The impact of model approximation in multiparametric model predictive control

Katz, Justin; Burnak, Baris; Pistikopoulos, Efstratios N.

doi:10.1016/j.cherd.2018.09.034

Cited by 16 publications

(8 citation statements)

References 33 publications

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“…The high fidelity model in Equation 3 41 In this study, we use subspace identification techniques via the MATLAB System Identification Toolbox, which yields discrete time state space models in the following form.…”

Section: Model Approximationmentioning

confidence: 99%

“…Therefore, we develop an approximate model that mimics the dynamic behavior outlined by the high fidelity model. Numerous approximation techniques have been implemented to develop reduced order models to derive explicit MPC, such as subspace identification, Box–Jenkins, Output Error, and Autoregressive Exogenous models 41 . In this study, we use subspace identification techniques via the MATLAB System Identification Toolbox, which yields discrete time state space models in the following form.

\begin{matrix} lefttrue \\ {boldx}_{k + 1} = A {boldx}_{k} + B {boldu}_{k} + C {boldd}_{k} \\ {\overset{y}{true}}_{k} = D {boldx}_{k} + E {boldu}_{k} + F {boldd}_{k} \end{matrix}

where

{\overset{false^}{boldy}}_{k}

is the predicted output at discrete time k .…”

Section: Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

Burnak

Pistikopoulos

2020

AIChE Journal

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Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed‐integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed‐loop implementation. We use multi‐parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base‐2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.

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Section: Model Approximationmentioning

confidence: 99%

\begin{matrix} lefttrue \\ {boldx}_{k + 1} = A {boldx}_{k} + B {boldu}_{k} + C {boldd}_{k} \\ {\overset{y}{true}}_{k} = D {boldx}_{k} + E {boldu}_{k} + F {boldd}_{k} \end{matrix}

where

{\overset{false^}{boldy}}_{k}

is the predicted output at discrete time k .…”

Section: Problem Formulationmentioning

confidence: 99%

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

Burnak

Pistikopoulos

2020

AIChE Journal

Self Cite

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“…Acquiring satisfactory closed-loop performance relies heavily on developing accurate approximate models. Katz et al 45 investigated the effects of approximating the high fidelity models by simpler models in the context of multiparametric programming, and introduced novel error metrics to evaluate open and closed-loop performances. In this work, we use the open and closed loop metrics introduced in Katz et al to increase the confidence of the developed approximate models.…”

Section: Parametric Fault-tolerant Control Frameworkmentioning

confidence: 99%

Integrated Data-Driven Process Monitoring and Explicit Fault-Tolerant Multiparametric Control

Onel

Burnak

Pistikopoulos

2019

Ind. Eng. Chem. Res.

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We propose a novel active fault-tolerant control strategy that combines machine learning based process monitoring and explicit/multiparametric model predictive control (mp-MPC). The strategy features (i) data-driven fault detection and diagnosis models by using the support vector machine (SVM) algorithm, (ii) ranking via a nonlinear, kernel-dependent, SVM-based feature selection algorithm, (iii) data-driven regression models for fault magnitude estimation via the random forest algorithm, and (iv) a parametric optimization and control (PAROC) framework for the design of the explicit/multiparametric model predictive controller. The resulting explicit control strategies correspond to affine functions of the system states and the magnitude of the detected fault. A semibatch process, an example for penicillin production, is presented to demonstrate how the proposed framework ensures smart operation for which rapid switches between a priori computed explicit control action strategies are enabled by continuous process monitoring information.

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“…effective way to reduce computational burden and improve the applicability of advanced control frameworks for large-scale processes. [8,9] It aims to approximate the original system with an appropriately simplified model while capturing the essential dynamics. Popular methods for model approximation can be broadly classified into three categories: model reduction based on firstprinciple models (e.g., proper orthogonal decomposition [POD]), [10] traditional data-based system identification (e.g., subspace identification), [14][15][16][17] and machine-learning-based model identification.…”

Section: Introductionmentioning

confidence: 99%

A comparative study of model approximation methods applied to economicMPC

Huang¹,

Liu²,

Liu

et al. 2022

Can J Chem Eng

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Economic model predictive control (EMPC) has attracted significant attention in recent years and is recognized as a promising advanced process control method for next‐generation smart manufacturing. It has the potential to not only improve economic performance but also significantly increase computational complexity. Model approximation has been a standard approach for reducing computational complexity in process control. In this work, we perform a study on three types of representative model approximation methods applied to EMPC, including model reduction based on available first‐principle models (e.g., proper orthogonal decomposition), system identification based on input–output data (e.g., subspace identification) that results in an explicitly expressed mathematical model, and neural networks based on input–output data. A representative algorithm from each model approximation method is considered. Two processes that are very different in dynamic nature and complexity were selected as benchmark processes for computational complexity and economic performance comparison, namely, an alkylation process and a wastewater treatment plant. The strengths and drawbacks of each method are summarized according to the simulation results, with future research direction regarding control‐oriented model approximation proposed at the end.

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The impact of model approximation in multiparametric model predictive control

Cited by 16 publications

References 33 publications

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

Integrated Data-Driven Process Monitoring and Explicit Fault-Tolerant Multiparametric Control

A comparative study of model approximation methods applied to economicMPC

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