Identification Of State-space Models Research Articles

Bootstrap Statistical Tests of Rank Determination for System Identification

Identification of multivariate state-space models involves the specification of the dimension of the state vector. This note evaluates the performance of some asymptotic statistical tests of rank determination together with their bootstrapped versions against information criteria (IC) methods. Results show that certain bootstrapped procedures improve upon the performance of the corresponding asymptotic tests, and statistical tests have in general a better performance than IC methods.

Analysis of Takagi-Sugeno Fuzzy Models in System Identification for Model-Based Control

This article analyzes Takagi-Sugeno (TS) fuzzy models in system identification for model-based controller design. TS fuzzy model-based controls have been proposed to overcome the long-standing criticism of lack of stability of fuzzy controls. However, the application of these controllers is limited as TS fuzzy models for controller design can only be obtained by transformation of nonlinear mathematical models. The proposal that fuzzy controls be used as control methods for uncertain systems has deviated from the original intention of fuzzy control. In this work, we investigate the possibility of extending TS fuzzy model-based control into uncertain systems. We show the limitation of these control methods and clarify the gap between fuzzy model based-control and fuzzy model identification. For the identification of constant-affine state-space models a subspace identification algorithm is proposed to identify the true local dynamics with zero initial conditions.

Identification of MIMO state space models for helicopter dynamics

A considerable amount of work has been dedicated in the past to the problem of identification of helicopter flight dynamics, both in the time and frequency domain, however, limited attention has been devoted so far to the application of subspace methods to the problem. The aim of this paper is to show that subspace based identification techniques can be used to determine accurate discrete-time and continuous-time linear models for helicopter dynamics. The identification techniques are applied to simulated data generated by a physical model that describes coupled rotor-fuselage dynamics for a realistic rotorcraft.

Subspace-based identification methods using schur complement approach

This paper shows a new interpretation of the subspace-based identification methods by using Schur complement approach. MOESP (MIMO output error state space model identification) algorithms are considered. Instead of the data matrices, we start to consider a data product moment consisted of the Hankel matrices of input-output data. It is shown that the instrumental variables (IV) extensions of data matrices in the MOESP can be expressed as modifications of the data product moment. It enables us to treat the IV-MOESP algorithms under a unified framework, and we also show that the interpretation can be applicable to the errors-in-variables (EIV) problems and the framework still can be kept.

Identification of discrete-time state affine state space models using cumulants

This paper is concerned with the identification of discrete-time, time invariant, state affine state space models driven by an independent identically distributed (IID) random input, and in the presence of process and measurement noise. The identification problem is treated using a cumulant based approach. It is shown that the input–output and input–state crosscumulant equations in the time domain have the form of a linear autonomous system. An algorithmic procedure is then developed, for the computation of the unknown system matrices, based on a standard deterministic linear subspace identification algorithm, provided the input signal has some persistent excitation properties. The special case of Gaussian IID input is also examined. The proposed method is computationally very efficient and its accuracy is illustrated by simulations.

Identification of a deterministic constant-affine state space model with known initial conditions

Constant-affine state space models arise naturally from the linearisation of nonlinear state space models at either on or off equilibriums. Therefore this model structure has a clear interpretation from the dynamical systems point of view and is closely related to model-based technologies such as model-based control. In this paper, the authors investigate some properties of this model structure and propose two system identification algorithms for the deterministic constant-affine state space model with known initial conditions. The first algorithm is based on a subspace identification algorithm, while the second is built on nonlinear least squares.

Subspace identification for continuous-time stochastic systems via distribution-based approach

This paper presents a novel approach for system identification of continuous-time stochastic state space models from random input–output continuous data. The approach is based on the introduction of random distribution theory in describing (higher) time derivatives of stochastic processes, and the input–output algebraic relationship is derived which is treated in the time-domain. The efficacy of the approach is examined by comparing with other approaches employing the filters.

A PMF-based subspace method for continuous-time model identification. Application to a multivariable winding process

This paper presents a methodology for system identification of continuous-time state-space models from finite sampled input-output signals. The estimation problem of the consecutive time-derivatives and integrals of the input-output signals is considered. The appropriate frequency characteristcs of a linear filtering based on the Poisson moment functionals in regards to the derivative or integral estimation problem is shown. The proposed method combines therefore the Poisson moment functionals technique with subspace based state-space system identification methods. The developed algorithm is based on a generalized singular value decomposition to compensate the noise colouring caused by the linear prefiltering of the input-output data. Rules of thumb are presented to choose the design parameters and new regards to the selection of the Poisson filter cut-off frequency are introduced. Finally, the proposed method is applied to a multivariable winding processes. The experimental results emphasize the applicability of the developed methodology.

Residual models and stochastic realization in state-space identification

This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Our formulation includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.

The CONTSID Toolbox: A Matlab Toolbox for Continuous-Time System Identification

This paper presents the CONTSID toolbox for the identification of continuous-time transfer function or state-space models for linear time-invariant SISO and MIMO systems from sampled input/output data. The acronym CONTSID stands for CONtinuous-Time System IDentification toolbox. It has been designed as an addon to the Mathwork's system identification toolbox and has been given a similar setup. The toolbox is a collection of m-files and operates exclusively in the command line mode. It comprises most of the direct parametric continuous-time model identification methods from a discrete-time set of measurements, both classical ones as the state-variable filter method and more recent ones as subspace-based methods. The toolbox also includes tools for evaluating the estimated model properties.

