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.

Arun K. Tangirala

Department Of Chemical Engineering

Data processing

Dynamical systems

Energy transfer

Spectrum Analysis

CAUSALITY ANALYSIS

Controller structures

DATA-DRIVEN ANALYSIS

Frequency domains

Interaction

Operating condition

PROCESS MODELING

SYNTHETIC PROCESS

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

Interaction assessment in multivariable control systems through causality analysis

IFAC Proceedings Volumes (IFAC-PapersOnline)

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.

Industrial and Engineering Chemistry Research

Metrics for Interaction Assessment in Multivariable Control Systems Using Directional Analysis

Learning temporal causal relationships between time series is an important tool for the identification of causal network structures in linear dynamic systems from measurements. The main objective in network reconstruction is to identify the causal interactions between the variables and determine the connectivity strengths from time-series data. Among several recently introduced data-driven causality measures, partial directed coherence (PDC), directed partial correlation (DPC) and direct power transfer (DPT) have been shown to be effective in both identifying the causal interactions as well as quantifying the strength of connectivity. However, all the existing approaches assume that the observations are available at all time instants and fail to cater to the case of missing observations. This paper presents a method to reconstruct the causal graph from data with missing observations using sparse optimization (SPOPT) techniques. The method is particularly devised for jointly stationary multivariate processes that have vector autoregressive (VAR) structure representations. Demonstrations on different linear causal dynamic systems illustrate the efficacy of the proposed method with respect to the reconstruction of causal networks. © 2017 IEEE.

2017 4th International Conference on Control, Decision and Information Technologies, CoDIT 2017

Reconstruction of causal graphs for multivariate processes in the presence of missing data

Identification of network structure and quantifying the connectivity strengths in multivariate systems is an important problem in many scientific areas. Data-driven approach to network reconstruction based on causality measures is an emerging field of research in this respect. Among several recently introduced data-driven causality measures, the partial directed coherence (PDC) and direct power transfer (DPT) have been shown to be very effective for linear systems. While the PDC is useful in reconstructing the network, DPT has been proved to be effective in both identifying the network structure as well as quantifying the strength of connectivity. In this work, we study the problem of obtaining efficient estimates of network connectivity strengths, which has hitherto not been addressed in the literature. To this end, we study two different estimation methods for network connectivity strengths and demonstrate that the goodness of estimates depends on nature of the data generating process (DGP). In order to characterize the multivariate DGP, we introduce two statistics, namely, the vector-valued autocorrelation function (VACF) and the vector-valued partial autocorrelation function (VPACF), and estimators of the same. Our studies show that the parametric models used in estimating connectivity strengths should be commensurate with the dynamics of the process as characterized by the newly introduced VACF and VPACF. Simulation studies are presented under different scenarios to support our findings and the newly introduced measures. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Fulltext

IFAC-PapersOnLine

Estimation of network connectivity strengths in linear causal dynamic systems

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.

ISA Transactions

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.

Biological Cybernetics

Quantitative analysis of directional strengths in jointly stationary linear multivariate processes

Control Engineering Practice

Detection of control loop interactions and prioritization of control loop maintenance

Multi-loop PI controller design based on the direct synthesis for interacting multi-time delay processes

Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Publisher	IFAC Secretariat
ISSN	14746670
Open Access	No