Data-Based Uncertainty Modeling by Convex Optimization Techniques

Häggblom, Kurt E.

doi:10.3182/20060402-4-br-2902.00091

Cited by 5 publications

(9 citation statements)

References 8 publications

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“…will be violated with the already determined  , or satisfied only loosely, at a number of frequencies. It is straightforward to determine a new  at every considered frequency to tightly satisfy (16) with the model () Gs . However, a better approach to do a partial re-optimization by using parameters of ( j ) G  that appear linearly in the constraint corresponding to (14), i.e.,…”

Section: Finding a Nominal Modelmentioning

confidence: 99%

“…A standard type of uncertainty model is one where the uncertainty description is in the form of a linear fractional transformation (LFT) [14]. The size of the uncertainty required to cover a given set of models depends not only on the set of models, but also on the nominal model [15,16]. In this paper, a method is proposed for finding the nominal model of an LFT uncertainty model that minimizes the -gap metric with respect to a set of known models.…”

Section: Introductionmentioning

confidence: 99%

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Identification of an LFT uncertainty model by minimizing the ν-gap metric

Häggblom

2014

2014 European Control Conference (ECC)

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An uncertainty model in the form of a linear fractional transformation (LFT) is composed of a nominal model augmented by an uncertainty description. The size of the uncertainty required to cover a given set of models depends not only on the set of models, but also on the nominal model. Thus, the size of the uncertainty can be minimized by choosing the nominal model optimally according to some metric. If the uncertainty model is to be used for control design, a suitable metric is the -gap metric. It is shown that the optimal solution in terms of the -gap metric has to satisfy a bilinear matrix inequality (BMI) for every model in the model set. To solve this nonconvex optimization problem, the BMIs are linearized to enable an iterative solution constrained by linear matrix inequalities (LMIs), where each iteration is a convex optimization problem. It is proved that the iteration converges to the optimal solution satisfying the BMIs. Because the solution is obtained as the frequency response at selected frequencies, the final model is determined by fitting a model to the frequency responses. A state-space model is used because the fitting can then easily be done subject to the same BMIs/LMIs to guarantee an optimal model. The procedure is illustrated by an application to uncertainty modeling of the product composition dynamics of a distillation column.

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Section: Finding a Nominal Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Identification of an LFT uncertainty model by minimizing the ν-gap metric

Häggblom

2014

2014 European Control Conference (ECC)

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“…The nominal model is typically computed by simply averaging the frequency response data. Approaches to construct uncertainty models from time domain data have also been presented in [6]- [9]. This paper uses convex optimization to construct uncertainty sets from experimental frequency response data.…”

Section: Department Of Aerospace Engineering and Mechanics University Ofmentioning

confidence: 99%

Uncertainty modeling for hard disk drives

Honda

Seiler

2014

2014 American Control Conference

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A modern hard disk drive uses a dual-stage actuator to read/write data on a track with width less than 100nm. The dual-stage actuator requires an advanced controller to achieve high performance on millions of hard disk drives. This paper presents a numerical algorithm utilizing convex optimization to create an uncertainty model, for the purpose of synthesizing a robust controller, from a set of experimental frequency response data. Furthermore several practical issues of constructing an uncertainty model for the dual-stage actuator are described. The proposed method is applied to a set of frequency response data of dual-stage actuators from numerous hard disk drives to create an uncertainty model of the actuator. Then the uncertainty model is used to synthesize a robust control law, which is implemented and experimentally tested on a hard drive.

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“…According to [2], it is essential that the identification methods deliver optimal uncertainty sets, including a nominal model, rather than an uncertainty bound around a prefixed nominal model. Thus, the uncertainty set should be minimized over both the nominal model and the uncertainty bound, as done, e.g., in [3]. For an LFT type of uncertainty, it has recently been shown that the ∞  norm of the uncertainty is a rigorous measure of the worst-case degradation of the stability margin for a system under feedback control irrespective of the particular type of uncertainty structure [4].…”

Section: Introductionmentioning

confidence: 99%

Finding an LFT uncertainty model with minimal uncertainty

Häggblom

2013

2013 European Control Conference (ECC)

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In this paper, we present a procedure for finding the best LFT uncertainty model by minimizing the  -infinity norm of the uncertainty set with respect to a nominal model subject to known input-output data. The main problem is how to express the data-matching constraints for convenient use in the optimization problem. For some uncertainty structures, they can readily be formulated as a set of linear matrix inequalities (LMIs), for some other structures, LMIs are obtained after certain transformations. There are also cases, when the constraints result in bilinear matrix inequalities (BMIs), which can be linearized to enable an efficient iterative solution. Essentially all LFT uncertainty structures are considered. An application to distillation modeling is included.

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Data-Based Uncertainty Modeling by Convex Optimization Techniques

Cited by 5 publications

References 8 publications

Identification of an LFT uncertainty model by minimizing the ν-gap metric

Identification of an LFT uncertainty model by minimizing the ν-gap metric

Uncertainty modeling for hard disk drives

Finding an LFT uncertainty model with minimal uncertainty

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Data-Based Uncertainty Modeling by Convex Optimization Techniques

Cited by 5 publications

References 8 publications

Identification of an LFT uncertainty model by minimizing the &#x03BD;-gap metric

Identification of an LFT uncertainty model by minimizing the &#x03BD;-gap metric

Uncertainty modeling for hard disk drives

Finding an LFT uncertainty model with minimal uncertainty

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Identification of an LFT uncertainty model by minimizing the ν-gap metric

Identification of an LFT uncertainty model by minimizing the ν-gap metric