Identifiability conditions for linear multivariable systems operating under feedback

Söderström, Torsten; Ljung, Lennart; Gustavsson, Ivar

doi:10.1109/tac.1976.1101376

Cited by 87 publications

(45 citation statements)

References 5 publications

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“…Results in [1], [2], [3], [4] seemed to fully answer all questions about the identifiability of closed-loop systems under different feedback configurations and for different assumptions about the excitation signals and the measured signals. Recently, there has been a renewed interest in closedloop identification in the context of least costly identification experiment for control [5], [6].…”

Section: Introductionmentioning

confidence: 82%

“…It does not refer to a particular set of N data. Definition 2.2: An experiment z(t) is called informative with respect to a model set M if, for any two models W (1) and W (2) in that set,…”

Section: Informative Experiments For a Model Structurementioning

confidence: 99%

“…Indeed, some of these definitions are unnecessarily demanding in terms of a realistic identification setup. For example, the main result in [2] states that in the case of a time-invariant controller a MIMO closed-loop system is strongly system identifiable if and only if all reference inputs are excited by persistently exciting signals. On the basis of such results, it is assumed by many in the system identification community that it is necessary to excite all external reference inputs if one wants to identify a system under closed-loop conditions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Closed-loop identification of MIMO systems: a new look at identifiability and experiment design

Bazanella

Gevers

Mišković

2007

2007 European Control Conference (ECC)

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Abstract-This paper addresses a question raised by a leading expert in the identification of multivariable systems: "Is it necessary to excite all reference signals for the identification of a multivariable system operating in closed loop with a linear time-invariant controller?" On the basis of earlier results on identifiability of closed-loop systems, he conjectured that this was necessary. We show that it is not, on the basis of a careful re-examination of the notions of identifiability and informative experiments for closed-loop systems.

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Section: Introductionmentioning

confidence: 82%

“…It does not refer to a particular set of N data. Definition 2.2: An experiment z(t) is called informative with respect to a model set M if, for any two models W (1) and W (2) in that set,…”

Section: Informative Experiments For a Model Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Closed-loop identification of MIMO systems: a new look at identifiability and experiment design

Bazanella

Gevers

Mišković

2007

2007 European Control Conference (ECC)

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“…joint input-output identification (e.g. [6], [7]), instrumental variable ( [8], [9]) or direct identification ( [10], [11]). Recently developed methods are for example two-stage [12] or dual-Youla parameterization (e.g.…”

Section: Identificationmentioning

confidence: 99%

Identification and parameter-varying decoupling of a 3-DOF platform with manipulator

Gajdusek

Damen

Bosch

2008

2008 International Symposium on Power Electronics, Electrical Drives, Automation and Motion

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Abstract--The paper describes identification and a new parameter-varying decoupling method for a 3-degree-offreedom (DOF) platform with a manipulator on top of it, which is magnetically levitated by 9 voice-coil actuators. The identification has been performed in closed-loop using two different indirect approaches. In the first approach timedomain data of the system were processed using Ho-Kalman algorithm. The second approach was based on frequencyresponse measurements. The 3 DOFs of the platform are coupled and the coupling is even varying as the manipulator on top is moving. In order to design separate SISO controllers for each DOF of the platform, a new decoupling method has been developed which uses frequency response measurements of the system obtained for different positions of the manipulator.

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“…A discussion on this topic can be found in [14]. The interested reader is also referred to [15], [16], [17].…”

Section: Introductionmentioning

confidence: 99%

On the distinguishability of discrete linear time-invariant dynamic systems

Rosa¹,

Silvestre²

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-This paper introduces the notion of absolutely distinguishable discrete dynamic systems, with particular applicability to linear time-invariant (LTI) systems. The motivation for this novel type of distinguishability stems, in particular, from the stability and performance requirements of worst-case adaptive control methodologies. The main results presented herein show that, in most practical cases, a persistence of excitation type of condition and a minimum number of iterations are required to properly distinguish two dynamic systems. We also demonstrate that the former constraint can be written as a lower bound on the intensity of the exogenous disturbances. The applicability of the developed theory is illustrated with a set of examples.

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Identifiability conditions for linear multivariable systems operating under feedback

Cited by 87 publications

References 5 publications

Closed-loop identification of MIMO systems: a new look at identifiability and experiment design

Closed-loop identification of MIMO systems: a new look at identifiability and experiment design

Identification and parameter-varying decoupling of a 3-DOF platform with manipulator

On the distinguishability of discrete linear time-invariant dynamic systems

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