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  • 1.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Applications Oriented Input Design in Time-Domain Through Cyclic Methods2014Conference paper (Refereed)
    Abstract [en]

    In this paper we propose a method for applications oriented input design for linear systems in open-loop under time-domain constraints on the amplitude of input and output signals. The method guarantees a desired control performance for the estimated model in minimum time, by imposing some lower bound on the information matrix. The problem is formulated as a time-domain optimization problem, which is non-convex. This is addressed through an alternating method, where we separate the problem into two steps and at each step we optimize the cost function with respect to one of two variables. We alternate between these two steps until convergence. A time recursive input design algorithm is performed, which enables us to use the algorithm with control. Therefore, a receding horizon framework is used to solve each optimization problem. Finally, we illustrate the method with a numerical example which shows the good ability of the proposed approach in generating an optimal input signal.

  • 2.
    Gevers, Michel
    et al.
    Vrije Universiteit Brussels.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pintelon, Rik
    Vrije Universiteit Brussels.
    Schoukens, Johan
    Vrije Universiteit Brussels.
    The transient impulse response modeling method and the local polynomial method for nonparametric system identification2012In: 16th IFAC Symposium on System Identification, IFAC , 2012, p. 55-60Conference paper (Refereed)
    Abstract [en]

    This paper analyzes two recent methods for the nonparametric estimation of the Frequency Response Function (FRF) from input-output data using Prediction Error identification. Such FRF estimate can be the main goal of the identification exercise, or it can be a tool for the computation of a nonparametric estimate of the noise spectrum. We show that the choice of the method depends on the signal to noise ratio and on the objective. The method that delivers the best FRF estimate may not deliver the best estimate of the noise spectrum. Our theoretical analysis is illustrated by simulations.

  • 3.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Structured System Identification and Nonparametric Frequency Response Estimation2014Doctoral thesis, monograph (Other academic)
    Abstract [en]

    To keep up with the ever increasing demand on performance and efficiency of control systems, accurate models are needed. System identification is concerned with the estimation and validation of mathematical models of dynamical systems from experimental data. The main problem considered in this thesis is how to take advantage of structural information in system identification. Including this additional information can significantly improve the quality of the identified model.First, the problem of input design for networked systems is considered. Results from closed-loop input design are generalized to the networked case. The main difference between the networked setting and the classical open- or closed-loop setting is the possibility of using measurable, or known, disturbances to improve the excitation. Such  disturbances cannot be affected during the experiment and are common in industrial applications.A framework to include the additional information about the measurable disturbances in the input design is presented. The framework is evaluated in two simulation examples and several interesting observations are made.Second, the result from an input design is often the correlation properties of the input signal.The question is then how to generate the input signal that can be applied to the system with the given properties.  This thesis presents a novel signal generation method that is able to handle input and output constraints. In industrial applications, it is often vital to satisfy constraints on both the input and the output signals during the system identification experiment. The method is formulated as a reference tracking Model Predictive Controller (MPC), with the desired correlation properties of the signal as reference, while satisfying the input and output constraints on the considered system.  The core of the algorithm is the formulation of the signal generation as an MPC which allows the use existing tools to make the algorithm robust and adaptive. The proposed method is evaluated in several simulation studies and successfully applied to a physical lab process.Third, nonparametric estimates of the frequency response function of a system are used in almost all engineering fields. The final contribution of this thesis is to present a novel nonparametric method, called the Transient and Impulse Response Modeling Method (TRIMM). The method is inspired by the local polynomial method, but uses more information about the known structure of the leakage error in the estimation of the frequency response. The bias and variance errors of TRIMM are analyzed and the results are used to connect system properties and the choice of user parameters with the performance of the method. The analysis can also be used to compare the performance of different methods and to give guidelines to the user on how to choose method.

