| 31. |
- 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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| 32. |
- Barenthin, Märta, et al.
(författare)
-
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
-
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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| 33. |
- Barenthin, Märta, 1979-
(författare)
-
On input design in system identification for control
- 2006
-
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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| 34. |
- Barenthin, Märta, et al.
(författare)
-
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
-
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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| 35. |
- Barenthin Syberg, Märta, 1979-
(författare)
-
Complexity Issues, Validation and Input Design for Control in System Identification
- 2008
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification is about constructing and validating modelsfrom measured data. When designing system identificationexperiments in control applications, there are many aspects toconsider. One important aspect is the choice of model structure.Another crucial issue is the design of input signals. Once a modelof the system has been estimated, it is essential to validate theclosed loop performance if the feedback controller is based onthis model. In this thesis we consider the prediction-erroridentification method. We study model structure complexity issues,input design and model validation for control. To describe real-life systems with high accuracy, models of veryhigh complexity are typically needed. However, the variance of themodel estimate usually increases with the model order. In thisthesis we investigate why system identification, despite thisrather pessimistic observation, is successfully applied in theindustrial practise as a reliable modelling tool. It is shown thatby designing suitable input signals for the identificationexperiment, we obtain accurate estimates of the frequency functionalso for very complex systems. The input power spectrum can beused to shape the model quality. A key tool in input design is tointroduce a linear parametrization of the spectrum. With thisparametrization, several optimal input design problems can berewritten as convex optimization problems. Another problem considered is to design controllers withguaranteed robust stability and prescribed robust performanceusing models identified from experimental data. These models areuncertain due to process noise, measurement noise and unmodelleddynamics. In this thesis we only consider errors due tomeasurement noise. The model uncertainty is represented byellipsoidal confidence regions in the model parameter space. Wedevelop tools to cope with these ellipsoids for scalar andmultivariable models. These tools are used for designing robustcontrollers, for validating the closed loop performance and forimproving the model with input design. Therefore this thesis ispart of the research effort to connect prediction-erroridentification methods and robust control theory. The stability of the closed loop system can be validated using thesmall gain theorem. A critical issue is thus to have an accurateestimate of the L2-gain of the system. The key tosolve this problem is to find the input signal that maximizes thegain. One approach is to use a model of the system to design theinput signal. An alternative approach is to let the system itselfdetermine a suitable input sequence in repeated experiments. Insuch an approach no model of the system is required. Proceduresfor gain estimation of linear and nonlinear systems are discussedand compared.
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| 36. |
- Bereza-Jarocinski, Robert, et al.
(författare)
-
Stochastic Approximation for Identification of Non-Linear Differential-Algebraic Equations with Process Disturbances
- 2022
-
Ingår i: 2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781665467612 - 9781665467605 - 9781665467629 ; , s. 6712-6717
-
Konferensbidrag (refereegranskat)abstract
- Differential-algebraic equations, commonly used to model physical systems, are the basis for many equation-based object-oriented modeling languages. When systems described by such equations are influenced by unknown process disturbances, estimating unknown parameters from experimental data becomes difficult. This is because of problems with the existence of well-defined solutions and the computational tractability of estimators. In this paper, we propose a way to minimize a cost function-whose minimizer is a consistent estimator of the true parameters-using stochastic gradient descent. This approach scales significantly better with the number of unknown parameters than other currently available methods for the same type of problem. The performance of the method is demonstrated through a simulation study with three unknown parameters. The experiments show a significantly reduced variance of the estimator, compared to an output error method neglecting the influence of process disturbances, as well as an ability to reduce the estimation bias of parameters that the output error method particularly struggles with.
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| 37. |
- Bombois, Xavier, et al.
(författare)
-
Identification for robust H-2 deconvolution filtering
- 2010
-
Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 46:3, s. 577-584
-
Tidskriftsartikel (refereegranskat)abstract
- This paper addresses robust deconvolution filtering when the system and noise dynamics are obtained by parametric system identification. Consistent with standard identification methods, the uncertainty in the estimated parameters is represented by an ellipsoidal uncertainty region. Three problems are considered: (1) computation of the worst case H-2 performance of a given deconvolution filter in this uncertainty set; (2) design of a filter which minimizes the worst case H-2 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 H-2 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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| 38. |
- Bombois, X., et al.
(författare)
-
Network topology detection via uncertainty analysis of an identified static model
- 2021
-
Ingår i: IFAC PAPERSONLINE. - : Elsevier BV. - 2405-8963. ; , s. 595-600
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we propose a methodology to detect the topology of a dynamic network that is based on the analysis of the uncertainty of the static characteristic of the matrix of transfer functions between the external excitations and the node signals.
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| 39. |
- Bombois, Xavier, et al.
(författare)
-
On the informativity of direct identification experiments in dynamical networks
- 2023
-
Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 148, s. 110742-
-
Tidskriftsartikel (refereegranskat)abstract
- Data informativity is a crucial property to ensure the consistency of the prediction error estimate. This property has thus been extensively studied in the open-loop and in the closed-loop cases, but has only been briefly touched upon in the dynamic network case. In this paper, we consider the prediction error identification of the modules in a row of a dynamic network using the full input approach. Our main contribution is to propose a number of easily verifiable data informativity conditions for this identification problem. Among these conditions, we distinguish a sufficient data informativity condition that can be verified based on the topology of the network and a necessary and sufficient data informativity condition that can be verified via a rank condition on a matrix of coefficients that are related to a full-order model structure of the network. These data informativity conditions allow to determine different situations (i.e., different excitation patterns) leading to data informativity. In order to be able to distinguish between these different situations, we also propose an optimal experiment design problem that allows to determine the excitation pattern yielding a certain pre-specified accuracy with the least excitation power.
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| 40. |
- Bombois, Xavier, et al.
(författare)
-
Optimal experiment design for hypothesis testing applied to functional magnetic resonance imaging
- 2011
-
Ingår i: Proceedings of the 18th IFAC World Congress. ; , s. 9953-9958
-
Konferensbidrag (refereegranskat)abstract
- Hypothesis testing is a classical methodology of making decisions using experimental data. In hypothesis testing one seeks to discover evidence that either accepts or rejects a given null hypothesis H0. The alternative hypothesis H1 is the hypothesis that is accepted when H0 is rejected. In hypothesis testing, the probability of deciding H1 when in fact H0 is true is known as the false alarm rate, whereas the probability of deciding H1when in fact H1is true is known as the detection rate (or power) of the test. It is not possible to optimize both rates simultaneously. In this paper, we consider the problem of determining the data to be used for hypothesis testing that maximize the detection rate for a given false alarm rate. We consider in particular a hypothesis test which is relevant in functional magnetic resonance imaging (fMRI).
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