Optimal operation of process plants under partial shutdown conditions

A systematic strategy for optimal plant operation during partial shutdowns is proposed. We consider the situation where one or more process units are shut down due to failure or maintenance but where the remaining units are able to continue operation to some degree. The goal of the strategy is to manipulate the plant degrees‐of‐freedom—during and after the shutdown—such that production is restored in a cost‐optimal fashion while meeting safety and operational constraints. Optimal control trajectories are obtained through the solution of a dynamic optimization problem. A novel multitiered optimization approach allows the prioritization of multiple competing objectives and the specification of trade‐offs between them. Uncertainty in the downtime estimate, a crucial parameter in shutdown optimization, is addressed through reoptimization. We employ a transient predictive control algorithm for implementing the computed control policy under feedback. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4151–4168, 2013     

A dynamic programming based approach for explicit model predictive control of hybrid systems

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multi-parametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function.     

Identification of models for control of wet granulation

The modeling work in this paper provides insight on improved control and design (including measurement selection) of a granulation process. Two different control strategies (MPC and PID) are evaluated on an experimentally validated granulation model. This model is based on earlier work done at The University of Sheffield, UK and Organon, The Netherlands [C.F.W. Sanders, W. Oostra, A.D. Salman, M.J. Hounslow, Development of a predictive high-shear granulation model; experimental and modeling results, 7th World Congress of Chemical Engineering, Glasgow (2005), C11-002]. The granulation kinetics were measured in a 10 liter batch granulator with an experimental design that included four process variables. The aggregation rates were extracted with a Discretized Population Balance (DPB) model. Knowledge of the process kinetics was used to model a continuous (well mixed) granulator. The controller model for the Model Predictive Controller is a linearized state space model, derived from the nonlinear DPB model. It has the four process variables from the experimental design and a feed ratio as input variables. Since the DPB model describes the whole Granule Size Distribution (GSD), candidate sets of lumped output variables were evaluated. When measuring controller performance based on the full granule size distribution, it is shown that a PID controller can actually produce results that fluctuate more than the open-loop response. An MPC controller improves stability on both process outputs and the full granule size distribution. The work shows that measuring and controlling specific number based lumped outputs result in a more stable process than when mass based lumped outputs are used. The paper describes a general strategy of using lab scale batch experiments to design and control (small or large scale) continuous granulators. The continuous experiments in this paper are based on simulation, therefore future experimental validation will elucidate further the link between batch and continuous granulation.     

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.     

On-line batch process monitoring using dynamic PCA and dynamic PLS models

Producing value-added products of high-quality is the common objective in industries. This objective is more difficult to achieve in batch processes whose key quality measurements are not available on-line. In order to reduce the variations of the product quality, an on-line batch monitoring scheme is developed based on the multivariate statistical process control. It suggests using the past measured process variables without real-time quality measurement at the end of the batch run. The method, referred to as BDPCA and BDPLS, integrates the time-lagged windows of process dynamic behavior with the principal component analysis and partial least square respectively for on-line batch monitoring. Like traditional MPCA and MPLS approaches, the only information needed to set up the control chart is the historical data collected from the past successful batches. This leads to simple monitoring charts, easy tracking of the progress in each batch run and monitoring the occurrence of the observable upsets. BDPCA and BDPLS models only collect the previous data during the batch run without expensive computations to anticipate the future measurements. Three examples are used to investigate the potential application of the proposed method and make a comparison with some traditional on-line MPCA and MPLS algorithms.     

Considerations on nonlinear model predictive control techniques

The nonlinear model predictive control (NMPC) is an on-line application based on nonlinear convolution models. It is an appealing control methodology, but it is difficult to implement and its solution is not so performing since it unavoidably means to solve a usually large-scale, constrained, and multidimensional optimization. To increase the difficulty, this optimization problem is subject to computationally heavy differential and algebraic constraints constituting the same convolution model and the least squares nature of the objective function easily leads to narrow valleys and multimodality issues.Beyond a short review of the state-of-the-art, the paper is aimed at highlighting the possibility to exploit at best the intrinsic features of the specific system one is going to control using the NMPC. The idea is to give the NMPC the possibility to automatically select the best combination of algorithms (differential solvers and optimizers) in accordance with the specific problem to be solved. From this perspective, the NMPC could be easily extended to many scientific fields traditionally far from process systems and computer-aided process engineering and the user has not to worry about which specific differential solvers and optimizers are needed to solve his/her problem.     