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    thesis
  • 4.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Using Structural Information in System Identification2012Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Recent advances in small and cheap communication and sensing have opened up for large scale systems with intricate interconnections and interactions. These applications pose new challenges for analysis and control design. To keep up with the increasing demand on performance and efficiency, accurate models of these systems are needed.  Often some prior knowledge of the system, such as system structure, is available.Prior knowledge should whenever possible be used in system identification to improve the model estimate.This thesis addresses the problem of using prior information about the overall structure of the system in system identification.  Two special structures are considered, the cascade and the parallel serial structure.  The motivation for looking at these structures are two folded; they are common in industrial applications and they can be used to build up almost all interesting feedforward interconnected systems.  The effect of sensor placement, input signals and common dynamics of the subsystems on the quality of the estimated models for these two structures is considered.In many control applications it is vital that the model has a physical interpretation. Hence, it is important that the system identification method retains the physical interpretation of the identified model. However, it has proven hard to incorporate prior knowledge of structure in subspace methods. This thesis presents two methods for identifying systems with known structures using subspace methods.  The first method utilizes that the state-space matrices of a system on cascade form have a certain structure. The idea is to find a transform that takes the identified system back to this form. The second method uses the known structure of the extended observability matrix. The state-space matrices for the subsystems can then be found by solving linear least squares problems. However, the method is only applicable if the second subsystem has order one. But this is a common case in practice. The two methods are applied to a two tank lab process with promising results.Nonparametric estimates of the frequency response function of systems are used in most engineering fields. The second contribution of this thesis is a new method for estimating the frequency response. The method uses the known structure of the transient or leakage error. The feasibility of the method is tested in simulations. For the two cases considered, one with a large amount of random systems, the second with a resonant system, the method shows good performance compared to current state of the art methods.

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    fulltext
  • 5.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Non-parametric frequency function estimation using transient impulse response modelling2012In: 16th IFAC Symposium on System Identification, IFAC , 2012, p. 43-48Conference paper (Refereed)
    Abstract [en]

    Recently, Hägg, Hjalmarsson and Wahlberg proposed a novel non-parametric method that directly estimates the frequency response at N equidistant frequencies when N measurements are available. The specific feature of the method is that together with these estimates, the transient, or, equivalently, the leakage, is explicitly estimated. The estimates are obtained by solving a least-squares problem. The method involves three design variables, the number of estimated transient terms, a number of auxiliary impulse response coefficients (that also are estimated), and the size of a frequency window. At present there is no analysis of how these design variables affect the properties of the method, which we will call TRIMM (TRansient Impulse response Modeling Method). In this contribution we provide bias and variance analysis for two extreme cases of the window size. We show that at one extreme value, the method coincides with the Empirical Transfer Function Estimate, and at the other extreme it is close to directly estimating a FIR model. This indicates that TRIMM provides an intermediate between non-parametric and parametric estimation. The results allows us to quantify bias and variance errors at the two extreme cases under study, and gives insight into how to choose the design variables in a systematic way.

  • 6.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Least Squares Approach to Direct Frequency Response Estimation2011In: 2011 50th IEEE Conference On Decision And Control And European Control Conference (CDC-ECC), IEEE , 2011, p. 2160-2165Conference paper (Refereed)
    Abstract [en]

    Traditionally, the frequency response function has been estimated directly by dividing the discrete Fourier transforms of the output and the input of the system. This approach suffers from leakage errors and noise sensitivity. Lately these errors have been studied in detail. The main observation is that the error has a smooth frequency characteristic that is highly structured. The recently proposed local polynomial method uses this smoothness, and tries to estimate the frequency response function along with a smooth approximation of the error term. In this paper we propose a method, closely related to the local polynomial method, but instead of using the smoothness of the error we explore the structure even further. The proposed approach to estimate the frequency response function seems promising, as illustrated by simulations and comparison with current state of the art methods.

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    fulltext
  • 7.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ebadat, Afrooz
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Input Signal Generation for Constrained Multiple-Input Multple-Output Systems2014In: Proceedings of 19th World Congress of the International Federation of Automatic Control 2014, IFAC , 2014Conference paper (Refereed)
    Abstract [en]

    In this paper we extend a recent method for generating an input signal with a desired auto-correlation function while satisfying both input and output constraints for the system it is to be applied to. This is an important problem in system identication, firstly, the properties of the identified model is highly dependent on the used excitation signal during the experiment and secondly, on real processes, due to actuator saturation and safety considerations, it is important to constraint the input and output from the process. The proposed method corresponds to a nonlinear model predictive control problem and here we extend it to consider general input horizons and also to the multiple-input multiple-output case. In general this corresponds to solving a multivariate polynomial of order four in each time step. Here two dierent methods for solving this problem are considered: one based on convex relaxation and one based on a cyclic algorithm. The performance of the algorithm is successfully veried by simulations and the implications of dierent lengths of the input horizon is discussed.

