Experiences from Subspace System Identification - Comments from Process Industry Users and Researchers

2008 47th IEEE Conference on Decision and Control

2008

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Abstract-General black-box system identification techniques such as subspace system identification and FIR/ARX least squares system identification are commonly used to identify multi-input multi-output models from experimental data. However, in many applications there are a priori given structural information. Here the focus is on linear dynamical systems with a cascade structure, and with one input signal and two output signals. Models of such systems are important in e.g. cascade control applications. It is possible to incorporate such a structure in a prediction error method, which, however, is based on rather advanced numerical non-convex optimization techniques to calculate the corresponding structured model estimate. We will instead study how to use model approximation techniques to approximate a general black-box estimate with a structured model. This will avoid the use of numerical optimization and works well with e.g. subspace system identification, which is a standard method in process industry where cascade systems are very common. The problems of cascade structural model approximation and model reduction are rather non-standard, and we will study several new methods. The basic idea is to first find a higher order but structured model approximation using standard H ∞ model matching techniques, and then in a second step use so-called structured balanced model reduction to find lower order structured approximation. Structured balanced model reduction is a rather new approach, with powerful model order selection tools and error bound results. The results of the corresponding two step model approximation approach seem promising, as illustrated by a simple numerical example. I. INTRODUCTIONSystem identification deals with estimation and validation of models of dynamical systems from experimental data. Most system identification methods concern, however, single-input single-output (SISO) systems. Many of these results can be generalized to multi-input multi-output (MIMO) systems. In particular, subspace system identification methods have shown very useful when dealing with MIMO systems. This is a black-box technique to identify state-space models and it is difficult to take a priori information of the underlying system into account to specify the model structure. The current work has been motivated by a discussion on use of subspace identification in process industry presented in [17]. In this application area it is common to first identify unstructured sub-models, which then in a second step are merged into a high order model. The complexity of this combined model has then to be reduced in order to apply e.g. model predictive control algorithms. In industry, simple standard model reduction techniques, such as balanced model reduction, are used, which do not take the structure into account.

Section: Comes Frommentioning

confidence: 89%

Section: Discussionmentioning

confidence: 99%

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confidence: 99%

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Cascade structural model approximation of identified state space models

2008 47th IEEE Conference on Decision and Control

2008

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“…This class of systems generalizes cascaded systems. This problem is partly motivated by the discussion on the use of structural system identification given in Wahlberg et al (2007), and collaboration with Honeywell Prague Laboratory on boiler control, see e.g., Baramov et al (2007). Classical methods in system identification consider singleinput single-output (SISO) systems, and can often be extended to multiple-input multiple-output (MIMO) systems, see e.g., Zhu (1998) for a process control perspective.…”

Section: Introductionmentioning

confidence: 99%

On Identification of Parallel Cascade Serial Systems

Hägg

IFAC Proceedings Volumes

2011

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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.

“…1, using subspace methods. The current work has been motivated by a discussion on use of subspace identification in process industry presented in [3]. In particular systems with one input signal and two output…”

Section: Introductionmentioning

confidence: 99%

On subspace identification of cascade structured systems

Hägg

49th IEEE Conference on Decision and Control (CDC)

2010

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Abstract-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.