Decentralized Control System Design under Uncertainty Using Mixed‐Integer Optimization

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. In this contribution, the optimal control structure and the optimal controller parameters are determined simultaneously using mixed‐integer dynamic optimization (MIDO) under uncertainty, to account for nonlinear process dynamics and various disturbance scenarios. Application of the sigma point method is proposed in order to approximate the expectation and the variance of a chosen performance index with a minimum number of points to solve the MIDO problem under uncertainty. The proposed methodology is demonstrated with a benchmark problem of an inferential control for a reactive distillation column. The results are compared with established heuristic design methods and with previous deterministic approaches.     

Optimal model-based aeration control policies in a sequencing batch reactor

We present a non-linear programming formulation for the computation of optimal aeration policies in a sequencing batch reactor for wastewater streams treatment. We assume that organic matter and nitrogen are the main pollutants to be removed to meet water quality targets. The novelty of the work lies in the fact that no binary variables are required to compute the switching time between the aerobic and anoxic stages of the water treatment process leading to a simpler, robust and easier to compute optimization formulation. Moreover, because the control valve, through which air is fed to the reactor, can take either its minimum or maximum bounds as well as any fractional values between such bounds, improved optimal aeration profiles are reported. Such improved profiles mean that shorter processing times are required, compared to previous solutions, leading also to a reduction in the operation cost of the wastewater treatment process. Although the optimal operation policies were computed for a typical home wastewater stream, the optimization formulation can also be extended for the treatment of other polluted streams.     

Optimal processing pathway for the production of biodiesel from microalgal biomass: A superstructure based approach

In this study, we propose a mixed integer nonlinear programming (MINLP) model for superstructure based optimization of biodiesel production from microalgal biomass. The proposed superstructure includes a number of major processing steps for the production of biodiesel from microalgal biomass, such as the harvesting of microalgal biomass, pretreatments including drying and cell disruption of harvested biomass, lipid extraction, transesterification, and post-transesterfication purification. The proposed model is used to find the optimal processing pathway among the large number of potential pathways that exist for the production of biodiesel from microalgae. The proposed methodology is tested by implementing on a specific case with different choices of objective functions. The MINLP model is implemented and solved in GAMS using a database built in Excel. The results from the optimization are analyzed and their significances are discussed.     

Optimal maintenance scheduling of a gas engine power plant using generalized disjunctive programming

A new continuous‐time model for long‐term scheduling of a gas engine power plant with parallel units is presented. Gas engines are shut down according to a regular maintenance plan that limits the number of hours spent online. To minimize salary expenditure with skilled labor, a single maintenance team is considered which is unavailable during certain periods of time. Other challenging constraints involve constant minimum and variable maximum power demands. The objective is to maximize the revenue from electricity sales assuming seasonal variations in electricity pricing by reducing idle times and shutdowns in high‐tariff periods. By first developing a generalized disjunctive programming model and then applying both big‐M and hull reformulation techniques, we reduce the burden of finding the appropriate set of mixed‐integer linear constraints. Through the solution of a real‐life problem, we show that the proposed formulations are very efficient computationally, while gaining valuable insights about the system. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2083–2097, 2014     

D-RM Builder: A software tool for generating fast and accurate nonlinear dynamic reduced models from high-fidelity models

Dynamic reduced models (D-RMs) derived from rigorous models are highly desired for speeding up dynamic simulations. A useful software tool named D-RM Builder was developed to automatically generate data-driven D-RMs from high-fidelity dynamic models. It allows a user to configure input/output variables, sample input space and generate sequences of step changes, launch high-fidelity model simulations, fit simulation results to a D-RM, and finally visualize and validate the D-RM. The Decoupled A-B Net (DABNet) nonlinear system identification model was used as the main D-RM type and was enhanced to model nonlinear multiple input and multiple output dynamic systems with options for double-pole formulation to handle fast/slow time scales and pole value optimization. The D-RM Builder tool has been successfully used to generate D-RMs for a highly nonlinear pH neutralization reactor system and a two-time-scale bubbling fluidized bed adsorber-reactor for CO₂ capture.     

