Low-order Model Identification Research Articles

Identification of Low Order Systems in a Loewner Framework

This paper considers the problem of non-parametric identification of low-order models from time-domain experimental data using a combination of Caratheodory Fejer and Loewner-based interpolation, followed by a Loewner matrix Balanced Reduction (LBR) step. As we show in the paper, the Loewner matrix is an estimator for the trace norm of a system, playing a role similar to the one played by the Hankel matrix. However, utilizing Zolotarev numbers to establish decay rate bounds for singular values reveals that the decay of singular values in the Loewner matrix is considerably faster than that in the Hankel matrix. Thus, Loewner-based methods yield lower order systems, with the same error bound, than comparable ones based on Hankel matrices. The effectiveness of our method is demonstrated through a numerical example.

Campus Microgrid Data-Driven Model Identification and Secondary Voltage Control

Microgrids deal with challenges presented by intermittent distributed generation, electrical faults and mode transition. To address these issues, to understand their static and dynamic behavior, and to develop control systems, it is necessary to reproduce their stable operation and transient response through mathematical models. This paper presents a data-driven low-order model identification methodology applied to voltage characterization in a photovoltaic system of a real campus microgrid for secondary voltage regulation. First, a literature review is presented focusing on secondary voltage modeling strategies and control. Then, experimental data is used to estimate and validate a low-order MIMO (multiple input–multiple output) model of the microgrid, considering reactive power, solar irradiance, and power demand inputs and the voltage output of the grid node. The obtained model reproduced the real system response with an accuracy of 88.4%. This model is used for dynamical analysis of the microgrid and the development of a secondary voltage control system based on model predictive control (MPC). The MPC strategy uses polytopic invariant sets as terminal sets to guarantee stability. Simulations are carried out to evaluate the controller performance using experimental data from solar irradiance and power demand as the system disturbances. Successful regulation of the secondary voltage output is obtained with a fast response despite the wide range of disturbance values.

Low-Order Model Identification and Adaptive Observer-Based Predictive Control for Strip Temperature of Heating Section in Annealing Furnace

The heating section of an annealing furnace is a plant that raises the temperature of steel strips to the desired target temperature to ensure that the strips achieve the desired material properties. Model predictive control (MPC) has been used to increase the temperature in previously published studies, because it reflects the geometrical and material characteristics of the strip. An accurate temperature predictive model for the annealing furnace is required for the optimization of the MPC. For a large and complex annealing furnace, nonlinear models from existing studies are computationally expensive. Therefore, we propose identification method of a linear low-order model, and then apply it to the MPC. In addition, we introduce parameter estimation and an adaptive observer for the estimation to address difficulties in identifying unknown parameters. To verify the identified model and adaptive observer-based MPC, control results from the tracking of target temperature are shown and analyzed through a simulation with conditions close to the actual operation conditions. Furthermore, the simulation results of the proposed method are compared with those of the PI controller and nonlinear MPC. The proposed method solves the problems caused by the massive computational complexity and absence of sensors. The proposed method allows for the accurate control of the temperature using MPC in various types of annealing furnaces.

Identification of low-order models using Laguerre basis function expansions

In this paper, a method for identification of low-order output-error models expressed in terms of Laguerre basis functions is presented. The identification problem is formulated as a rank-constrained optimization problem in the Laguerre domain, which can be solved efficiently using nuclear norm regularization. Since the identified models are of low order, a minimal state-space realization of the system can be obtained without the use of additional approximative model-order reduction steps.

Nonlinear dimension reduction based neural modeling for distributed parameter processes

Many chemical processes are nonlinear distributed parameter systems with unknown uncertainties. For this class of infinite-dimensional systems, the low-order model identification from process data is very important in practice. The dimension reduction with a principal component analysis (PCA) is only a linear approximation for nonlinear problem. In this study, a nonlinear dimension reduction based low-order neural model identification approach is proposed for nonlinear distributed parameter processes. First, a nonlinear principal component analysis (NL-PCA) network is designed for the nonlinear dimension reduction, which can transform the high-dimensional spatio-temporal data into a low-dimensional time domain. Then, a neural system can be easily identified to model this low-dimensional temporal data. Finally, the spatio-temporal dynamics can be reproduced using the nonlinear time/space reconstruction. The simulations on a typical nonlinear transport-reaction process show that the proposed approach can achieve a better performance than the linear PCA based modeling approach.

