| 1. |
- Barenthin, Märta, et al.
(author)
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Applications of mixed H2 and H∞ input design in identification
- 2005
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Conference paper (peer-reviewed)abstract
- The objective of this contribution is to quantify benefits of optimal input design compared to the use of standard identification input signals, e.g. PRBS signals for some common, and important, application areas of system identification. Two benchmark problems taken from process control and control of flexible mechanical structures are considered. We present results both when the design is based on knowledge of the true system (in general the optimal design depends on the system itself) and for a practical two step procedure when an initial model estimate is used in the design instead of the true system. The results show that there is a substantial reduction in experiment time and input excitation level. A discussion on the sensitivity of the optimal input design to model estimates is provided.
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| 2. |
- Barenthin, Märta, et al.
(author)
-
Gain estimation for Hammerstein systems
- 2006
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In: IFAC Proceedings Volumes (IFAC-PapersOnline). ; , s. 784-789
-
Conference paper (peer-reviewed)abstract
- In this paper, we discuss and compare three different approaches for L2- gain estimation of Hammerstein systems. The objective is to find the input signal that maximizes the gain. A fundamental difference between two of the approaches is the class, or structure, of the input signals. The first approach involves describing functions and therefore the class of input signals is sinusoids. In this case we assume that we have a model of the system and we search for the amplitude and frequency that give the largest gain. In the second approach, no structure on the input signal is assumed in advance and the system does not have to be modelled first. The maximizing input is found using an iterative procedure called power iterations. In the last approach, a new iterative procedure tailored for memoryless nonlinearities is used to find the maximizing input for the unmodelled nonlinear part of the Hammerstein system. The approaches are illustrated by numerical examples.
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| 3. |
- Barenthin, Märta, et al.
(author)
-
Identification and control: Joint input design and H-infinity state feedback with ellipsoidal parametric uncertainty via LMIs
- 2008
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 44:2, s. 543-551
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Journal article (peer-reviewed)abstract
- One obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods. In this contribution we present a joint robust state feedback control/input design procedure which guarantees stability and prescribed closed-loop performance using models identified from experimental data. This means that given H-infinity specifications on the closed-loop transfer function are translated into sufficient requirements on the input signal spectrum used to identify the process. The condition takes the form of a linear matrix inequality.
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| 4. |
- Barenthin, Märta, et al.
(author)
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Identification for control of multivariable systems: Controller validation and experiment design via LMIs
- 2008
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 44:12, s. 3070-3078
-
Journal article (peer-reviewed)abstract
- This paper presents a new controller validation method for linear multivariable time-invariant models. Classical prediction error system identification methods deliver uncertainty regions which are nonstandard in the robust control literature. Our controller validation criterion computes an upper bound for the worst case performance, measured in terms of the H-infinity-norm of a weighted closed loop transfer matrix, achieved by a given controller over all plants in such uncertainty sets. This upper bound on the worst case performance is computed via an LMI-based optimization problem and is deduced via the separation of graph framework. Our main technical contribution is to derive, within that framework, a very general parametrization for the set of multipliers corresponding to the nonstandard uncertainty regions resulting from PE identification of MIMO systems. The proposed approach also allows for iterative experiment design. The results of this paper are asymptotic in the data length and it is assumed that the model structure is flexible enough to capture the true system.
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| 5. |
- Barenthin, Märta, et al.
(author)
-
Mixed H-2 and H-Infinity$ Input Design for Multivariable Systems
- 2006
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In: 14th IFAC Symposium on System Identification. ; , s. 1335-1340
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Conference paper (peer-reviewed)abstract
- In this contribution a new procedure for input design for identification of linear multivariable systems is proposed. The goal is to minimize the input power used in the system identification experiment. The quality constraint on the estimated model is formulated in H∞. The input design problem is converted to linear matrix inequalities by a separation of graphs theorem. For illustration, the proposed method is applied on a chemical distillation column and the result shows that it is optimal to amplify the low gain direction of the plant.
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| 6. |
- Barenthin, Märta, et al.
(author)
-
Validation of stability for an induction machine drive using power iterations
- 2005
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In: Proceedings of the 16th IFAC World Congress, 2005. - Prague. - 9783902661753 ; , s. 892-897
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Conference paper (peer-reviewed)abstract
- This work is an extension of the paper (Mosskull et al., 2003), in which the modelling, identification and stability of an nonlinear induction machine drive is studied. The validation of the stability margins of the system is refined by an improved estimate of the induced L2 loop gain of the system. This is done with a procedure called power iterations where input sequences suitable for estimating the gain are generated iteratively through experiments on the system. The power iterations result in higher gain estimates compared to the experiments previously presented. This implies that more accurate estimates are obtained as, in general, only lower bounds can be obtained as estimates for the gain. The new gain estimates are well below one, which suggests that the feedback system is stable. The experiments are performed on an industrial hardware/software simulation platform. in this paper we also discuss the power iterations from a more general point of view. The usefulness of the method for gain estimation of nonlinear systems is illustrated through simulation examples. The basic principles of the method are provided.
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| 7. |
- Bombois, Xavier, et al.
(author)
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Optimal input design for robust H2 deconvolution filtering
- 2009
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In: 15th IFAC Symposium on System Identification, SYSID 2009. - : Elsevier BV. ; , s. 934-939
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Conference paper (peer-reviewed)abstract
- Deconvolution filtering where the system and noise dynamics are obtained by parametric system identification is considered. Consistent with standard identification methods, ellipsoidal uncertainty in the estimated parameters is considered. Three problems are considered: 1) Computation of the worst case H2 performance of a given deconvolution filter in this uncertainty set. 2) Design of a filter which minimizes the worst case H2 performance in this uncertainty set. 3) Input design for the identification experiment, subject to a limited input power budget, such that the filter in 2) gives the smallest possible worst-case H2 performance. It is shown that there are convex relaxations of the optimization problems corresponding to 1) and 2) while the third problem can be treated via iterating between two convex optimization problems.
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| 8. |
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| 9. |
- Gerencser, Laszlo, et al.
(author)
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Adaptive input design for ARX systems
- 2007
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In: Proceedings of the European Control Conference. - : Institute of Electrical and Electronics Engineers Inc.. - 9783952417386 ; , s. 5707-5714
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Conference paper (peer-reviewed)abstract
- A key problem in optimal input design is that the solution depends on system parameters to be identified. In this contribution we provide formal results for convergence and asymptotic optimality of an adaptive input design method based on the certainty equivalence principle, i.e. for each time step an optimal input design problem is solved using the present parameter estimate and one sample of this input is applied to the system. The results apply to stable ARX systems with the input restricted to be generated by white noise filtered through an FIR filter, or a binary signal obtained from the latter by a static nonlinearity.
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| 10. |
- Gerencsér, Laszlo, et al.
(author)
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Adaptive input design in system identification
- 2005
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In: 2005 44TH IEEE CONFERENCE ON DECISION AND CONTROL & EUROPEAN CONTROL CONFERENCE. - Seville. - 0780395689 - 9780780395688 - 0780395670 ; , s. 4988-4993
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Conference paper (peer-reviewed)abstract
- Recently there have been significant developments in re-casting experiment design problems in system identification as convex optimization problems. The practical implementation of these methods is hampered by the fact that typically the "data" in the optimization problem depend on the to be identified system. In this contribution we propose an adaptive certainty equivalence solution based on a recursively identified model. The input design is adapted by taking one Newton step using data from the last identified model.
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