A switched system formulation for optimal integration of scheduling and control in multi-product continuous processes

Andrés‐Martínez, Oswaldo; Ricardez‐Sandoval, Luis A.

doi:10.1016/j.jprocont.2021.08.017

Cited by 14 publications

(20 citation statements)

References 59 publications

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“…In our previous study, 16 we derived an integrated model of optimal scheduling and control for N products to be manufactured each during only one out of M subintervals of time, hence N = M. The formulation was developed following a switched dynamic system approach. Here, we summarize the integrated formulation and adapt it for closed-loop implementation.…”

Section: Scheduling Formulationmentioning

confidence: 99%

“…The size h i 0 of each finite element i' = 1,…, n f is an additional decision variable so that the location of s t j (the end of transition time as illustrated in Figure 2) is optimality chosen. 16 Bounds on these variables are imposed as h min ≤ h i 0 ≤ h max . In order to guarantee that a binary solution is obtained at each rescheduling before passing the new σ tr to the NMPC, the following condition is evaluated: b J pen ≤ ϵ ρ , where ϵ ρ is a user-defined tolerance.…”

Section: Solution Strategymentioning

confidence: 99%

“…It is usually straightforward to find a value of δ sufficiently large that provides binary solutions for different case studies. 16 Alternatively, a binary solution can be constructed with a projection method like those revised in Meyer et al 46 The steady state control and state values associated with the nominal solution as well as the demands can be used as initial guess when solving problem (R). More systematic initialization strategies such as that presented in Beal et al 15 can be applied to find solutions in short CPU times.…”

Section: Solution Strategymentioning

confidence: 99%

“…Relaxation and initialization strategies have also been applied to solve the integrated problem with nonlinear programming (NLP) solvers using less computational effort 15 . A slight change of paradigm was proposed in our previous study for multi‐product continuous processes, where the integration of scheduling and process dynamics was accomplished with a switched system formulation 16 . The result is an optimal control problem that can be solved as an NLP model avoiding the computational challenges of traditional MINLP formulations.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, we present a novel online scheduling and control framework. In our previous study, 16 a switched system formulation that can be efficiently solved to obtain production sequences and control profiles in an open‐loop environment was presented. If disturbances enter the system or demands are updated during operation, the open‐loop schedule/control decisions may not be optimal or may become dynamically infeasible.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A nested online scheduling and nonlinear model predictive control framework for multi‐product continuous systems

Andrés‐Martínez

Ricardez‐Sandoval

2022

AIChE Journal

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In the pursuit of integrated scheduling and control frameworks for chemical processes, it is important to develop accurate integrated models and computational strategies such that optimal decisions can be made in a dynamic environment. In this study, a recently developed switched system formulation that integrates scheduling and control decisions is extended to closed-loop operation embedded with nonlinear model predictive control (NMPC). The resulting framework is a nested online scheduling and control loop that allows to obtain fast and accurate solutions as no model reduction is needed and no integer variables are involved in the formulations. In the outer loop, the integrated model is solved to calculate an optimal product switching sequence such that the process economics is optimized, whereas in the inner loop, an NMPC implements the scheduling decisions. The proposed scheme was tested on two multi-product continuous systems. Unexpected large disturbances and rush orders were handled effectively.

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Section: Scheduling Formulationmentioning

confidence: 99%

Section: Solution Strategymentioning

confidence: 99%

Section: Solution Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A nested online scheduling and nonlinear model predictive control framework for multi‐product continuous systems

Andrés‐Martínez

Ricardez‐Sandoval

2022

AIChE Journal

Self Cite

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Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

2022

Self Cite

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In the mid‐1950s, Pontryagin et al. published a principle that became a fundamental concept in optimal control (OC) theory. The principle provides theoretical and practical methods to find the solution of OC problems, in particular, open‐loop control problems. In chemical engineering, the principle has played an important role as a decision making framework for more than 60 years. This study gathers the main contributions on the application of the Pontryagin's principle to the dynamic optimization of chemical processes. A concise overview of the optimality conditions for a wide class of constrained OC problems is provided. Numerical methods to solve the necessary conditions and strategies to address inequality constraints are summarized. The information and illustrative case study presented in this work can be used as a guide to implement the principle in different settings. Opportunities for further application of the principle in relevant chemical engineering problems are also discussed.

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Integration of planning, scheduling, and control: A review and new perspectives

Andrés‐Martínez

Ricardez‐Sandoval

2022

Can J Chem Eng

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The competitive, profitable, and safe operation of chemical plants depends on tight and effective coordination among the different decision making levels of the enterprise, including planning, scheduling, and control. The optimal integration of these functions has become critical given the disruptive effects of the recent COVID-19 pandemic on the supply chains and the current trends in climate change. However, integrating multiple decision making levels creates modelling and computational challenges. In this study, we review the progress made in the integration of two and three decisions levels using mathematical programming and control theory tools. We highlight the model reduction and decomposition techniques that have been applied, as well as the main issues that remain unsolved. Perspectives on emergent areas of application and novel computing solutions are also discussed.

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A switched system formulation for optimal integration of scheduling and control in multi-product continuous processes

Cited by 14 publications

References 59 publications

A nested online scheduling and nonlinear model predictive control framework for multi‐product continuous systems

A nested online scheduling and nonlinear model predictive control framework for multi‐product continuous systems

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

Integration of planning, scheduling, and control: A review and new perspectives

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