Identification of Low Order Models for Large Scale Systems

Abstract Abstract In this paper we propose a novel procedure for obtaining a low order non-linear model of a large scale multi-phase, non-linear, reactive fluid flow systems. Our approach is based on the combinations of the methods of Proper Orthogonal Decomposition (POD), and non-linear System Identification (SID) techniques. The problem of non-linear model reduction is formulated as parameter estimation problem. In the first step POD is used to separate the spatial and temporal patterns and in the second step a model structure and it's parameters of linear and of non-linear polynomial type are identified to approximate the temporal patterns obtained by the POD in the first step. The proposed model structure treats POD modal coefficients as states rather than outputs of the identified model. The state space matrices which happens to be the parameters of a black-box to be identified, comes linearly in parameter estimation process. For the same reason, Ordinary Least Square (OLS) method is used to estimate the model parameters. The simplicity and reliability of the proposed method gives computationally very efficient linear and non-linear low order models for extremely large scale processes. The method is of generic nature. The efficiency of proposed approach is illustrated on a very large scale benchmark problem depicting Industrial Glass Manufacturing Process (IGMP). The results show good performance of the proposed method.

Identification of low-order unstable process model from closed-loop step test

Abstract Abstract Based on a closed-loop step response test, control-oriented low-order model identification algorithms are proposed for unstable processes. By using a damping factor to the closed-loop step response for realization of the Laplace transform, an algorithm for estimating the process frequency response is developed in terms of the closed-loop control structure used for identification. Correspondingly, two model identification algorithms are derived analytically for obtaining the widely used low-order process models of first-order-plus-dead-time (FOPDT) and second-order-plus-dead-time (SOPDT), respectively. Illustrative examples from the recent literature are used to demonstrate the effectiveness and merits of the proposed identification algorithms.

Low-Order Model Identification of Distributed Parameter Systems by a Combination of Singular Value Decomposition and the Karhunen−Loève Expansion

In this work, a new system identification method that combines the characteristics of singular value decomposition (SVD) and the Karhunen−Loeve (KL) expansion for distributed parameter systems is p...

Identification of highly accurate low order state space models in the frequency domain

This paper discusses an integrated approach for high accuracy and low order model identification. The approach integrates subspace-based identification algorithms with model reduction and parameter estimation algorithms to generate highly accurate low order models. The specific identification algorithm presented in the paper is the integrated frequency domain observability range space extraction and least square parameter estimation algorithm (IFORSELS). IFORSELS is an iterative algorithm which integrates the frequency domain observability range space extraction (FORSE) algorithm, the balanced realization model reduction algorithm, and the logarithmic and additive least square parameter estimation algorithms in an iterative fashion. It is capable of achieving much higher modeling accuracy using a lower order model than that achieved using a higher order model by subspace-based algorithms, such as FORSE.

Identification of Highly Accurate Low Order State Space Models in the Frequency Domain

This paper discusses an integrated approach for high accuracy and low order model identification. The approach integrates subspace-based identification algorithms with model reduction and parameter estimation algorithms to generate highly accmate low order models. The specific identification algorithm presented in the paper is the Integrated Frequency domain Observability Range Space Extraction and Least Square parameter estimation algorithm (IFORSELS). IFORSELS is an iterative algorithm which integrates the Frequency domain Observability Range Space Extraction (FORSE) algorithm, the Balanced Realization model reduction algorithm, and the Logarithmic and Additive Least Square parameter estimation algorithms in an iterativp fashion. It is capable of achieving much higher modeling accmacy using a lower order model than that achieved using a higher order model by subspace-based algorithms, such as FORSE.

Multivariable Control of a Continuous Crystallization Process Using Experimental Input-Output Models

Results from closed-loop control of a continuous evaporative crystallization process on the basis of identified input-output models are presented. Experimental results show that open-loop identification of a crystallization process may lead to poor models as the process has a tendency to oscillate. Improved experimental conditions are achieved under feedback control, using a simple single-loop PI controller. Identification of low-order models, on the basis of closed-loop data, is studied using linear multivariable input-output models. Controllability analysis reveals that only two output quantities can be controlled independently: the mass production rate and a quantity related to the density of small crystals (fines) in the system. A two input two output model predictive controller (MPC) is designed and tested on the pilot crystallizer. Experimental results show that an improvement of the performance of the closed-loop system is obtained.