H2/H∞ Control Without Lyapunov Matrix or Frequency Weights

Abbas-Turki, Mohamed; Duc, Gilles; Clément, Benoı̂t

doi:10.3182/20050703-6-cz-1902.00559

Cited by 4 publications

(4 citation statements)

References 5 publications

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“…The design follows two steps: the first one considers only the time domain performance of the rigid model through H 2 norm constraints on both channels given above [1]. The second step adds a roll-off constraint to attenuate the bending modes.…”

Section: Numerical Validationmentioning

confidence: 99%

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Multi-objective Synthesis Using LMI Formulations for Application of the Cutting Plane Algorithm

Abbas-Turki

Duc

Clément

2006

European Journal of Control

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The problem of designing a controller to meet different specifications or deciding that no such controller exists is addressed in this paper by linking three types of tools: the Youla parameterization allows searching for a controller in a convex set; formulations using Linear Matrix Inequalities (LMI) are proposed for different practical specifications; the corresponding convex problem is solved using a Cutting Plane Algorithm (CPA). Such an approach is developed by overcoming the problem of the huge number of additional variables which often occurs in the LMI framework, particulary when used in conjunction with the Youla parameterization. Its efficiency is discussed by considering two practical control problems.

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Section: Numerical Validationmentioning

confidence: 99%

“…• the formulation of the multiobjective problem as a convex one either by finding an appropriate transformation or by doing some relaxation to recover the convexity; 1 • the numerical feasibility (i.e. the amount of time calculation and memory space involved).…”

Section: Introductionmentioning

confidence: 99%

Multi-objective Synthesis Using LMI Formulations for Application of the Cutting Plane Algorithm

Abbas-Turki

Duc

Clément

2006

European Journal of Control

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“…Note also that H ∞ and H 2 norms constraints can be added to the specifications: the convenient LMI reformulations to be used are given in [2], [3].…”

Section: Discussionmentioning

confidence: 99%

“…The case of H ∞ and H 2 norms constraints has been presented in [2], [3]. By using the Youla parameterization, which defines a convex set describing all stabilizing controllers [4], all these specifications are expressed as matrix inequalities which are linear in the decision variables (LMI), provided a particular base is chosen for the Youla parameter.…”

Section: Introductionmentioning

confidence: 99%

LMI formulations for designing controllers according to time response and stability margin constraints

Abbas-Turki

Duc

Clément³

Proceedings of the 44th IEEE Conference on Decision and Control

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Designing a controller with respect to time and frequency-domain objectives remains a difficult problem, although both kinds are generally present in the manufacturer specifications. In general, the temporal objectives are replaced by frequency dependent ones, which in major cases do not fit the actual expectations. In this paper, convex mathematical translations of both kinds of objectives are proposed using Linear Matrix Inequalities (LMI). The application of Youla parameterization allows to restore the linearity in the compensator parameters, but a huge state space representation of the system is induced. Thus the Cutting Plane Algorithm (CPA) is efficiently used to overcome the problem of having a huge number of added variables, which often occurs in Semi-Definite Programming (SDP) particulary when used in conjunction with the Youla parameterization.

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Multi-objective control synthesis with mixed frequency small gain specifications: Youla parameterization approach

Zhang

Yang

2008

2008 Chinese Control and Decision Conference

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H2/H∞ Control Without Lyapunov Matrix or Frequency Weights

Cited by 4 publications

References 5 publications

Multi-objective Synthesis Using LMI Formulations for Application of the Cutting Plane Algorithm

Multi-objective Synthesis Using LMI Formulations for Application of the Cutting Plane Algorithm

LMI formulations for designing controllers according to time response and stability margin constraints

Multi-objective control synthesis with mixed frequency small gain specifications: Youla parameterization approach

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