An LMI approach to the identification and (in)validation of LPV systems

Sznaier, Mario; Mazzaro, C.

doi:10.1007/bfb0110629

Cited by 11 publications

(15 citation statements)

References 24 publications

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“…The precompensator is parameterized such that F(r(t), q −1 ) is linear in its parameters and can be expressed as (8) and q ∈ R n , with n = (n +1)(n +1), is the vector of controller parameters:…”

Section: Precompensator Parameterizationmentioning

confidence: 99%

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Data‐driven tuning of linear parameter‐varying precompensators

Butcher

Karimi

2010

Adaptive Control & Signal

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SUMMARYMethods for direct data-driven tuning of the parameters of precompensators for LPV systems are developed. Since the commutativity property is not always satisfied for LPV systems, previously proposed methods for LTI systems that use this property cannot be directly adapted. When the ideal precompensator giving perfect mean tracking exists in the proposed precompensator parameterisation, the LPV transfer operators do commute and an algorithm using only two experiments on the real system is proposed. It is shown that this algorithm gives consistent estimates of the ideal parameters despite the presence of stochastic disturbances. For the more general case, when the ideal precompensator does not belong to the set of parameterised precompensators, another technique is developed. This technique requires a number of experiments equal to twice the number of precompensator parameters and it is shown that the calculated parameters minimise the mean squared tracking error. The theoretical results are demonstrated in simulation.

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Section: Precompensator Parameterizationmentioning

confidence: 99%

“…Research into the problem of identifying LPV systems has been active in recent years (see e.g. [6][7][8][9]). In [10] a method is proposed for the identification of the parameters of single-input single-output (SISO) LPV systems in input-output form.…”

Section: Introductionmentioning

confidence: 99%

Data‐driven tuning of linear parameter‐varying precompensators

Butcher

Karimi

2010

Adaptive Control & Signal

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“…Here, a robust control framework was used to determine the minimum levels of external noise and model uncertainty which do not (in)validate the experimental data. This has been recently extended to more general LPV models ( [8], [9]). …”

Section: Introductionmentioning

confidence: 97%

Model selection: From LTI to switched-LPV

Peña

Bianchi

2012

2012 American Control Conference (ACC)

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A practical problem for control engineers is the selection of the most adequate model of a physical plant in order to design a controller which should achieve a desired performance level. For this selection the required performance, the resulting model uncertainty and a well-established robust controller design methodology play important roles. They determine the structure and complexity of the desired model, i.e. higher performance and low uncertainty levels require higher model complexity in general. Hence an identification procedure focused on the desired performance, rather than on a good mimic of the system dynamics, could prove useful. Here we present an open discussion on this problem illustrated by two examples, both described by nonlinear equations: a Diabetes Mellitus glucose-insulin dynamics and a 2DOF magnetic bearing system. The first may be described as an LTI model plus uncertainty and the second needs to be described as a switched-LPV model in order to guarantee the required performance.

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“…[7] presents a simple ARX method; [8] proposes a control-oriented identification framework that relies on solution of a set of Linear Matrix Inequalities. [9] considers robust invalidation of candidate LPV models.…”

Section: Introductionmentioning

confidence: 99%

Incremental closed-loop identification of linear parameter varying systems

Bendtsen

Trangbaek

2011

Proceedings of the 2011 American Control Conference

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Abstract-This paper deals with system identification for control of linear parameter varying systems. In practical applications, it is often important to be able to identify small plant changes in an incremental manner without shutting down the system and/or disconnecting the controller; unfortunately, closed-loop system identification is more difficult than openloop identification. In this paper we prove that the so-called Hansen Scheme, a technique known from linear time-invariant systems theory for transforming closed-loop system identification problems into open-loop-like problems, can be extended to accommodate linear parameter varying systems as well.

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An LMI approach to the identification and (in)validation of LPV systems

Cited by 11 publications

References 24 publications

Data‐driven tuning of linear parameter‐varying precompensators

Data‐driven tuning of linear parameter‐varying precompensators

Model selection: From LTI to switched-LPV

Incremental closed-loop identification of linear parameter varying systems

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