Achievable PID performance using sums of squares programming

Data driven control loop performance assessment techniques assume that the data being analyzed correspond to single plant-controller configuration. However, in an industrial setting where processes are affected due to the presence of feedstock variability and drifts, the plant-controller configuration changes with time. Also, user-defined benchmarking of control loops (common in industrial plants) requires that the data corresponding to optimal operation of the controller be known. However, such information might not be available beforehand in which case it is necessary to extract the same from routine plant operating data. A technique that addresses these fundamental requirements for ensuring reliable performance assessment is proposed. The proposed technique performs a recursive binary segmentation of the data and makes use of the fact that changes in controller settings translate to variations in plant output for identifying regions corresponding to single plant-controller configurations. The statistical properties of the data in each such window are then compared with the theoretically expected behavior to extract the data corresponding to optimal configuration. This approach has been applied on: (1) raw plant output, (2) Hurst exponent, and (3) minimum variance index of the process data. Simulation examples demonstrate the applicability of proposed approach in industrial settings. A comparison of the three routes is provided with regard to the amount of data needed and the efficacy achieved. Key results are emphasized and a framework for applying this technique is described. This tool is of significance to industries interested in an automated analysis of large scale control loop data for multiple process variables that is otherwise left unutilized.

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“…The next two systems are univariate systems taken from Ref. . System 3 is described as follows (

\nabla = 1 - q^{- 1}

)

\begin{matrix} T = \frac{q^{- 6}}{1 - 0.8 q^{- 1}} \\ N = \frac{1 - 0.2 q^{- 1}}{\nabla (1 + 0.4 q^{- 1}) (1 - 0.3 q^{- 1}) (1 - 0.5 q^{- 1})} \end{matrix}

while the last system (System 4) is described as follows

T = \frac{q^{- 6}}{1 - 0.8 q^{- 1}}

N = \frac{1 + 0.6 q^{- 1}}{\nabla (1 - 0.5 q^{- 1}) (1 - 0.6 q^{- 1}) (1 + 0.7 q^{- 1})}

…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The notation followed in Ref. , that is,

Q = \frac{a + b q^{- 1}}{\nabla}

has been used here where

\nabla

is the shorthand notation for

1 - q^{- 1}

. The outputs have been concatenated and plotted in Figure with settings listed in Table .…”

Section: Background and Motivationmentioning

confidence: 99%

A novel framework for integrating data mining with control loop performance assessment

2015

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“…and the F i and g i are computed according to (21). The value of the unknown controller parameters are found by,…”

Section: Lqg Cpi For Decentralized Restricted Structure Controllersmentioning

confidence: 99%

“…(e) Compute the frequency-dependent polynomials f r (20). (f) Assemble the matrices ¹F k ; g k º from (21). (g) Compute parameters of RS PID controllers x k as follows:…”

Section: Define the Following Initial Valuesmentioning

confidence: 99%

“…This alternating between two convex problems is similar to the approach used elsewhere in the design of low order optimal controllers [7][8][9][10][11][12][13][14][15]. Other references which have worked on various aspects of CPA of fixed structure PID controllers include [16][17][18][19][20][21][22].When one is able to impose a specific structure onto the controller, such as the PID, then the 'choice' of the control structure becomes a new additional design parameter. For a SISO system, the number of choices might be limited to a few (e.g., PI, PID, and PD).…”

mentioning

confidence: 99%

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Design and assessment of variable-structure LQG PID multivariable controllers

Mousavi

Nobakhti

2016

Optim. Control Appl. Meth.

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Summary Control Performance Assessment (CPA) and tuning of PID controllers are studied in this paper. We propose a framework for systematic analysis of the tradeoff between the structural complexity of the controller and its performance. As the measure of the controller performance, an LQG based index is used. The problem is augmented with an additional term which forces sparsity on the complexity of a decentralized PID controller. The desired complexity is controlled via a weighting parameter which determines the cost of each additional element (i.e., P, I, and D terms). The result is a decentralized multivariable PID controller in which the complexity of each loop controller is optimized such that the desired LQG Performance Index is achieved with the lowest controller complexity. For larger multivariable systems, this will translate into a substantially reduced set of controller parameters. Copyright © 2016 John Wiley & Sons, Ltd.

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Determining the state of a process control system: Current trends and future challenges

Shardt

Zhao

et al. 2011

Can J Chem Eng

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In many industrial plants, multiple, interconnected control loops are common. Their maintenance and improvement requires detailed controller performance assessment to determine not only whether they are behaving well, but also to determine the potential cause of any observed problems. Techniques for performance assessment can be divided into two broad categories (1) performance assessment of regulatory control loops; and (2) performance assessment of supervisory control loops that evaluate the economic performance of advanced control strategies, such as model predictive control (MPC). A comprehensive review of the literature on the industrial applications of performance assessment, as well as some of the currently available software, is also presented. © 2011 Canadian Society for Chemical Engineering

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Achievable PID performance using sums of squares programming

Cited by 61 publications

References 11 publications

A novel framework for integrating data mining with control loop performance assessment

A novel framework for integrating data mining with control loop performance assessment

Design and assessment of variable-structure LQG PID multivariable controllers

Determining the state of a process control system: Current trends and future challenges

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