Identification Of Multivariable Systems Research Articles

Iterative Identification for Multivariable Systems with Time-Delays Based on Basis Pursuit De-Noising and Auxiliary Model

This paper focuses on the joint estimation of parameters and time-delays of the multiple-input single-output output-error systems. Since the time-delays are unknown, an effective identification model with a high dimensional and sparse parameter vector is established based on overparameterization. Then, the identification problem is converted to a sparse optimization problem. Based on the basis pursuit de-noising criterion and the auxiliary model identification idea, an auxiliary model based basis pursuit de-noising iterative algorithm is presented. The parameters are estimated by solving a quadratic program, and the unavailable terms in the information vector are updated by the auxiliary model outputs iteratively. The time-delays are estimated according to the sparse structure of the parameter vector. The proposed method can obtain effective estimates of the parameters and time-delays from few sampled data. The simulation results illustrate the effectiveness of the proposed algorithm.

A fast online multivariable identification method for greenhouse environment control problems

Abstract Growing and pruning radial basis function (GAP-RBF) is extended for identification and control of multivariable nonlinear systems in this work. The proposed MGAP-RBF algorithm utilizes a sliding data window in the growing criterion and limits the number of hidden neurons by introducing a soft constraint in the pruning strategy to reduce the effect of disturbance and to improve learning speed, respectively. The performance of the proposed method is tested through some benchmark problems, and the results show that the proposed method can gain faster speed than the original GAP-RBF method and Ran algorithm, and more importantly, it can obtain an overwhelming advantages especially for some large-scale data sets with some complex attributes. Finally, the proposed method is applied to online PID tuning on a greenhouse environment control process. Simulation results show the proposed MGAP-RBF algorithm has better performance than the traditional RBF method and the original GAP-RBF method, in particular, it is faster and provides a more compact network with reduced computational complexity than the original GAP-RBF method.

Identification of hydraulic resistance parameters in hydraulic network model

The main purpose of the work is to develop and analyze new identification algorithm for multivariate multi-connected implicit system. Computational experiments and nonparametric statistics are implemented. The result of the work is a qualitatively new identification and output forecasting algorithm for multivariate systems. Based on the proposed algorithm a new class of generalized multivariate implicit nonparametric models is suggested. The significance of the research is subject to the fact that the majority of complex technical objects is usually described by large-scale nonlinear systems of equations up to input and output variables. Even if random effects in such models could be neglected a procedure of numerical solving the equation systems were either unstable or it would last too long to be implemented in forecasting of continuous process in the controlled object. Any delay in model calculation can also impact negatively on real-time control procedure. Using the proposed approach one can substitute solving the equation by estimation of the solution based on sample including measurements of input and output variables. Moreover, compared to counterparts, using the proposed approach it is possible to develop a single model for a range of input effects as it is presented in the research. Modelling and identification of multivariate systems is one of the most urgent tasks. Nowadays the development modelling methods does not keep up with the continuous and unlimited increase in the volume of information. To solve this problem, the authors proposed a new approach to constructing models of multidimensional systems. The scientific novelty of the article is as follows. A new modification of the nonparametric algorithm for identification of multidimensional systems has been proposed and tested. It makes possible to improve the accuracy and speed of computations.

Input-Output pairs detection in a distillation column operating in closed-loop

The detection of no-model input-output (IO) pairs is important because it can speed up the multivariable system identification process, since all the pairs with null transfer functions are previously discarded and it can also improve the identified model quality and so improve the performance of model based controllers. In the available literature, the methods focus just on the open-loop case, since in this case there is not the effect of the controller forcing the main diagonal in the transfer matrix to one and all other terms to zero. In this paper, a modification of a previous method that is able to detect no-model IO pairs in closed-loop systems is presented. Tests are performed using the traditional methods and the proposed one to show its effectiveness.

Non-parametric identification of multivariable systems: A local rational modeling approach with application to a vibration isolation benchmark

Abstract Frequency response function (FRF) identification is often used as a basis for control systems design and as a starting point for subsequent parametric system identification. The aim of this paper is to develop a multiple-input multiple-output (MIMO) local parametric modeling approach for FRF identification of lightly damped mechanical systems with improved speed and accuracy. The proposed method is based on local rational models, which can efficiently handle the lightly-damped resonant dynamics. A key aspect herein is the freedom in the multivariable rational model parametrizations. Several choices for such multivariable rational model parametrizations are proposed and investigated. For systems with many inputs and outputs the required number of model parameters can rapidly increase, adversely affecting the performance of the local modeling approach. Therefore, low-order model structures are investigated. The structure of these low-order parametrizations leads to an undesired directionality in the identification problem. To address this, an iterative local rational modeling algorithm is proposed. As a special case recently developed SISO algorithms are recovered. The proposed approach is successfully demonstrated on simulations and on an active vibration isolation system benchmark, confirming good performance of the method using significantly less parameters compared with alternative approaches.