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    fulltext
  • 8.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Robust and Adaptive Excitation Signal Generation for Input and Output Constrained Systems2013In: 2013 European Control Conference, ECC 2013, IEEE , 2013, p. 1416-1421Conference paper (Refereed)
    Abstract [en]

    Generating signals with a prespecified autocorrelation, available from some input design, while satisfying constraints on input and output signals of the systems which the signal is to be applied on is an important problem in system identification. This paper extends a recently proposed method for such signal generation. The method is modified to be robust to uncertainties in the system model. An adaptive formulation is also given which allows for improving the input design online. The adaptive method is compared to the true optimal input design on a simulation example. The robustness properties of the method are illustrated on an experimental setup.

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    fulltext
  • 9.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Schoukens, Johan
    Vrije Universiteit Brussel, ELEC Department.
    Gevers, Michel
    ICTEAM, Universite Catholique de Louvain,.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    The Transient Impulse Response Modeling Method for Non-parametric System Identication2016In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 68, p. 314-328Article in journal (Refereed)
    Abstract [en]

    A method for the nonparametric estimation of the Frequency Response Function (FRF) was introduced in [5] and latercalled Transient Impulse Response Modeling Method (trimm). We present here a slightly improved version of the originalmethod and, more importantly, we thoroughly analyze the method in terms of bias and variance errors. This analysis leads toguidelines for the choice of the design parameters of the trimm method. Our theoretical expressions for the bias and varianceerrors are validated by simulations which, at the same time, highlight the eect of the design parameters on the performanceof the method.

  • 10.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Optimal Input Design for Feed-forward Control2013In: Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, IEEE conference proceedings, 2013, p. 7174-7180Conference paper (Refereed)
    Abstract [en]

    This paper considers optimal input design when the intended use of the identified model is to construct a feed-forward controller based on measurable disturbances. The objective is to find a minimum power excitation signal to be used in a system identification experiment, such that the corresponding model-based feed-forward controller guarantees, with a given probability, that the variance of the output signal is within given specifications. To start with, some low order model problems are analytically solved and fundamental properties of the optimal input signal solution are presented. The optimal input signal contains feed-forward control and depends on the noise model and transfer function of the system in a specific way. Next, we show how to apply the partial correlation approach to closed loop optimal experiment design to the general feed-forward problem. A framework for optimal input signal design for feed-forward control is presented and numerically evaluated on a temperature control problem.

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  • 11.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Optimal Input Design for Networked Systems2014In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 53, p. 275-281Article in journal (Refereed)
    Abstract [en]

    The topic of this paper is optimal input signal design for identification of interconnected/networked dynamic systems. We consider the case when it is only possible to design some of the input signals, while the rest of the inputs are only measurable. This is most common in industrial applications, where external excitation can only be applied to some subsystems. One example is feed-forward control from measurable disturbances. The optimal input signal will be correlated with the measured signals. The main purpose of this paper is to reveal how to re-formulate the input design problem for networked systems as an input design problem for feedback control systems. We can then use the powerful partial correlation approach for optimal closed loop input design. This means that the corresponding networked optimal input design problem can be formulated as a semi-denite program, for which there are ecient numerical methods. We evaluate this approach using two numerical examples with important applications. The result reveals some non-trivial interesting properties of the optimal input signals.

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  • 12.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Identification of Parallel Cascade Serial Systems2011In: IFAC Proceedings Volumes (IFAC-PapersOnline), IFAC , 2011Conference paper (Refereed)
    Abstract [en]

    We consider identification of systems with a parallel serial (cascade) structure with multiple-input and multiple-output signals. The statistical properties of estimated models are studied with respect to input signals and possible sensor locations. The quality of the estimates are analyzed by means of the asymptotic covariance matrix of the estimated parameters. This is an extension of previous work on identification of cascaded linear systems. The key result concerns systems where the sub-systems have common dynamics. An interesting observation is that for this case the variance for the parameters belonging to the unmeasured subsystem always is larger than for the other sub-systems. This is not true for general parameters. The variance results can be used for optimal input and sensor location design. The results are illustrated by some simple FIR examples and numerical evaluations.

