A time scale-bridging approach for integrating production scheduling and process control

In this paper, we propose a novel framework for integrating scheduling and nonlinear control of continuous processes. We introduce the time scale-bridging model (SBM) as an explicit, low-order representation of the closed-loop input–output dynamics of the process. The SBM then represents the process dynamics in a scheduling framework geared towards calculating the optimal time-varying setpoint vector for the process control system. The proposed framework accounts for process dynamics at the scheduling stage, while maintaining closed-loop stability and disturbance rejection properties via feedback control during the production cycle. Using two case studies, a CSTR and a polymerization reactor, we show that SBM-based scheduling has significant computational advantages compared to existing integrated scheduling and control formulations. Moreover, we show that the economic performance of our framework is comparable to that of existing approaches when a perfect process model is available, with the added benefit of superior robustness to plant-model mismatch.     

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

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.     

Dynamic models and fault diagnosis‐based triggers for closed‐loop scheduling

Establishing an explicit feedback connection between production management and process control decisions is a key requirement for more nimble and cost effective process operations in today's variable market conditions. Past research efforts focused on embedding dynamic process information in the production scheduling problem. In this article, we propose a novel framework for closing the scheduling loop, based on considering the process‐level events and disturbances that impact the implementation of scheduling decisions. We emphasize the role of a comprehensive fault detection, isolation and reconstruction mechanism as a trigger for rescheduling decisions and for reflecting the process capabilities altered by these events in the rescheduling problem formulation. Our framework is agnostic to the process type, and we present two (continuous process, sequential batch process) case studies to demonstrate its applicability. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1959–1973, 2017     

NONLINEAR MODEL PREDICTIVE CONTROL

Nonlinear Model Predictive Control (NMPC), a strategy for constrained, feedback control of nonlinear processes, has been developed. The algorithm uses a simultaneous solution and optimization approach to determine the open-loop optimal manipulated variable trajectory at each sampling instant. Feedback is incorporated via an estimator, which uses process measurements to infer unmeasured state and disturbance values. These are used by the controller to determine the future optimal control policy. This scheme can be used to control processes described by different kinds of models, such as nonlinear ordinary differential/algebraic equations, partial differential/algebraic equations, integra-differential equations and delay equations. The advantages of the proposed NMPC scheme are demonstrated with the start-up of a non-isothermal, non-adiabatic CSTR with an irreversible, first-order reaction. The set-point corresponds to an open-loop unstable steady state. Comparisons have been made with controllers designed using (1) nonlinear variable transformations, (2) a linear controller tuned using the internal model control approach, and (3) open-loop optimal control. NMPC was able to bring the controlled variable to its set-point quickly and smoothly from a wide variety of initial conditions. Unlike the other controllers, NMPC dealt with constraints in an explicit manner without any degradation in the quality of control. NMPC also demonstrated superior performance in the presence of a moderate amount of error in the model parameters, and the process was brought to its set-point without steady-state offset.     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

Variations in parameters such as processing times, yields, and availability of materials and utilities can have a detrimental effect in the optimality and/or feasibility of an otherwise “optimal” production schedule. In this article, we propose a multi‐stage adjustable robust optimization approach to alleviate the risk from such operational uncertainties during scheduling decisions. We derive a novel robust counterpart of a deterministic scheduling model, and we show how to obey the observability and non‐anticipativity restrictions that are necessary for the resulting solution policy to be implementable in practice. We also develop decision‐dependent uncertainty sets to model the endogenous uncertainty that is inherently present in process scheduling applications. A computational study reveals that, given a chosen level of robustness, adjusting decisions to past parameter realizations leads to significant improvements, both in terms of worst‐case objective as well as objective in expectation, compared to the traditional robust scheduling approaches. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1646–1667, 2016     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

Integrated batch‐to‐batch and nonlinear model predictive control for polymorphic transformation in pharmaceutical crystallization