A Novel Networked Online Recursive Identification Method for Multivariable Systems With Incomplete Measurement Information

Network-based identification of multivariable systems plays a key role in future smart manufacturing systems in achieving the goals of industry 4.0. The incomplete information caused by network traffic congestion or cyber attacks in the networked environment will inevitably deteriorate the performance of system identification, and in the extreme cases, it will cause nonconvergence of the identifier. Unlike the traditional recursive least-squares algorithms based on the complete data, this paper investigates a novel networked online recursive identification method for multivariable systems with incomplete information. In this new algorithm, the characteristics of data packet dropouts are first formulated as a Bernoulli process, and the lost data are compensated by an auxiliary model. A new information set including networked parameters is then constructed, and the corresponding networked online identification algorithm for multivariable systems is proposed. The proposed algorithm can overcome the negative effect of data packet losses on the identification performance and can be updated recursively. Furthermore, using the Lyapunov and martingale methods, the convergence rate of the proposed algorithm as well as its computational complexity is analyzed in detail. Simulation examples confirm the feasibility and efficiency of the proposed method.

Detection of no-model input-output pairs in closed-loop systems

The detection of no-model input-output (IO) pairs is important because it can speed up the multivariable system identification process, since all the pairs with null transfer functions are previously discarded and it can also improve the identified model quality, thus improving the performance of model based controllers. In the available literature, the methods focus just on the open-loop case, since in this case there is not the effect of the controller forcing the main diagonal in the transfer matrix to one and all the other terms to zero. In this paper, a modification of a previous method able to detect no-model IO pairs in open-loop systems is presented, but adapted to perform this duty in closed-loop systems. Tests are performed by using the traditional methods and the proposed one to show its effectiveness.

Matchable-Observable Linear Models and Direct Filter Tuning: An Approach to Multivariable Identification

Identification of linear time-invariant multivariable systems can best be understood as comprising three separate problems: selection of system model structure, filter design, and parameter estimation itself. Approaching the first using matchable-observable models originally developed in the adaptive control literature and the second via direct or derivative-free optimization, effective least-squares algorithms can be used for parameter estimation. The accuracy, robustness and moderate computational demands of the methods proposed are demonstrated via simulations with randomly generated models and applied to identification using real process data. The results obtained are comparable or superior to the best results obtained using standard implementations of the algorithms described in the literature.

Multivariate soft repulsive system identification for constructing rule-based classification systems: Application to trauma clinical data

Rule-based classification systems constructed upon linguistic terms in the antecedent and consequent of the rules lack sufficient generalization capabilities. This paper proposes a new multivariate fuzzy system identification algorithm to design binary rule-based classification structures through making use of the repulsive forces between the cluster prototypes of different class labels. This approach is coupled with the potential discrimination power of each dimension in the feature space to increase the generalization potential. To address this issue, first the multivariate variant of a newly proposed soft clustering algorithm along with its mathematical foundations is proposed. Next, the discriminatory power of each individual feature is computed, using the multivariate membership values in the proposed clustering algorithm to achieve the most accurate firing degree in each rule. The main advantage of this method is to handle unbalanced datasets yielding superior true positive measure while keeping the false positive rate low enough to avoid the natural bias toward class labels containing larger number of training samples. To validate the proposed approaches, a series of numerical experiments on publicly available datasets and a real clinical dataset collected by our team were conducted. Simulation results demonstrated achievement of the primary goals of this research.

Adaptive design of experiments for model order estimation in subspace identification

The first step in subspace methods for identification of multivariable systems is the estimation of the order of the model to be identified. Model order estimation is especially difficult for ill-conditioned systems. In previous work we showed heuristically that appropriately designed experiments with rotated PRBS inputs greatly facilitate model order estimation, hence overall model accuracy. However, design of such experiments depends on the very system to be identified. To overcome that difficulty, in this paper we propose an adaptive design of experiments. The proposed approach follows rigorous justification of the need for rotated PRBS inputs, and is tested through computer simulations on two case studies involving a high-purity distillation column and a fluidized catalytic cracking unit. Comparisons of the approach to open- and closed-loop alternatives are presented, and suggestions for further development are made.

