Identification Of Linear Multivariable Systems Research Articles

Three Approaches for System Identification by Impulse Response Fitting

This paper addresses the problem of the identification of multivariable linear systems from measured or estimated samples of the impulse response. Most techniques are based on a low rank approximation of a block-Hankel matrix computed by a truncated singular value decomposition. The main drawback of such approaches is that the block-Hankel structure is not preserved in the approximation. Therefore these methods do not actually perform a term-wise fitting on the samples of the impulse response. Since the beginning of the 1990s, several algorithms were proposed for computing low rank approximations that maintain the matrix structure. But the methods available up until now still include limitations.In this article, three general and equivalent solutions to this identification problem are proposed in the general case of multiple-input multiple-output (MIMO) systems. They derive from a specific parametrization and perform a term-wise minimization of a least squares criterion on the samples of the impulse response.

MIXED H2 AND H∞ INPUT DESIGN FOR MULTIVARIABLE SYSTEMS

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.

Relay Tuning of Multivariable PI Controllers

A new method for identification of linear multivariable systems using relay feedback is presented. The procedure is a combination of sequential to simultaneous loop closing and relay experiments that are often used for tuning scalar systems. Once the plant transfer matrix is identified at a certain given frequency, Maciejowski technique is used to design multivariable PI controllers. A simulation example is given to illustrate both the identification and design method. Comparative results are shown to demonstrate that the new tuning method has the best set-point response performance. The results can be considered as a significant step towards autotuning of multivariable PI controllers.

Recursive relaxation identification of linear multivariable systems with its parallel algorithm

In this paper, we propose a new method for the identification of discrete-time linear multivariable systems. This method comprises three recursive computation schemes including two parameter estimate schemes for both state equation and observation equation, respectively, and the state estimate scheme via Kalman filtering. We call this method the recursive relaxation identification, abbreviated as RRI. Compared with the existing methods, the RRI algorithm has advantages of simplification, fast computation, and high efficiency, and is suitable for fast real-time on-line adaptive identification of linear multivariable systems.

Fully Parametrized State-Space Models in System Identification

In this paper we consider identification of multivariable linear systems using state-space models. A new model structure which is fully parametrized is introduced. All systems of a given order. can be described with this model structure and thus relieve us from all the internal structural issues otherwise inherent in the multivariable state-space identification problem. We present an identification algorithm which minimize a regularized prediction error criterion. We show that the proposed model structure retains the statistical properties of the standard identifiable model structures. The proposed identification algorithm is shown to locally converge to the set of true systems. Examples are given illustrating the results as well as showing the practical use of the proposed model structure using real data.

Linear system identification via an asymptotically stable observer

This paper presents a formulation for identification of linear multivariable systems from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero corresponding to a deadbeat observer. In this formulation, the Markov parameters of the observer are first identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to realize a state space model of the system. The basic mathematical formulation is derived, and numerical examples are presented to illustrate the proposed method.

Identification of multivariable linear systems from input/output measurements

A stochastic approximation technique for multi-input multi-output (MIMO) system identification is proposed where the technique is based on state space formalization of a system with known indices. The proposed method is applicable to digital computer implementation. Convergence of the technique is shown, and an example showing its effectiveness when compared with another approximation technique is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Parameter and structure identification of linear multivariable systems

In this paper, a parameter and structure identification scheme, which can be used for both continuous and discrete time systems, is presented. This scheme has an “on-line” nature and it incorporates standard techniques such as state variable filters and adaptation laws developed through stability analysis. The canonical form being used is based on the output injection which is constructed to assign all the poles of the system to α, an arbitrary chosen real number. It is therefore named the “α-canonical form”.

A New and Wider Class of Overlapping Forms for the Presentation of Multivariable Systems

Abstract One approach to the identification of multivariable linear systems is to use one of several “overlapping” or forms. They are uniquely identifiable. The structure of each pseudocanonical form is determined by a set of structure indices, that indicate which particular rows of the Hankel matrix of Markov parameters have been selected to form a basis. In this paper, we relax the traditional constraints on the selection of these rows. This allows for more flexibility and enhances the chances of obtaining a numerically well-conditioned basis.