Polymorphism, a phenomenon in which a substance can have more than one crystal form, is a frequently encountered phenomenon in pharmaceutical compounds. Different polymorphs can have very different physical properties such as crystal shape, solubility, hardness, color, melting point, and chemical reactivity, so that it is important to ensure consistent production of the desired polymorph. In this study, an integrated batch‐to‐batch and nonlinear model predictive control (B2B‐NMPC) strategy based on a hybrid model is developed for the polymorphic transformation of L ‐glutamic acid from the metastable α‐form to the stable β‐form crystals. The hybrid model comprising of a nominal first‐principles model and a correction factor based on an updated PLS model is used to predict the process variables and final product quality. At each sampling instance during a batch, extended predictive self‐adaptive control (EPSAC) is employed as a NMPC technique to calculate the control action by using the current hybrid model as a predictor. At the end of the batch, the PLS model is updated by utilizing the measurements from the batch and the above procedure is repeated to obtain new control actions for the next batch. In a simulation study using a previously reported model for a polymorphic crystallization with experimentally determined parameters, the proposed B2B‐NMPC control strategy produces better performance, where it satisfies all the state constraints and produces faster and smoother convergence, than the standard batch‐to‐batch strategy. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Dynamic optimization oriented modeling and nonlinear model predictive control of the wet limestone FGD system

Nonlinear model predictive control (NMPC) scheme is an effective method of multi-objective optimization control in complex industrial systems. In this paper, a NMPC scheme for the wet limestone flue gas desulphurization (WFGD) system is proposed which provides a more flexible framework of optimal control and decision-making compared with PID scheme. At first, a mathematical model of the FGD process is deduced which is suitable for NMPC structure. To equipoise the model's accuracy and conciseness, the wet limestone FGD system is separated into several modules. Based on the conservation laws, a model with reasonable simplification is developed to describe dynamics of different modules for the purpose of controller design. Then, by addressing economic objectives directly into the NMPC scheme, the NMPC controller can minimize economic cost and track the set-point simultaneously. The accuracy of model is validated by the field data of a 1000 MW thermal power plant in Henan Province, China. The simulation results show that the NMPC strategy improves the economic performance and ensures the emission requirement at the same time. In the meantime, the control scheme satisfies the multiobjective control requirements under complex operation conditions (e.g., boiler load fluctuation and set point variation). The mathematical model and NMPC structure provides the basic work for the future development of advanced optimized control algorithms in the wet limestone FGD systems.     

Towards the integration of process design,control and scheduling: Are we getting closer?

The integration of design and control, control and scheduling and design, control and scheduling, all have been core PSE challenges. While significant progress has been achieved over the years, it is fair to say that at the moment there is not a generally accepted methodology and/or “protocol” for such an integration – it is also interesting to note that currently, there is not a commercially available software [or even in a prototype form] system to fully support such an activity.Here, we present the foundations for such an integrated framework and especially a software platform that enables such integration based on research developments over the last 25 years. In particular, we describe PAROC, a prototype software system which allows for the representation, modeling and solution of integrated design, scheduling and control problems. Its main features include: (i) a high-fidelity dynamic model representation, also involving global sensitivity analysis, parameter estimation and mixed integer dynamic optimization capabilities; (ii) a suite/toolbox of model approximation methods; (iii) a host of multi-parametric programming solvers for mixed continuous/integer problems; (iv) a state-space modeling representation capability for scheduling and control problems; and (v) an advanced toolkit for multi-parametric/explicit Model Predictive Control and moving horizon reactive scheduling problems. Algorithms that enable the integration capabilities of the systems for design, scheduling and control are presented on a case of a series of cogeneration units.     

Model predictive control for the self-optimized operation in wastewater treatment plants: Analysis of dynamic issues

This paper describes a procedure to find the best controlled variables in an economic sense for the activated sludge process in a wastewater treatment plant, despite the large load disturbances. A novel dynamic analysis of the closed loop control of these variables has been performed, considering a nonlinear model predictive controller (NMPC) and a particular distributed NMPC-PI control structure where the PI is devoted to control the process active constraints and the NMPC the self-optimizing variables. The well-known self-optimizing control methodology has been applied, considering the most important measurements of the process. This methodology provides the optimum combination of measurements to keep constant with minimum economic loss. In order to avoid nonfeasible dynamic operation, a preselection of the measurements has been performed, based on the nonlinear model of the process and evaluating the possibility of keeping their values constant in the presence of typical disturbances.     