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    IR-EE-RT 2010:054
  • 13.
    Hägg, Per
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On subspace identification of cascade structured systems2010In: Proceedings of the IEEE Conference on Decision and Control, IEEE , 2010, p. 2843-2848Conference paper (Refereed)
    Abstract [en]

    In identification it is important to take a priori structural information into account in many applications, something that is difficult when using subspace methods. Here will study how to incorporate a special structure, a cascade structure with two subsystems. Two new methods are derived for estimating system with this structure. The problem when using subspace identification on cascade structured system is that the states from the first subsystem are mixed with states from the second subsystem via a unknown similarity transform. The first indirect method finds a similarity transform that takes the system back to a form such that the subsystems can be recovered. The second method uses the fact that the structure of the extended observability matrix is known for cascade systems. However, it only works when both subsystems have order one. In practice this is still a common case. The results of the two methods seem promising, as illustrated by applying the methods to a real process, the double tank process. The performance is comparable with state of the art methods. Finally the problem of optimal input design for cascade systems are introduced, and illustrated by a simple example.

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    IR-EE-RT 2010:021
  • 14.
    Larsson, Christian A.
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Generation of signals with specified second-order properties for constrained systems2016In: International journal of adaptive control and signal processing (Print), ISSN 0890-6327, E-ISSN 1099-1115, Vol. 30, no 3, p. 456-472Article in journal (Refereed)
    Abstract [en]

    This contribution considers the problem of realizing an input signal with a desired autocorrelation sequence satisfying both input and output constraints for the system it is to be applied to. This is an important problem in system identification, firstly, because the quality and accuracy of the identified model are highly dependent on the excitation signal used during the experiment and secondly, because on real processes, it is often important to constrain the input and output of the process because of actuator saturation and safety considerations. The signal generation is formulated as a model predictive controller with probabilistic constraints to make the algorithm robust to model uncertainties and process noise. The corresponding optimization problem is then solved with tools from scenario-based stochastic optimization. To reduce the model uncertainties, the method is made adaptive where a new model of the system and its uncertainties are reidentified. The algorithm is successfully applied to a simulation example and in a practical experiment for the identification of a quadruple tank lab process.

  • 15.
    Larsson, Christian
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Generation of excitation signals with prescribed autocorrelation for input and output constrained systems2013In: 2013 American Control Conference (ACC), American Automatic Control Council , 2013, p. 3918-3923Conference paper (Refereed)
    Abstract [en]

    This paper considers the problem of realizing an input signal with a desired autocorrelation sequence satisfying both input and output constraints for the system it is to be applied to. This is a important problem in system identification. Firstly, the properties of the identified model are highly dependent on the used excitation signal during the experiment and secondly, on real processes, due to actuator saturation and safety considerations, it is important to constrain the inputs and outputs of the process. The proposed method is formulated as a nonlinear model predictive control problem. In general this corresponds to solving a non-convex optimization problem. Here we show how this can be solved in one particular case. For this special case convergence is established for generation of pseudo-white noise. The performance of the algorithm is successfully verified by simulations for a few different autocorrelation sequences, with and without input and output constraints.

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    fulltext
  • 16.
    Sandberg, Henrik
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Approximative model reconstruction of cascade systems2014In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 69, no 1, p. 90-97Article in journal (Refereed)
    Abstract [en]

    This letter considers how to approximately reconstruct a cascade system from a given unstructured system estimate. Many system identification methods, including subspace methods, provide reliable but generally unstructured black-box models. The problem we consider is how to find cascade systems that are close to such black-box models. For this, we use model matching techniques and optimal weighted Hankel-norm approximation to obtain accurate low-order cascade systems. We show that it is possible to bound the reconstruction error in terms of an error tolerance parameter and weighted Hankel singular values. The suggested methods are illustrated on both a numerical example and a real double tank system with experimental data.

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