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Two-stage dynamic real-time optimization framework using parameter-dependent differential dynamic programming

COMPUTERS & CHEMICAL ENGINEERING 2025年 192卷

作者： Jung, Hyein Kim, Jong Woo Lee, Jong Min Seoul Natl Univ Dept Chem & Biol Engn 1 Gwanak Ro Seoul 08826 South Korea Incheon Natl Univ Innovat Ctr Chem Engn Dept Energy & Chem Engn 119 Acad Ro Incheon 22012 South Korea

The purpose of chemical process control includes proactive adjustment of the operation to make the most profit out of it. Within this context, real-time optimization (RTO) is proposed and extended to dynamic RTO (DRTO) in the hierarchical control structure, usually having model predictive control (MPC) below. However, online tractability confined the model complexity of RTO and MPC, which results in model inconsistency and, even, incompatible solutions. Here we use parameter-dependent differential dynamic programming (PDDP) to incorporate the closed-loop behavior of the controller in an RTO layer to reduce problem complexity and online computation time. The adaptive control performance of PDDP and the efficacy of closed-loop DRTO formulation with PDDP is demonstrated with the reaction-storage-separation network system control. Consequently, PDDP provides a useful parameterization method to express closed-loop system dynamics, which enables fast feedback control and integrated plant optimization.

关键词： Differential dynamic programming dynamic real-time optimization Economic optimization Parametric disturbance

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State and parameter estimation in closed-loop dynamic real-time optimization - A comparative study

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COMPUTERS & CHEMICAL ENGINEERING 2025年 194卷

作者： Matias, Jose Swartz, Christopher L. E. McMaster Univ Dept Chem Engn 1280 Main St W Hamilton ON L8S 4L7 Canada Katholieke Univ Leuven Dept Chem Engn Jan Pieter Nayerlaan 5 B-2860 St Katelijne Waver Belgium

dynamic real-time optimization (DRTO) schemes have risen in popularity as plant environments have become increasingly dynamic due to globalization and deregulated energy markets. Inclusion of the impact of the plant control system on the predicted response gives rise to closed-loop DRTO (CL-DRTO). To avoid using a potentially inaccurate nominal model in CL-DRTO, this work explores incorporating plant measurements through various model updating strategies: bias update, state estimation, and combined parameter and state estimation, the latter two utilizing moving horizon estimation. The strategies are applied to two case studies, a distillation column and a continuous stirred tank reactor. Our findings suggest that the combined state and parameter estimation approach provides improvement in economic performance and fewer constraint violations when parametric uncertainty affects system dynamics nonlinearly. Conversely, the bias update strategy achieves satisfactory economic performance when the propagation of parameter uncertainty in the dynamic model is linear or mildly nonlinear.

关键词： dynamic real-time optimization State and parameter estimation Bias update Output disturbance Model updating strategies Plant feedback Moving-horizon estimation

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dynamic real-time optimization for nonlinear systems with Lyapunov stabilizing MPC

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JOURNAL OF PROCESS CONTROL 2022年 114卷 1-15页

作者： MacKinnon, Lloyd Ramesh, Praveen Sundaresan Mhaskar, Prashant Swartz, Christopher L. E. McMaster Univ Dept Chem Engn 1280 Main St West Hamilton ON L8S 4L8 Canada

The present work addresses the problem of stabilizing dynamic real-time optimization and control of nonlinear systems. dynamic real-time optimization (DRTO) is a framework for computing an optimal operating trajectory for a plant and providing corresponding set-points for an underlying control algorithm to track. This technique can be enhanced by directly modeling the underlying control algorithm (such as an MPC) in a closed-loop DRTO (CL-DRTO). This allows the CL-DRTO to predict both the controller and plant responses to set-point changes, improving performance of the overall system. Certain systems are additionally complicated by the existence of unstable steady states, which make control of the system substantially more difficult. A number of stabilizing MPC techniques have been developed in order to handle this, and a closed-loop DRTO formulation was recently proposed to handle linear systems. This work seeks to bring the improved performance of a CLDRTO to stabilizing control systems by formulating a CL-DRTO which utilizes and explicitly models an underlying Lyapunov stabilizing MPC to achieve stabilization for nonlinear systems. The proposed formulation is compared to the previously developed formulation to demonstrate the improved closed-loop control and performance. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Lyapunov stability constraints Closed-loop dynamic real-time optimization Nonlinear model predictive control Process economics

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dynamic real-time optimization of batch processes using Pontryagin's minimum principle and set-membership adaptation

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COMPUTERS & CHEMICAL ENGINEERING 2019年 128卷 488-495页

作者： Paulen, Radoslav Fikar, Miroslav Slovak Univ Technol Bratislava Fac Chem & Food Technol Radlinskeho 9 Bratislava Slovakia