Structural identification of linear multivariable systems using overlapping forms: a new parametrization

Abstract The choice of a parametrization for the representation of a linear multivariable control system amounts to the selection of a basis of the rows of the Hankel matrix of Markov elements. The so-called ‘ overlapping ’ or ‘ pseudo-canonical ’ forms are traditionally obtained by imposing two selection rules : a block selection rule and a chain selection rule. In this paper, these constraints are relaxed to requiring only a chain selection rule. This allows for more flexibility in selecting numerically well-conditioned parametrizations.

Comments on "The range error test in the structural identification of linear multivariable systems"

Some observations on the procedure proposed in for selecting the structure of linear systems are offered.

A Computational Algorithm for Identification of Linear Multivariable systems

An efficient computational algorithm for finding the minimal realization of discrete linear multivariable systems from input/output data is proposed. The algorithm uses orthogonal transformations only and its implementation includes the modern linear algebra software.

Optimal instrumental-variable methods for identification of multivariable linear systems

The identification of multivariable linear systems using instrumental-variable (IV) methods is discussed. The emphasis is on accuracy properties. The IV estimates of multi-input-multi-output system parameters are proved to be asymptotically Gaussian distributed under weak conditions. An explicit expression for the covariance matrix of the parameter estimates is given. It is then shown how this matrix can be optimized by appropriately choosing the IV variant. The optimal accuracy so obtained is for some model structures equal to that corresponding to a prediction error method.

The range error test in the structural identification of linear multivariable systems

Among the approaches that have been proposed in recent years for the identification of discrete-time linear multivariable systems, very efficient procedures are based on the introduction of a set of input-output canonical models and on the separate determination of the process structure (structural identification) and parameters (parametric identification). This paper introduces a new simple test which allows us to perform the structural identification without the drawbacks usually associated with singularity tests. The proposed test gives an a priori prediction of the model performance in order to avoid trial and error procedures in the determination of a suitable structure for the process to be identified.

Determination of the Structure of a Canonical Model for the Identification of Linear Multivariable Systems

Determination of the Structure of a Canonical Model for the Identification of Linear Multivariable Systems

Structural identification and software package for linear multivariable systems

This paper is concerned with the structural identification of linear multivariable systems and an interactive identification package. The structural identification is done by taking the time-invariant subsystem from the realizations of the input-output relations identified using data of disjoint time intervals, and the statistical hypothesis test is employed to determine the order, where the input-output relation is identified based on the generalized least squares method using the possibly larger model for the plant. The identification package is for the identification of the input-output relation of a linear multivariable system, for the structural identification based on the realization and for data management.

Optimal input design for the identification of linear multivariable systems with disjoint parametrization

This paper considers the problem of generating test signals for parameter estimation in linear multi-input multi-output stochastic systems using a frequency domain approach. The model is disjointly parametrized and the input signals are power-constrained and chosen to be optimal in the sense of maximizing system information where the criterion employed is a scalar function of the inverse Fisher information matrix. Independence of the input components is shown to be consistent with optimality and this leads to a sufficient condition for local identifiability and a reduction in the size of the design optimization problem.

Determination of the Structure of a Canonical Model for the Identification of Linear Multivariable Systems

An algorithm is presented for determining the structural parameters of a canonical form which has been used much for the identification of linear multivariable discrete-time systems. The cases of noise-free as well as noisy data are considered. The algorithm utilizes the residual error technique and does not need the knowledge of the noise characteristics. The proposed algorithm is applied to the identification of simulated examples with different noise levels.

Experiences with a Modeling and Identification Package: A Power Plant Study

This paper presents a package for modeling and identification of linear multivariable systems from only the knowledge of input - output data. The method, that is original, belongs to the least squares family and applies new efficient factorization algorithms drawn from the numerical linear algebra literature. Performances of the package and comparisons with other methods on a simulated real size power plant are illustrated.

Recursive estimation of the parameters of linear multivariable systems

A recursive algorithm is proposed for the identification of linear multivariable systems. Utilization of a canonical state space model minimizes the number of parameters to be estimated. The problem of identification in the presence of noise is solved by using a recursive generalized least-squares method.