A multi-level simulation approach for the crude oil loading/unloading scheduling problem

An integrated approach for refinery production scheduling and unit operation optimization problems is presented. Each problem is at a different decision making layer and has an independent objective function and model. The objective function at the operational level is an on-line maximization of the difference between the product revenue and the energy and environmental costs of the main refinery units. It is modeled as an NLP and is constrained by ranges on the unit's operating condition as well as product quality constraints. The production scheduling layer is modeled as an MILP with the objective of minimizing the logistical costs of unloading the crude oil over a day-to-week time horizon. The objective function is a linear sum of the unloading, sea waiting, inventory, and setup costs. The nonlinear simulation model for the process units is used to find optimized refining costs and revenue for a blend of two crudes. Multiple linear regression of the individual crude oil flow rates within the crude oil percentage range allowed by the facility is then used to derive linear refining cost and revenue functions. Along with logistics costs, the refining costs or revenue are considered in the MILP scheduling objective function. Results show that this integrated approach can lead to a decrease of production and logistics costs or increased profit, provide a more intelligent crude schedule, and identify production level scheduling decisions which have a tradeoff benefit with the operational mode of the refinery.     

Integrated B2B‐NMPC control strategy for batch/semibatch crystallization processes

The uncertainty in crystallization kinetics is of major concern in manufacturing processes, which can result in deterioration of most model‐based control strategies. In this study, uncertainties in crystallization kinetic parameters were characterized by Bayesian probability distributions. An integrated B2B‐NMPC control strategy was proposed to first update the kinetic parameters from batch to batch using a multiway partial least‐squares (MPLS) model, which described the variances of kinetic parameters from that of process variables and batch‐end product qualities. The process model with updated kinetic parameters was then incorporated into an NMPC design, the extended prediction self‐adaptive control (EPSAC), for online control of the final product qualities. Promising performance of the proposed integrated strategy was demonstrated in a simulated semibatch pH‐shift reactive crystallization process to handle major crystallization kinetic uncertainties of L‐glutamic acid, wherein smoother and faster convergences than the conventional B2B control were observed when process dynamics were shifted among three scenarios of kinetic uncertainties. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Multistage nonlinear model predictive control for pumping treatment in hydraulic fracturing

Hydraulic fracturing has gained increasing attention as it allows the constrained natural gas and crude oil to flow out of low-permeability shale formations and significantly increase production. Perilous operating states of extremely high pressure also raise some safety concerns, requiring us to formulate an appropriate dynamic model, and provide a careful engineering control to ensure safe operating conditions. Moreover, uncertainties due to spatially varying rock properties increase the difficulties in control of the fracturing process. In this work, we formulate a first-principles model by considering the fracture evolution, mass transport of substances in the slurry, changing fluid properties, and the monitored operating pressure on the ground level. Next, we implement nonlinear model predictive control (NMPC) to control the process under a set of final requirements and process constraints. Our results show that the performance of standard NMPC degrades when the rock uncertainty causes the parameter mismatch between the process and the predictive model in the controller. With standard NMPC, designed with a nominal model, the process fails to meet the terminal requirements of fracture geometry, and pressure is violated in one of the parameter mismatch cases. Therefore, we resort to multistage NMPC, which considers uncertainty evolution in a scenario tree with separate control sequences to address constraint violations. We demonstrate that multistage NMPC presents good performance by showing constraint satisfaction whether the uncertain rock parameter realization is time-invariant or time-variant. We also simulate the process with multistage NMPC including different numbers of scenarios and compare their control performance. Our investigation demonstrates that multistage NMPC effectively manages parametric uncertainties attributed to non-homogeneous rock formation, and provides a promising control strategy for the hydraulic fracturing process.     