Simultaneous structure and parameter identification of multivariate systems by matrix decomposition

Structure determination and parameter identification of multivariate systems are crucial but rather difficult issues in system identification. Due to the explosive growth of process data along with the scale increase of industrial processes, directional links between variables of such complex processes are often undistinguishable, which is indispensable to model structure determination but is often assumed to be known beforehand in most identification methods. In this article, a new modelling approach is developed to simultaneously estimate the model parameters and structures (including model orders as well as the directional links between different process variables) of multivariate systems. A vector auto-regressive (VAR) form is utilized as the model formulation in this algorithm. The key technique lies in constructing an interleaved information matrix with respect to a multiple model structure formulated for the VAR representation. Then by utilizing the upper diagonal factorization, all the parameter estimates of all path models with orders from zero to m, as well as the corresponding cost function values, can be obtained simultaneously. The effectiveness of the proposed method is demonstrated via a numerical example and a distillation column system.

Hierarchical multi-innovation extended stochastic gradient algorithms for input nonlinear multivariable OEMA systems by the key-term separation principle

This paper focuses on the identification of input nonlinear multivariable systems (i.e., Hammerstein multi-input multi-output nonlinear systems) described by output-error moving average models. Based on the key-term separation principle, we separate a proper key term in the nonlinear system and transform a complex nonlinear optimization problem into a pseudo-linear optimization problem which does not involve the products of the parameters between the linear parts and the nonlinear parts. Thus, a hierarchical extended stochastic gradient (H-ESG) algorithm is given and a hierarchical multi-innovation extended stochastic gradient (H-MI-ESG) algorithm is derived for the nonlinear systems. The proposed H-MI-ESG algorithm is an extension of the H-ESG algorithms. Compared with the over-parameterization-based least-squares identification algorithm, the H-ESG and H-MI-ESG algorithms have high computational efficiency. The simulation results show the effectiveness of the proposed algorithms.

Identifiability of dynamic networks with part of the nodes noise-free

In dynamic network identification a major goal is to uniquely identify the topology and dynamic links between the measured node variables. It is common practice to assume that process noises affect every output in multivariable system identification, and every node in dynamic networks with a full rank noise process. For many practical situations this assumption might be overly strong. This leads to the question of how to handle situations where the process noise is not full rank, i.e. when the number of white noise processes driving the network is strictly smaller than the number of nodes. In this paper a first step towards answering this question is taken by addressing the case of a dynamic network where some nodes are noise-free, and others are disturbed with a (correlated) process noise. In this situation the predictor filters that generate the one-step-ahead prediction of the node signals are non-unique, and the appropriate identification criterion leads to a constrained optimization problem. It is assessed when it is possible to distinguish between models on the basis of this criterion, leading to new notions of network identifiability. It appears that a sufficient condition for network identifiability is that every node signal in the network is excited by an external excitation signal or a process noise signal that is uncorrelated with other node excitations.

Real-time dynamic process control loop identification, tuning and optimization software

In today’s globally competitive marketplace, industrial plants are looking at new ways to increase plant efficiency, production rates, safety and reliability. Engineer education, training and plant optimization play a key role in satisfying technological, economical and environmental constraints. Furthermore, control system optimization is the basis for system improvement and advanced process control (APC) implementation.Only a small minority of plants use modern software for controller tuning, simulation, APC or optimization. The reasons are absence of engineering knowledge, unavailability of practical and robust process control software tools for system identification, simulation and parameter optimization and running plants conservatively due to fear of causing shutdowns and plant problems.This paper presents a process control simulator and loop optimizer applied to a temperature control application. This paper also illustrates the application of software for quick and easy multivariable closed-loop system identification using data from a plant’s historian. Such software can tremendously help to improve control education of students and plant personnel.

Evaluation of Experiment Designs for MIMO Identification by Cross-Validation

Guidelines for design of input perturbations for identification of multivariable systems are given. The focus is on control-oriented identification, but for comparison some general-purpose designs are also considered. The information needed for design of input perturbations such as double rectangular pulses, pseudo-random binary sequences, and multi-sinusoidal signals can be obtained from a simple step test. Such a test also gives information about the directionality properties of the system. This information can be used to design control-oriented experiments as shown in the paper. The design techniques are illustrated by realistic simulations of a moderately ill-conditioned 3×3 system. The identified models, and thus the experiment designs, are evaluated by cross-validations. According to this evaluation, the directional input designs are superior to standard input designs for identification of MIMO systems.

