The delay estimation problem for open-loop single-input single-output (SISO) systems has been widely studied to the effect that well-established methods are available now. On the other hand, the delay estimation for MIMO systems remains a challenge to-date due to the presence of interactions among input and output variables. In this work, a method based on partial coherence functions (PCF) and Hilbert transform (HT) relation is presented to estimate time-delay for MIMO systems. The key step in the proposed method involves decoupling interactions using the PCF. The HT relation provides a platform for obtaining robust estimates of the time-delay by exploiting the causal nature of the relationship. The highlight of this method in contrast to conventional correlation-based techniques is that the problem formulation explicitly incorporates the delay parameter. In addition, the proposed method uses frequency-domain analysis which allows one to take into effects of noise in a straightforward way. Under closed-loop conditions, time-delay is estimated by introducing a dither signal at the controller output. Results from simulation and experimental studies are presented to demonstrate the effectiveness and potential of this method. © 2009 Elsevier Ltd. All rights reserved.

Arun K. Tangirala

Department Of Chemical Engineering

Closed-loop

CONTROLLER OUTPUTS

CORRELATION-BASED TECHNIQUES

DELAY ESTIMATION

Delay parameters

DITHER SIGNALS

Experimental studies

Hilbert transform

HILBERT TRANSFORM RELATION

Input and outputs

instrumentation

MULTIVARIATE SYSTEMS

Open loops

PARTIAL COHERENCE

Problem formulation

ROBUST ESTIMATE

Single input single output systems

Time delay estimation

COHERENT LIGHT

Decoding

Delay control systems

Estimation

Frequency domain analysis

Instruments

Mathematical transformations

MIMO systems

Multiplexing

Process control

Time delay

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Chemical Engineering Science

The extent of approximation in modelling a given process, characterized by the model-plant mismatch (MPM), amongst other factors, critically determines the performance of a model-based control scheme. It is necessary therefore to carry out model maintenance and correction on a regular basis. However, a complete re-identification is usually a costly exercise. Therefore, it is highly desirable to precisely determine the specific elements that are in mismatch and re-identify only those parameters. In the recent times, the plant-model ratio (PMR) was proposed as an effective metric for diagnosing MPM in single-input single-output (SISO) systems from closed loop data. The PMR facilitates unique detection of mismatch in gain, dynamics and delay. A straightforward application of PMR to multivariable closed-loop systems is challenging primarily due to the confounding effects of other inputs and loop-to-loop interactions under closed-loop conditions. Furthermore, the metric requires high-frequency excitation for identification of delay mismatch. In this work, we first present a method to overcome the latter requirement using Hilbert transform relation and partial cross-spectral densities. Subsequently, we present the key contribution of this work, that of generalizing the PMR approach to multivariable control systems. Two threshold-based hypothesis tests are presented for diagnosing mismatch in gain and dynamics. Three simulation case studies are presented to demonstrate the efficacy of the proposed method. © 2018 Elsevier Ltd

Journal of Process Control

Detection and diagnosis of model-plant mismatch in multivariable model-based control schemes

System identification (SI) using small samples is a problem of interest in several applications. However, parameter estimation in these situations is a challenge since classical identification techniques (based on prediction-error methods) are guaranteed to be efficient and consistent only under asymptotic (large sample) conditions. In addition these techniques need the knowledge of delay and order of the process prior to estimation of parameters which is difficult to obtain especially when dealing with multi-input multi-output (MIMO) systems. This paper presents a method for identifying MIMO models which have auto-regressive with exogenous (ARX) input structure without the knowledge of delay and order of the process, using the ideas of sparse matrix optimization (SMO). The formulation of the proposed method consists of a constrained one norm minimization on the parameter matrix to induce sparsity. Three case studies, including one on real time data, are discussed to present the efficacy of the proposed method. Results show that the estimates obtained using the proposed algorithm have lower variance than the traditional least square estimates. © 2017 IEEE.

