This work presents a novel method for assessing and quantifying the level of interactions in multivariable control systems in a hierarchical manner. The proposed metrics are based on the total directed (causal) power transfer between a pair of variables, constructed from a jointly linear stationary representation of the process. Three prime features of these metrics, specifically, (i) the ease of interpretation and versatility in accommodating different controller structures and operating conditions, (ii) the ability to use both first-principles linearized and data-driven (empirical) models, and (iii) the means for quantifying and evaluating the suitability of a decentralized versus a centralized control scheme, make them highly practical and valuable in the design and assessment of multivariable control schemes. An important outcome of this work is also an operator-friendly visual tool for inspection of interactions in various loops that can be generated for different tuning methods and controller configurations. Simulation studies of four different benchmark processes are presented to demonstrate the efficacy of the proposed method. © 2017 American Chemical Society.

Arun K. Tangirala

Department Of Chemical Engineering

Control system analysis

Control systems

Controllers

Energy transfer

hierarchical systems

Centralized control

Controller structures

DIRECTIONAL ANALYSIS

First principles

Multivariable control

Operating condition

POWER TRANSFERS

Simulation studies

Multivariable control systems

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

Industrial and Engineering Chemistry Research

Model structure selection is an important step in high-dimensional time-series modelling. Traditionally AIC and BIC have been used for this purpose, however, only post model estimation. On the other hand, modern approaches use penalized regression methods, but the optimization is in a user-specified model class. In this work, we propose a pre-estimation approach based on two novel correlation functions, namely, the scalar autocorrelation function (SACF) and the scalar inverse autocorrelation function (SIACF) for identifying the appropriate model class among the vector autoregressive (VAR), vector moving average (VMA), and mixed (VARMA) classes. In addition, these scalar functions theoretically provide the exact order of VAR and VMA processes, and are computationally feather light even for high-dimensional series. The proposed functions are obtained through two linear constructs of the given multivariate process with a lagged-correlation equivalence constraint. The key benefit is that only two correlation functions need to be examined as against the standard M2 correlation and M2 inverse (or partial) correlation plots for an M-dimensional process. This benefit extends to conducting whiteness test in multivariate time-series modelling and is particularly pronounced under small sample conditions, wherein parsimony, structure and class of the identified model is crucial in achieving efficient estimates. Theoretical proofs and case studies are presented to establish the properties and to demonstrate the utility of proposed correlation functions. © 2019 ISA

ISA Transactions

Scalar correlation functions for model structure selection in high-dimensional time-series modelling

Multivariable dynamical processes are characterized by complex cause and effect relationships among variables. Reconstruction of these causal connections from data, especially based on the concept of Granger causality (GC), has attracted significant attention in process engineering with applications to interaction assessment, topology reconstruction, and fault detection. The standard practice for reconstruction of GC networks has been along the parametric route that deploys vector autoregressive (VAR) models but without giving due importance to the structural characteristics of data generating process (DGP). In this work, we first demonstrate that the presence of a mismatch between model structure and DGP leads to biased and/or inefficient estimates of causality measures and, hence, the strengths (weights) of causal connections. This issue is further aggravated for small sample sizes wherein additionally spurious causal relationships are detected. In this respect, we present, second, a systematic methodology for efficient reconstruction of weighted GC networks for stationary multivariable linear dynamical processes. This methodology uses a combination of sparse optimization and recently introduced scalar correlation functions to select the most appropriate and parsimonious model structure. Applications to synthetic and environmental processes are presented to demonstrate the efficacy of the proposed approach. © 2019 American Chemical Society.

Efficient Reconstruction of Granger-Causal Networks in Linear Multivariable Dynamical Processes

Multivariable control systems are continually challenged by the presence of interactions among control loops. The issue of interactions is even more pronounced in systems involving multiloop (decentralized) control schemes. This paper presents a novel method to assess the level of interactions in multivariable control systems. The proposed approach is based on the total directed energy transfer between a pair of variables. The merit of the method lies in its ease of interpretation and versatility in accommodating different controller structures and operating conditions. Further, the method can be applied for both theoretical (when a process model is known)as well as data-driven analysis (when operating data is available). Implementation on synthetic processes are illustrated to demonstrate the usefulness of the proposed approach. © 2014 IFAC.

IFAC Proceedings Volumes (IFAC-PapersOnline)

Interaction assessment in multivariable control systems through causality analysis

Interactions among control loops are a critical and challenging issue in the control of multivariable systems. The focus of this work is on the analysis and quantification of interactions in multiloop or decentralized control systems. Existing interaction measures suffer from one or more of the following limitations: (i) the lack of a direct connection to a performance metric, (ii) assumption of the availability of process models and (iii) the approximate and/or a heuristic nature of the approach to their development, resulting only in approximate indicators of interaction. This work presents an exact quantifier of interaction that arises out of a directional decomposition of the loop variance using methods of causality (directional) analysis in frequency-domain. The main result is that the spectrum of the filtered output can be decomposed into (i) an interaction-and-feedback invariant term and (ii) an interaction-dependent term. The associated filter can be derived from the closed-loop data and is related to the diagonal element of the multiloop sensitivity function. The invariant term for each output is the spectral density of that output when the corresponding loop is under open-loop conditions. It is further shown to be solely a function of the control pairing. Variance measures corresponding to the invariant and interaction terms are introduced. The utility of the measure is that it can be computed from closed loop data as well as from the process model. Applications to simulated systems and a real time distillation process are presented to demonstrate the theoretical ideas. © 2013 Elsevier Ltd. All rights reserved.

Automatica

Quantification of interaction in multiloop control systems using directed spectral decomposition

In this article, two methods of designing a centralized control system for multi-input, multi-output (MIMO) processes are presented. Centralized proportional-integral (PI) controllers are designed based on a direct synthesis method. The inverse of the process transfer function matrix in the direct synthesis method is approximated based on the relative gain array concept. The method is further improved by using a relative normalized gain array, and an equivalent transfer function for each element in the process transfer function matrix is derived for the closed-loop control system. The transpose of the effective transfer function is used to approximate the inverse of the process transfer function matrix. The simulation studies demonstrate the effectiveness of this method. The proposed centralized controllers reduce the interactions better than recently reported decentralized controllers do. A centralized controller designed based on a relative normalized gain array (RNGA) gives a better performance than a centralized controller designed based on a relative gain array (RGA). © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Centralized PI controllers for interacting multivariable processes by synthesis method

Identification and analysis of directed influences in multivariate systems is an important problem in many scientific areas. Recent studies in neuroscience have provided measures to determine the network structure of the process and to quantify the total effect in terms of energy transfer. These measures are based on joint stationary representations of a multivariate process using vector auto-regressive (VAR) models. A few important issues remain unaddressed though. The primary outcomes of this study are (i) a theoretical proof that the total coupling strength consists of three components, namely, the direct, indirect, and the interference produced by the direct and indirect effects, (ii) expressions to estimate/calculate these effects, and (iii) a result which shows that the well-known directed measure for linear systems, partial directed coherence (PDC) only aids in structure determination but does not provide a normalized measure of the direct energy transfer. Simulation case studies are shown to illustrate the theoretical results. © 2010 Springer-Verlag.

Journal	Data powered by TypesetIndustrial and Engineering Chemistry Research
Publisher	Data powered by TypesetAmerican Chemical Society
ISSN	08885885
Open Access	No