This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with frequent re-optimization. The main problem addressed in this study is the high computational burden that is usually required by such schemes. We propose an approach that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The uncertainty in the model predictions is treated explicitly using reachable sets that are projected into the optimality conditions. Adaptation of model parameters is performed online using set-membership estimation. A class of batch membrane separation processes is in the scope of the presented applications, where the benefits of the presented approach are outlined. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： dynamic real-time optimization Batch processes Membrane separation Set-membership estimation

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dynamic real-time optimization of distributed MPC systems using rigorous closed-loop prediction

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COMPUTERS & CHEMICAL ENGINEERING 2019年 122卷 356-371页

作者： Li, Hao Swartz, Christopher L. E. McMaster Univ Dept Chem Engn 1280 Main St W Hamilton ON L8S 4L7 Canada

A dynamic real-time optimization (DRTO) formulation with closed-loop prediction is used to coordinate distributed model predictive controllers (MPCs) by rigorously predicting the interaction between the distributed MPCs and full plant response in the DRTO formulation. This results a multi-level optimization problem that is solved by replacing the MPC quadratic programming subproblems by their equivalent Karush-Kuhn-Tucker (KKT) first-order optimality conditions to yield a single-level mathematical program with complementarity constraints (MPCC). The proposed formulation is able to perform both target tracking and economic optimization with significant performance improvement over decentralized control, and similar performance to centralized MPC. A linear dynamic case study illustrates the performance of the proposed strategy for coordination of distributed MPCs for different levels of plant interaction. The method is thereafter applied to a nonlinear integrated plant with recycle, where its performance in both set-point target tracking and economic optimization is demonstrated. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： dynamic real-time optimization Model predictive control Distributed control Economic optimization Coordination Closed-loop prediction

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dynamic real-time optimization with Closed-Loop Prediction

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AICHE JOURNAL 2017年第9期63卷 3896-3911页

作者： Jamaludin, Mohammad Zamry Swartz, Christopher L. E. McMaster Univ Dept Chem Engn 1280 Main St West Hamilton ON L8S 4L7 Canada

Process plants are operating in an increasingly global and dynamic environment, motivating the development of dynamic real-time optimization (DRTO) systems to account for transient behavior in the determination of economically optimal operating policies. This article considers optimization of closed-loop response dynamics at the DRTO level in a two-layer architecture, with constrained model predictive control (MPC) applied at the regulatory control level. A simultaneous solution approach is applied to the multilevel DRTO optimization problem, in which the convex MPC optimization subproblems are replaced by their necessary and sufficient Karush-Kuhn-Tucker optimality conditions, resulting in a single-level mathematical program with complementarity constraints. The performance of the closed-loop DRTO strategy is compared to that of the open-loop prediction counterpart through a multi-part case study that considers linear dynamic systems with different characteristics. The performance of the proposed strategy is further demonstrated through application to a nonlinear polymerization reactor grade transition problem. (C) 2017 American Institute of Chemical Engineers

关键词： dynamic real-time optimization MPC economic optimization mathematical program with complementarity constraints KKT conditions

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Advances in sensitivity-based nonlinear model predictive control and dynamic real-time optimization

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JOURNAL OF PROCESS CONTROL 2015年 30卷 104-116页

作者： Biegler, L. T. Yang, X. Fischer, G. A. G. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Petr Brasileiro SA Refineria Henrique Lage REVAP Sao Jose Dos Campos SP Brazil

Recent results in the development of efficient large-scale nonlinear programming (NLP) algorithms have led to fast, on-line realizations of optimization-based methods for nonlinear model predictive control (NMPC) and dynamic real-time optimization (D-RTO), with predictive nonlinear dynamic (e.g., first principle) models. For NMPC, optimization-based controllers are developed that lead to well-understood stability and robustness properties, even for large, complex plant models. The realization of NMPC requires the application of a fast NLP solver for time-critical, on-line optimization, as well as efficient NLP sensitivity tools that require 2-3 orders of magnitude less computation than the NLP solution. This leads to advanced step NMPC (asNMPC), which essentially eliminates computational delay. We also extend these capabilities to dynamic real-time optimization (D-RTO) with more general stage costs that are economically based. This overview also extends input to state stability (ISS) properties for asNMPC to handle active set changes, and also for D-RTO through convex regularizations. Two large scale distillation case studies, based on nonlinear first principle models, are presented that demonstrate the effectiveness of these approaches. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Nonlinear programming Nonlinear model predictive control dynamic real-time optimization

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THE UTILIZATION OF CLOSED-LOOP PREDICTION FOR dynamic real-time optimization

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CANADIAN JOURNAL OF CHEMICAL ENGINEERING 2017年第10期95卷 1968-1978页

