2002

Intl J Robust & Nonlinear

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SUMMARYThis paper discusses multivariable quantitative feedback design through the use of controllers with offdiagonal elements. Controller design for multivariable plants with significant uncertainty is simpler and potentially less conservative if some sort of dominance is achieved (by reducing the interaction effect of offdiagonal plant elements) before a diagonal (decentralized) controller design is attempted. Traditional approaches for achieving dominance are not applicable when plant uncertainty must be considered. This paper discusses parallel and series implementations and for the latter, a pseudo-Gauss elimination approach to the design has been developed. The interaction is measured using the Perron-Frobenius root of an interaction matrix. In some applications, it is possible to trade off individual plant cases against each other in order to reduce to the worst-case interaction over the entire plant set.

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New dominance concepts for multivariable control systems design

Cited by 21 publications

References 10 publications

Large scale system decentralized controller design based on locally imposed decomposition constraints

Large scale system decentralized controller design based on locally imposed decomposition constraints

Necessary and sufficient conditions for robust perfect tracking under variable structure control

Non‐diagonal controllers in MIMO quantitative feedback design

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