Auxiliary model-based interval-varying multi-innovation least squares identification for multivariable OE-like systems with scarce measurements

The identification problem of multivariable OE-like systems with scarce measurements is considered in this paper. By replacing the unknown inner variables in the information matrix with the outputs of the auxiliary model and by expanding the scalar innovation to an innovation vector, an auxiliary model-based multi-innovation least squares (AM-MILS) algorithm is proposed. In order to deal with the scarce measurement pattern, the algorithm takes the form of interval-varying recursive computation to skip the unavailable measurements including outliers. The introduction of the multi-innovation concept improves the parameter estimation accuracy and makes the identification algorithm more efficient. The convergence analysis shows that for the proposed algorithm, the parameter estimates can converge to their true values in the scarce output measurement pattern. Illustrative examples are given to demonstrate the effectiveness and accuracy of the proposed method.

Iterative identification methods for input nonlinear multivariable systems using the key-term separation principle

Identification for input nonlinear multivariable systems lies in that there exist the products of the parameters of the nonlinear block and the linear block. By means of the key-term separation principle, a subsystem least squares based iterative algorithm and a subsystem gradient based iterative algorithm are proposed for input nonlinear systems described by controlled autoregressive moving average models. Finally, the proposed methods are tested using numerical examples.

Multi-Objective Robust Active Vibration Control of an Arbitrary Thick Piezolaminated Beam

A multi-objective mixed / robust output feedback control synthesis with additional regional pole placement constraints in a linear matrix inequalities (LMI) framework is adopted for active vibration suppression of a simply supported, arbitrary thick, piezolaminated beam with continuously integrated sensor and actuator layers, in the face of high frequency unmodeled dynamics (residual uncertainties) and external disturbance. The structural formulation is based on a spatial state-space approach using the exact linear two-dimensional piezoelasticity theory and involving local/global transfer matrices. To assist control system design, subspace-based multivariable system identification is carried out by using the first four modes in the frequency range of 0–4000 rad/sec for control purpose, while the remaining high frequency (residual) modes in the control bandwidth are left as the uncertainty of modeling. The dynamic performance of vibration control system is demonstrated in both frequency and time domains for a three-layered sandwich beam including three pairs of piezoelectric actuator/sensor (Ba2NaNb5O15/PZT4) segments asymmetrically collocated on both sides of an orthotropic core for two different types of loading (i.e., impulsive load and random disturbance). The accuracy of dynamic analysis is established with the aid of a commercial finite element package and the data available in the literature.

Modeling and Synchronous Control of Dual Mechanically Coupled Linear Servo System

This paper presents a system modeling technique for a high-speed gantry-type machine tool driven by linear motors. One feed axis of the investigated machine tool is driven by the joint thrust from two parallel linear motors. These two parallel motors are coupled mechanically to form the Y-axis while another standalone motor fixed to a support forms the X-axis. The components in the X-axis, which is treated as the mechanical coupling, are carried by the slides of the Y-axis motors. This configuration is applied to improve the dynamic stiffness of the system and operation speed/acceleration. However, the precise synchronous control of the two parallel and coupled motors would be the major challenge. To overcome this challenge, a multivariable system identification method is developed in this paper. This method is used to construct an accurate system mathematical model for the target coupled system. A synchronous control scheme is then applied to the model obtained using the proposed technique. The performance of the system is experimentally verified with a high-speed S-curve motion profile. The results substantiate the constructed system model and demonstrate the effectiveness of the control scheme.

Economical Input Design for Identification of Multivariate Systems

In this article, we propose an optimization based formulation for design of optimal inputs for multivariate systems. A well designed identification experiment can generate good quality models while incurring significant costs. In a typical process plant, the nominal policy is to operate the plant at or near constraints to achieve economic benefits. In this work, we quantify the cost of the experiment carried out on such systems in terms of the deviation from the nominal operational policy. The objective is to minimize the cost incurred during the experiment without violating the operational constraints while guaranteeing model quality. The proposed economics based optimization formulation is non-convex and hence we present a twostep iterative algorithm. The inputs are realized as white noise sequence filtered through an M-tap multivariate FIR filter. The filter coeffcients are obtained by the spectral factorization. A detailed simulation study is presented to illustrate the proposed approach.