Economic model predictive control of nonlinear process systems using empirical models

Alanqar, Anas; Ellis, Matthew J.; Christofides, Panagiotis D.

doi:10.1002/aic.14683

Cited by 61 publications

(62 citation statements)

References 45 publications

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“…The LEMPC formulation is similar to that derived in Ref. using an empirical model. The LEMPC optimization problem incorporating the PNLSS empirical model is

\min_{u \in S (Δ)} \int_{t_{k}}^{t_{k + N}} L_{e} (\tilde{x} (τ), u (τ)) d τ

s . t . \dot{\overset{x}{true}} (t) = A \tilde{x} + P_{z} (\tilde{x}) + B u

\tilde{x} (t_{k}) = x (t_{k})

u (t) \in U, \forall t \in [t_{k}, t_{k + N})

\hat{V} (\tilde{x} (t)) \leq {\overset{ρ}{true}}_{e}, \forall t \in [t_{k}, t_{k + N}), if x (t_{k}) \in Ω_{{\overset{ρ}{true}}_{e}}

\partial \hat{V} (x (t_{k}

…”

Section: Empc Using Well‐conditioned Nonlinear Modelsmentioning

confidence: 99%

“…The formulation of EMPC to be used in this work is LEMPC, a receding horizon EMPC strategy that incorporates stability constraints based on an explicit stabilizing controller for a model of the nominal process. LEMPC uses a model of the process dynamics to predict the evolution of the process states with time.…”

Section: Empc Using Well‐conditioned Nonlinear Modelsmentioning

confidence: 99%

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On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

2015

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The focus of this work is on economic model predictive control (EMPC) that utilizes well-conditioned polynomial nonlinear state-space (PNLSS) models for processes with nonlinear dynamics. Specifically, the article initially addresses the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of PNLSS dynamic models which are well-conditioned over a broad region of process operation in the sense that they can be correctly integrated in real-time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state-space models identified via existing techniques. Working within the framework of PNLSS models, additional constraints are imposed in the identification procedure to ensure well-conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov-based EMPC (LEMPC) systems for nonlinear processes using the well-conditioned nonlinear models that can be readily implemented in real-time as the computational burden required to compute the control actions within the process sampling period is reduced. A stability analysis for this LEMPC design is provided that guarantees closed-loop stability of a process under certain conditions when an LEMPC based on a nonlinear empirical model is used. Finally, a classical chemical reactor example demonstrates both the system identification and LEMPC design techniques, and the significant advantages in terms of computation time reduction in LEMPC calculations when using the nonlinear empirical model.

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“…The LEMPC formulation is similar to that derived in Ref. using an empirical model. The LEMPC optimization problem incorporating the PNLSS empirical model is

\min_{u \in S (Δ)} \int_{t_{k}}^{t_{k + N}} L_{e} (\tilde{x} (τ), u (τ)) d τ

s . t . \dot{\overset{x}{true}} (t) = A \tilde{x} + P_{z} (\tilde{x}) + B u

\tilde{x} (t_{k}) = x (t_{k})

u (t) \in U, \forall t \in [t_{k}, t_{k + N})

\hat{V} (\tilde{x} (t)) \leq {\overset{ρ}{true}}_{e}, \forall t \in [t_{k}, t_{k + N}), if x (t_{k}) \in Ω_{{\overset{ρ}{true}}_{e}}

\partial \hat{V} (x (t_{k}

…”

Section: Empc Using Well‐conditioned Nonlinear Modelsmentioning

confidence: 99%

Section: Empc Using Well‐conditioned Nonlinear Modelsmentioning

confidence: 99%

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

2015

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“…Several prior works have developed LEMPC formulations including empirical models [43,44] when the model of Equation (1) is either unknown or undesirable for use (e.g., more computationally intensive than an empirical model). They have the following form:…”

Section: Lyapunov-based Economic Model Predictive Control With An Empmentioning

confidence: 99%

Responsive Economic Model Predictive Control for Next-Generation Manufacturing

Durand

2020

Mathematics

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There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance in the chemical process industries are anomalous conditions and the responses of operators and engineers to controller behavior. Enhancing responsiveness of an advanced control design known as economic model predictive control (EMPC) (which uses predictions of future process behavior to determine an economically optimal manner in which to operate a process) to unexpected conditions of these types would advance the move toward artificial intelligence properties for this controller beyond those which it has today and would provide new thoughts on interpretability and verification for the controller. This work provides theoretical studies which relate nonlinear systems considerations for EMPC to these higher-level concepts using two ideas for EMPC formulations motivated by specific situations related to self-modification of a control design after human perceptions of the process response are received and to controller handling of anomalies.

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“…Remark 1: For a rigorous stability analysis and additional simulations, the reader may refer to [1].…”

Section: Application To a Chemical Process Examplementioning

confidence: 99%

Economic model predictive control of nonlinear process systems using multiple empirical models

Alanqar

Ellis

Christofides

2015

2015 American Control Conference (ACC)

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Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first-principles or though system identification techniques. However, in industrial practice, it may be difficult in general to obtain an accurate first-principles model of the process. Motivated by this, in the present work, Lyapunov-based economic model predictive control (LEMPC) is designed with multiple linear empirical models. The different models are used to more accurately predict the behavior of a nonlinear system over a larger state-space region compared to using a single empirical linear model only. The LEMPC scheme is applied to a chemical process example to demonstrate its closed-loop stability and performance properties as well as significant computational advantages.

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Economic model predictive control of nonlinear process systems using empirical models

Cited by 61 publications

References 45 publications

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

Responsive Economic Model Predictive Control for Next-Generation Manufacturing

Economic model predictive control of nonlinear process systems using multiple empirical models

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