Integration of scheduling and control for batch processes using multi‐parametric model predictive control

Integration of scheduling and control results in Mixed Integer Nonlinear Programming (MINLP) which is computationally expensive. The online implementation of integrated scheduling and control requires repetitively solving the resulting MINLP at each time interval. (Zhuge and Ierapetritou, Ind Eng Chem Res. 2012;51:8550–8565) To address the online computation burden, we incorporare multi‐parametric Model Predictive Control (mp‐MPC) in the integration of scheduling and control. The proposed methodology involves the development of an integrated model using continuous‐time event‐point formulation for the scheduling level and the derived constraints from explicit MPC for the control level. Results of case studies of batch processes prove that the proposed approach guarantees efficient computation and thus facilitates the online implementation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3169–3183, 2014     

Nonlinear model predictive control for the polymorphic transformation of L‐glutamic acid crystals

Polymorphism, a phenomenon where a substance can have more than one crystal forms, has recently become a major interest to the food, speciality chemical, and pharmaceutical industries. The different physical properties for polymorphs such as solubility, morphology, and dissolution rate may jeopardize operability or product quality, resulting in significant effort in controlling crystallization processes to ensure consistent production of the desired polymorph. Here, a nonlinear model predictive control (NMPC) strategy is developed for the polymorphic transformation of L ‐glutamic acid from the metastable α‐form to the stable β‐form crystals. The robustness of the proposed NMPC strategy to parameter perturbations is compared with temperature control (T‐control), concentration control (C‐control), and quadratic matrix control with successive linearization (SL‐QDMC). Simulation studies show that T‐control is the least robust, whereas C‐control performs very robustly but long batch times may be required. SL‐QDMC performs rather poorly even when there is no plant‐model mismatch due to the high process nonlinearity, rendering successive linearization inaccurate. The NMPC strategy shows good overall robustness for two different control objectives, which were both within 7% of their optimal values, while satisfying all constraints on manipulated and state variables within the specified batch time. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Integrated production planning and scheduling using a decomposition framework

To ensure the consistency between planning and scheduling decisions, the integrated planning and scheduling problem should be addressed. Following the natural hierarchy of decision making, integrated planning and scheduling problem can be formulated as bilevel optimization problem with a single planning problem (upper level) and multiple scheduling subproblems (lower level). Equivalence between the proposed bilevel model and a single level formulation is proved considering the special structure of the problem. However, the resulting model is still computationally intractable because of the integrality restrictions and large size of the model. Thus a decomposition based solution algorithm is proposed in this paper. In the proposed method, the production feasibility requirement is modeled through penalty terms on the objective function of the scheduling subproblems, which is further proportional to the amount of unreachable production targets. To address the nonconvexity of the production cost function of the scheduling subproblems, a convex polyhedral underestimation of the production cost function is developed to improve the solution accuracy. The proposed decomposition framework is illustrated through examples which prove the effectiveness of the method.     

Nonlinear model predictive control of an industrial polymerization process

Nonlinear model predictive control (NMPC) is used to maintain and control polymer quality at specified production rates because the polymer quality measures have strong interacting nonlinearities with different temperatures and feed rates. Polymer quality measures that are available from the laboratory infrequently are controlled in closed-loop using a NMPC to set the temperature profile of the reactors. NMPC results in better control of polymer quality measures at different production rates as compared to using the nonlinear process model with reaction kinetics to implement offline targets for reactor temperatures.     

Economic model predictive control for inventory management in supply chains

In this paper, we propose economic model predictive control with guaranteed closed-loop properties for supply chain optimization. We propose a new multiobjective stage cost that captures economics as well as risk at a node, using a weighted sum of an economic cost and a tracking stage cost. We also demonstrate integration of scheduling with control using a supply chain example. We integrate a scheduling model for a multiproduct batch plant with a control model for inventory control in a supply chain. We show recursive feasibility of such integrated control problems by developing simple terminal conditions.