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| 2. |
- Barenthin, Märta, et al.
(författare)
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Applications of mixed H2 and H∞ input design in identification
- 2005
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Konferensbidrag (refereegranskat)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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| 3. |
- Barenthin, Märta, et al.
(författare)
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Data-driven methods for L2-gain estimation
- 2009
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Ingår i: IFAC Proceedings Volumes (IFAC-PapersOnline). ; , s. 1597-1602
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Konferensbidrag (refereegranskat)abstract
- In this paper we present and discuss some data-driven methods for estimation of the L2-gain of dynamical systems. Partial results on convergence and statistical properties are provided. The methods are based on multiple experiments on the system. The main idea is to directly estimate the maximizing input signal by using iterative experiments on the true system. We study such a data-driven method based on a stochastic gradient method. We show that this method is very closely related to the so-called power iteration method based on the power method in numerical analysis. Furthermore, it is shown that this method is applicable for linear systems with noisy measurements. We will also study L2-gain estimation of Hammerstein systems. The stochastic gradient method and the power iteration method are evaluated and compared in simulation examples. © 2009 IFAC.
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| 4. |
- Barenthin, Märta, et al.
(författare)
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Gain estimation for Hammerstein systems
- 2006
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Ingår i: IFAC Proceedings Volumes (IFAC-PapersOnline). ; , s. 784-789
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Konferensbidrag (refereegranskat)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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| 5. |
- Barenthin, Märta, et al.
(författare)
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Identification and control: Joint input design and H infinity state feedback with ellipsoidal parametric uncertainty
- 2005
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Ingår i: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. - 0780395670 ; , s. 6454-6459
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Konferensbidrag (refereegranskat)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 sufficient condition for the existence of a H-infinity state feedback controller for the multi-input/single-output case which accomodates for ellipsoidal parametric uncertainty. The condition takes the form of a linear matrix inequality whose solution also provides a set of valid feedback gains. The model class considered corresponds to systems with known poles but uncertain zero locations. A second important contribution of the paper is to integrate the input design problem in system identification with this control synthesis method. This means that given H-infinity specifications on the closed loop transfer function are translated into the requirements on the input signal spectrum used to identify the process so that the ellipsoidal model uncertainty resulting from model identification using this input spectrum will be shaped such that the control specifications are satisfied for all models in the uncertainty set and hence guaranteed for the true system. The procedures are illustrated on a numerical example.
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| 6. |
- Barenthin, Märta, et al.
(författare)
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Identification and control: Joint input design and H-infinity state feedback with ellipsoidal parametric uncertainty via LMIs
- 2008
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 44:2, s. 543-551
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Tidskriftsartikel (refereegranskat)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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| 7. |
- Barenthin, Märta, et al.
(författare)
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Identification for control of multivariable systems: Controller validation and experiment design via LMIs
- 2008
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 44:12, s. 3070-3078
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Tidskriftsartikel (refereegranskat)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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| 8. |
- Barenthin, Märta, et al.
(författare)
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Mixed H-2 and H-Infinity$ Input Design for Multivariable Systems
- 2006
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Ingår i: 14th IFAC Symposium on System Identification. ; , s. 1335-1340
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Konferensbidrag (refereegranskat)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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| 9. |
- Barenthin, Märta, 1979-
(författare)
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On input design in system identification for control
- 2006
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- There are many aspects to consider when designing system identification experiments in control applications. Input design is one important issue. This thesis considers input design both for identification of linear time-invariant models and for stability validation. Models obtained from system identification experiments are uncertain due to noise present in measurements. The input spectrum can be used to shape the model quality. A key tool in input design is to introduce a linear parametrization of the spectrum. With this parametrization a number of optimal input design problems can be formulated as convex optimization programs. An Achilles' heel in input design is that the solution depends on the system itself, and this problem can be handled by iterative procedures where the input design is based on a model of the system. Benefits of optimal input design are quantified for typical industrial applications. The result shows that the experiment time can be substantially shortened and that the input power can be reduced. Another contribution of the thesis is a procedure where input design is connected to robust control. For a certain system structure with uncertain parameters, it is shown that the existence of a feedback controller that guarantees a given performance specification can be formulated as a convex optimization program. Furthermore, a method for input design for multivariable systems is proposed. The constraint on the model quality is transformed to a linear matrix inequality using a separation of graphs theorem. The result indicates that in order to obtain a model suitable for control design, it is important to increase the power of the input in the low-gain direction of the system relative to the power in the high-gain direction. A critical issue when validating closed-loop stability is to obtain an accurate estimate of the maximum gain of the system. This problem boils down to finding the input signal that maximizes the gain. Procedures for gain estimation of nonlinear systems are proposed and compared. One approach uses a model of the system to design the optimal input. In other approaches, no model is required, and the system itself determines the optimal input sequence in repeated experiments.
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| 10. |
- Barenthin, Märta, et al.
(författare)
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Validation of stability for an induction machine drive using power iterations
- 2005
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Ingår i: Proceedings of the 16th IFAC World Congress, 2005. - Prague. - 9783902661753 ; , s. 892-897
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Konferensbidrag (refereegranskat)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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