2017 Indian Control Conference, ICC 2017 - Proceedings

Identification of MIMO ARX models from small samples using sparse matrix optimization

System identification (SI), especially from small samples, is a challenging problem and of interest in several applications. Standard prediction-error minimization methods (PEM), under these conditions, generally result in estimates with higher variance. Moreover, in the identification of parametric models, one often needs prior knowledge of the input-output delay, obtaining estimates of which, is not possible using classical methods when the delay is either comparable or greater than the sample size. In this work, we develop a compressed sensing (CS)-based method for identifying sparse equation-error models that includes both auto-regressive eXogenous (ARX) and AR moving average eXogenous (ARMAX) structures with large delays, small orders and small delays with large orders, but with missing coefficients. The outcome is an iterative basis pursuit de noising (IBPDN) algorithm for solving non-linear CS problems. In addition, we propose a semi-rigorous method to lower the mutual coherence of the regressor matrix so as to obtain lower variance parameter estimates with the CS techniques. Errors in parameter estimates are computed using the bootstrapping method. Simulation studies on three diverse examples are presented to demonstrate the efficacy of the proposed methodology. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Fulltext

IFAC-PapersOnLine

Identification of equation error models from small samples using compressed sensing techniques

Performance of any model-based control scheme depends on the quality of model. When these schemes deliver poor loop performance due to model-plant mismatch (MPM), a detection of the same needs to be in place. A recently introduced plant model ratio (PMR) not only detects MPM but also facilitates a unique identification of the source of mismatch, namely, gain, dynamics (time constant) and delay mismatches. The prime objective of this work is to improve the PMR approach in a few key aspects, namely, estimation and experimental effort, and assessment procedure by taking a fresh perspective of PMR and conducting a detailed theoretical study of its signatures. A rigorous assessment procedure based on the theoretical properties of PMR is devised. Three threshold-based hypotheses tests are proposed for significance testing of PMR. A key contribution of this work is the design of set-point with minimal excitation for diagnosis of MPM, based on the features of PMR. The revised methodology is demonstrated and compared with the existing method through simulation examples. The study also demonstrates the potential of the proposed method in serving as a prelude to full/partial model re-identification. © 2014 Elsevier Ltd. All rights reserved.

Improved methodology and set-point design for diagnosis of model-plant mismatch in control loops using plant-model ratio

Model-plant mismatch is a crucial factor that influences the performance of a closed-loop system. A new approach is proposed for the diagnosis of poor control loop performance due to model-plant mismatch (MPM) in the internal model control framework. In particular, the objective is to identify the mismatch in specific components of a transfer function model, namely, the gain, time-constant, and delay from closed-loop operating data. A new quantity G p/Gm, called the plant model ratio (PMR) in the frequency domain is introduced as a measure of model-plant mismatch. It is shown that there exists a unique signature in PMR for each combination of mismatch in model parameters, which is the key step in the proposed method. A method to estimate the PMR from closed-loop operating data is provided. Theoretical and practical aspects of the mapping between the type of MPM and the proposed PMR are presented. Simulation studies demonstrate the effectiveness of the proposed method. © 2010 American Chemical Society.

Industrial and Engineering Chemistry Research

Diagnosis of poor control loop performance due to model-plant mismatch

Performance assessment of MIMO systems based on I/O delay information

This work is aimed at the development of a state observer (steady state Kalman filter) for a multivariable system with unknown time delays, which is subjected to unmeasured disturbances. To design such a filter, we explore the feasibility of capturing system dynamics using generalized orthonormal basis filters (GOBF). A two step identification procedure is proposed by exploiting the fact that the GOBF based models have output error structure. The deterministic component of the model is identified in the first step and used to compute a residual signal. In the second step, a filter that whitens the residuals is estimated using GOBF and combined with the deterministic component. A minimal order state realization of the innovation form of the state model is then generated from this high order model using realization based sub-space based state space (4SID) identification algorithm. When time delays are not known a-priori, the similarity between GOBF and Pade approximation is used to estimates time delay matrix directly from multivariate data. The efficacy of the proposed modeling technique is demonstrated by carrying out simulation studies on the benchmark Shell control problem and experimental evaluation on a stirred tank heater (STH) system. From the analysis of simulation and experimental results, it can be inferred that the proposed approach produces fairly accurate estimates of the time delay matrix and the deterministic and stochastic components of the dynamic model. © 2005 Elsevier Ltd. All rights reserved.

From data to diagnosis and control using generalized orthonormal basis filters. Part I: Development of state observers

Journal of Neuroscience Methods

Delay estimation for cortico-peripheral relations

Industrial & Engineering Chemistry Research

Robust Control of a Multivariable Experimental Four-Tank System

The unitary interactor matrix and its estimation using closed-loop data

Time-delay estimation in multivariate systems using Hilbert transform relation and partial coherence functions

Journal	Chemical Engineering Science
ISSN	00092509
Open Access	No