Robust Controller Synthesis is Convex for Systems without Control Channel Uncertainties

Scherer, Carsten W.

doi:10.1007/978-1-4419-0895-7_2

Cited by 16 publications

(16 citation statements)

References 13 publications

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“…However, inequality (32) is not an LMI because of the presence of bilinear terms involving P and the state-space matrices of F. For example, the term  T (ρ)P involves the product of A F (ρ) and P, both of which are variables to be selected. Since Equation 32 is a bilinear matrix inequality (BMI), it will be referred to using the short form BMI WC (G(H, F), P, γ, Ψ, M) < 0.…”

Section: Output Estimationmentioning

confidence: 99%

“…23 It was later shown that the estimator and feedforward synthesis problems are special cases of a feedback structure that has no uncertainties in the control channel of the closed loop. 32 For such feedback structures, 12 provided a general synthesis framework for robust, gain-scheduled controllers. This general synthesis framework is restricted to linear fractional transform (LFT)-based LPV plants, whose state matrices are restricted to depend rationally on the scheduling parameters [33][34][35] Note that frequency-domain arguments are applicable for LFT-based LPV systems since the nominal plant is LTI.…”

Section: Introductionmentioning

confidence: 99%

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Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints

Venkataraman

Seiler

2017

Intl J Robust & Nonlinear

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Summary A method is presented for synthesizing output estimators and disturbance feedforward controllers for continuous‐time, uncertain, gridded, linear parameter‐varying (LPV) systems. Integral quadratic constraints are used to describe the uncertainty. Since the gridded LPV systems do not have a valid frequency‐domain interpretation, the time domain, dissipation inequality approach is followed. There are 2 main contributions. The first contribution is that a notion of duality is developed for the worst‐case gain analysis of uncertain, gridded LPV systems. This includes notions of dual LPV systems and dual integral quadratic constraints. Furthermore, several technical results are developed to demonstrate that the sufficient conditions for bounding the worst‐case gain of the primal and dual uncertain LPV systems are equivalent. The second contribution is that the convex conditions are derived for the synthesis of robust output estimators for uncertain LPV systems. The estimator synthesis conditions, together with the duality results, enable the convex synthesis of robust disturbance feedforward controllers. The effectiveness of the proposed method is demonstrated using a numerical example.

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Section: Output Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints

Venkataraman

Seiler

2017

Intl J Robust & Nonlinear

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“…In this section, we provide a brief preparatory recap on the well-known LMI formulation for the synthesis of optimal controllers that satisfy a particular quadratic performance criteria such as (4). For this purpose, let us extract from (3) the nominal plant…”

Section: Nominal Quadratic Performance Synthesismentioning

confidence: 99%

“…As a possible alternative, one could consider specialized problems and exploit the additional structure to arrive at a convex solution, as in [4,5] and the references therein. On the other hand, one can resort to a number of useful but nonoptimal methods, such as -synthesis [6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…Using dynamic(frequency dependent) IQC multipliers to reduce conservatism is considerably harder , for the reasons described in . Still, various special classes of robust synthesis problems, such as robust estimator and feed‐forward controller design , have been shown to fit into a general framework, if only the control channel is not affected by uncertainties .…”

Section: Introductionmentioning

confidence: 99%

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IQC-synthesis with general dynamic multipliers

Veenman

Scherer

2013

Int. J. Robust. Nonlinear Control

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SUMMARYAnalogously to the existing μ‐synthesis tools, we propose an alternative algorithm for the systematic design of robust controllers based on an iteration of standard nominal controller synthesis and integral quadratic constraint (IQC) analysis with general dynamic multipliers. The suggested algorithm enables us to perform robust controller synthesis for a significantly larger class of uncertainties if compared with the existing methods. Indeed, while the classical approaches are restricted to the use of real/complex time invariant or arbitrarily fast time‐varying parametric uncertainties, the IQC framework also offers, for example, the possibility to efficiently handle sector‐bounded and slope restricted nonlinearities or time‐varying parametric uncertainties and uncertain time‐varying time‐delays, both with bounds on the rate‐of‐variation. Secondly, in contrast to the classical approaches, the proposed techniques completely avoid gridding and curve‐fitting. We present new insights that allow us to reformulate the robust IQC analysis LMIs into a standard quadratic performance problem. This enables us to generate suitable initial conditions for each subsequent iteration step. Depending on the size of the problem, this can significantly speed up the synthesis process. The results are illustrated by means of two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.

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