A Study on Identification of State-Space Model for Refuse Incineration Plant

This paper identifies a discrete-time linear combustion model of Refuse Incineration Plant(RIP) which characterizes steam generation quantity, where the RIP is considered as a MIMO system with thirteen-inputs and one-output. The structure of RIP model is described as an ARX model which are analytically obtained from the combustion dynamics. Furthermore, using the Instrumental Variable(IV) identification algorithm, model structure and unknown parameters are identified from experimental input-output data sets, In result, it is shown that the identified ARX model well approximates the input-output combustion characteristics given by experimental data sets.

Subspace-based Identification for Continuous-Time Stochastic Systems via Distribution-Theoretic Approach

This paper presents a novel approach for system identification of continuous-time stochastic state space models from random input-output continuous data. The approach is based on the introduction of the random distribution theory in describing the (higher) time derivatives of stochastic processes, and the input-output algebraic relationship is derived which is treated in the time-domain. The efficacy of the approach proposed is examined by comparing with other approaches employing the filters.

Stochastic theory of continuous-time state-space identification

This paper presents theory, algorithms, and validation results for system identification of continuous-time state-space models from finite input-output sequences. The algorithms developed are methods of subspace model identification and stochastic realization adapted to the continuous-time context. The resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs, thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.

Multivariable identification of a winding process by subspace methods for tension control

The challenging problem of multivariable tension control in winding systems is addressed in this paper. Two control configurations, the SS model and the ST model configurations (SS: speed-speed and ST: speed-torque), are considered and applied to a pilot winding plant. The relevance of using linear models in such multivariable systems is examined. Tension simulations based on a proposed linear ST model yield interesting results in both open and closed-loops. Emphasis is also laid on the applicability of subspace methods to winding tension state-space model identification. Such methods simplify the problem of multivariable identification by reducing the associated polynomial model structural identification to the easier problem of order estimation. It is shown that the design of a Linear Quadratic Gaussian (LQG) controller capable of ensuring efficient performance over the entire winding zone can be based on an ‘average’ state-space model identified around a nominal operating point.

State-Space Model Identification of Deterministic Nonlinear Systems: Nonlinear Mapping Technology and Application of the Lyapunov Theory

This paper investigates the state-space mapping-based framework to identify deterministic nonlinear systems. The main intent is to introduce an innovative identification inroad by using nonlinear error mappings and to explore the theoretical aspects of the application of Lyapunov’s stability theory to systematically explore the convergence. This approach offers innovative and promising results. The Lyapunov stability theory has been widely used in stability analysis, and this paper demonstrates the application of the second method from parameter convergence perspectives. The systematic identification concept is introduced, and a novel scheme is developed by applying nonlinear error mappings. Another contribution is to demonstrate that in order to analyze the convergence, the nonquadratic Lyapunov candidates can be used. The unknown parameters of an electric drive, actuated by a permanent-magnet synchronous motor, are identified by using the experimental data. The example supports the procedure, and the simulation shows that the model dynamics match the experimentally measured states.

System Identification of Feedback and "Causality" Structure Using Canonical Variate Analysis

This paper addresses the problem of identification of components of a system that may involve unknown feedback around such a component as well as the presence of unmeasured disturbances. Further, the problem of comparing various hypotheses concerning the feedback structure among various components of an unknown system is discussed. The basic tool developed is an expression for the joint likelihood function of a process in terms of individual components of a system where measurements of the inputs and outputs of each component are available. It is show that maximum likelihood estimation of the whole structure decomposes into the separate maximum likelihood estimation of each component. This provides the basis for likelihood ratio tests of hypotheses for different feedback structures of the system. Canonical variate analysis provides a computationally stable procedure for the identification of state space models of the various component systems. These can then be combined to find the best system structure describing feedback and Granger causality.

Interpretation of Subspace Methods: Consistency Analysis

So called subspace methods for direct identification of linear state space models form a very useful alternative to maximum-likelihood type approaches, inthat they are non-iterative and offer effic ...

Continuous-Time Subspace Model Identification Method Using Laguerre Filtering

Abstract This paper introduces a time domain subspace model identification method, for the identification of continuous-time MIMO state-space models. The measured signals are assumed to be contaminated with both process and measurement noise. The method uses a bilinear transformation on the data, to identify the system in an alternative domain. Afterwards the system is transformed back. An example of the method is presented.

PMF-Based Subspace Method for Continuous-Time Model Identification Deterministic Study

This paper presents the use of the Poisson Moment Functionals (PMF) combined with Subspace based State-Space System IDentification (4SID) methods for continuous-time state-space model identification directly from sampled I/O data. The main purpose of this study is to show the PMF order limits and their consequences as deterministic errors on the estimation results. In particular, it seems that the 4SID estimation step of matrices B and D is the most sensitive to these deterministic disturbances. A double filtering technique is introduced by using a reduced order filter before estimating B and D in order to keep constant the estimation performances.

State Space Identification for a Pilot Distillation Column

Abstract The problem of black box identification of a linear MIMO model for a distillation column is considered and the N4SID subspace based algorithm for the identification of linear state space models is applied to a set of experimental data. Model order selection and experiment design are based on a simulation study, performed on a non linear model of the plant. The comparison of the response of the identified model with the response of the plant shows a very satisfactory degree of accordance.