作者： Jamaludin, Mohammad Z. Li, Hao Swartz, Christopher L. E. McMaster Univ Dept Chem Engn 1280 Main St West Hamilton ON L8S 4L7 Canada

real-time optimization (RTO) is a layer within the hierarchical process automation architecture in which economically optimal set-points are computed for the underlying plant control system. RTO calculations are traditionally based on steady-state models, but an increasingly global and dynamic marketplace has led to the development of dynamic RTO (DRTO) strategies. Typical DRTO approaches optimize process input trajectories based on the open-loop response dynamics of the process, with controller set-point trajectories constructed from the resulting output response. This paper describes recent developments that utilize closed-loop prediction in the DRTO calculations for MPC regulated processes. A rigorous closed-loop DRTO problem is formulated as a multilevel dynamic optimization problem due to the inclusion of a sequence of MPC quadratic programming subproblems to generate the closed-loop response dynamics. A simultaneous solution strategy is applied in which the MPC subproblems are replaced by their equivalent Karush-Kuhn-Tucker (KKT) optimality conditions, permitting reformulation of the original problem as a single-level mathematical program with complementarity constraints (MPCC). Closed-loop approximation techniques are proposed to reduce the dimension of the DRTO problem while maintaining good closed-loop prediction accuracy. The performance of the proposed approaches is illustrated using case studies. Conclusions are drawn, and further research directions identified.

关键词： dynamic real-time optimization model predictive control closed-loop prediction economic optimization Complementarity constraints

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Analysis and future perspectives for the application of dynamic real-time optimization to solar thermal plants: A review

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SOLAR ENERGY 2022年 241卷 275-291页

作者： Untrau, Alix Sochard, Sabine Marias, Frederic Reneaume, Jean-Michel Le Roux, Galo A. C. Serra, Sylvain Univ Pau & Pays Adour LaTEP E2S UPPA Pau France Univ Sao Paulo Escola Politecn Sao Paulo Brazil

This review provides a deep analysis of the different methodologies to improve the operation of solar thermal plants based on mathematical optimization. The various schemes found in the literature to determine the optimal operational strategy are classified depending on two criteria: time dependence (static or dynamic) and with feedback or not from the plant (real-time or offline). This review shows that offline dynamic optimization is performed on solar thermal plants in research papers but highlights the lack of real-time optimization studies. The analysis work conducted in this review, based on studies of the operation of solar systems but also on process engineering research articles, shows that dynamic real-time optimization seems capable of handling the intermittency of the solar radiation and well suited to improve the operation of a solar thermal plant. Indeed, the daily and seasonal variations of weather and heat demand associated with the uncertainty of their forecasts make the operation of such systems very challenging. This paper details the different ways to implement dynamic real-time optimization, and the possible improvements to the classical scheme. Perspectives on the application of dynamic real-time optimization in association with a planning phase to plan a smart use of storage are described. Although it has not been studied in depth in the literature, the dynamic real-time optimization of a solar thermal plant including storage should be investigated in order to maximize the benefits from the heat sold, extend the time period where the heat demand is met and reduce the consumption of back up fossil fuels.

关键词： Solar thermal energy dynamic real-time optimization Optimal operation Storage management

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Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization

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JOURNAL OF PROCESS CONTROL 2009年第8期19卷 1277-1288页

作者： Wuerth, Lynn Hannemann, Ralf Marquardt, Wolfgang Rhein Westfal TH Aachen AVT Lehrstuhl Prozesstech D-52056 Aachen Germany

Nonlinear model-predictive control (NMPC) and dynamic real-time optimization (DRTO) lead to a substantial improvement of the operation of complex nonlinear processes. Whereas the focus in NMPC is primarily on control performance by minimizing the deviation from a given set-point, the objective in DRTO is to achieve a profitable and flexible operation adapted to changing market conditions and process uncertainties by employing an economic optimization criterion. A method for solving dynamic optimization problems based on neigh boring-extremal updates suitable for applications in NMPC and DRTO is presented in this paper. If process operation is affected by small perturbations, efficient techniques for updating the nominal trajectories based on parametric sensitivities can be applied [J. Kadam, W. Marquardt, Sensitivity-based solution updates in closed-loop dynamic optimization, in: Proceedings of the DYC-OPS 7 Conference, Cambridge, USA, 20041;these updates do not require the solution of the rigorous optimization problem but rely on first and second-order sensitivities computed by composite adjoints. However for larger perturbations and strong nonlinearities, the fast updates obtained by the neighboring-extremal solutions are not sufficiently accurate, and the solution of the nonlinear optimization problem requires further iterations with updated sensitivities to give a feasible and optimal solution. The application of the method to a simulated semi-batch reactor demonstrates its capabilities. The presented method is discussed in comparison to other methods in the literature. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： dynamic real-time optimization Nonlinear model-predictive control Parametric sensitivity analysis Neighboring-extremal control Hessian Composite adjoints

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