Regulation of film thickness, surface roughness and porosity in thin film growth using deposition rate

This work focuses on distributed control of film thickness, surface roughness and porosity in a porous thin film deposition process using the deposition rate as the manipulated input. The deposition process includes adsorption and migration processes and it is modeled via kinetic Monte Carlo simulation on a triangular lattice with vacancies and overhangs allowed to develop inside the film. A distributed parameter (partial differential equation) dynamic model is derived to describe the evolution of the surface height profile of the thin film accounting for the effect of deposition rate. The dynamics of film porosity, evaluated as film site occupancy ratio, are described by an ordinary differential equation. The developed dynamic models are then used as the basis for the design of a model predictive control algorithm that includes penalty on the deviation of film thickness, surface roughness and film porosity from their respective set-point values. Simulation results demonstrate the applicability and effectiveness of the proposed modeling and control approach in the context of the deposition process under consideration.     

Optimal design and global sensitivity analysis of biomass supply chain networks for biofuels under uncertainty

Bio-fuels represent promising candidates for renewable liquid fuels. One of the challenges for the emerging industry is the high level of uncertainty in supply amounts, market demands, market prices, and processing technologies. These uncertainties complicate the assessment of investment decisions. This paper presents a model for the optimal design of biomass supply chain networks under uncertainty. The uncertainties manifest themselves as a large number of stochastic model parameters that could impact the overall profitability and design. The supply chain network we study covers the Southeastern region of the United States and includes biomass supply locations and amounts, candidate sites and capacities for two kinds of fuel conversion processing, and the logistics of transportation from the locations of forestry resources to the conversion sites and then to the final markets.To reduce the design problem to a manageable size the impact of each uncertain parameter on the objective function is computed for each end of the parameter's range. The parameters that cause the most change in the profit over their range are then combined into scenarios that are used to find a design through a two stage mixed integer stochastic program. The first stage decisions are the capital investment decisions including the size and location of the processing plants. The second stage recourse decisions are the biomass and product flows in each scenario. The objective is the maximization of the expected profit over the different scenarios. The robustness and global sensitivity analysis of the nominal design (for a single nominal scenario) vs. the robust design (for multiple scenarios) are analyzed using Monte Carlo simulation over the hypercube formed from the parameter ranges.     

An on-line constraint softening strategy to guarantee the feasibility of dynamic controller in double-layered MPC

A double-layered model predictive control(MPC),which is composed of a steady-state target calculation(SSTC) layer and a dynamic control layer,is a prevailing hierarchical structure in industrial process control.Based on the reason analysis of the dynamic controller infeasibility,an on-line constraints softening strategy is given.At first,a series of regions of attraction(ROA)of the dynamic controller is calculated according to the softened constraints;then a minimal ROA containing the current state is chosen and the corresponding softened constraint is adopted by the dynamic controller.Note that,the above measures are performed on-line because the centers of the above ROA are the steady-state targets calculated at each instant.The effectiveness of the presented strategy is illustrat-ed through two examples.     

Theoretical framework for formulating MIP scheduling models with multiple and non-uniform discrete-time grids

We present a framework for the formulation of MIP scheduling models based on multiple and nonuniform discrete time grids. In a previous work we showed that it is possible to use different (possibly non-uniform) time grids for each task, unit, and material. Here, we generalize these ideas to account for general resources, and a range of processing characteristics such as limited intermediate storage and changeovers. Each resource has its own grid based on resource consumption and availability allowing resource constraints to be modeled more accurately without increasing the number of binary variables. We develop algorithms to define the unit-, task-, material-, and resource-specific grids directly from problem data. Importantly, we prove that the multi-grid formulation is able to find a schedule with the same optimal objective as the discrete-time single-grid model with an arbitrarily fine grid. The proposed framework leads to the formulation of models with reduced number of binary variables and constraints, which are able to find good solutions faster than existing models.     

A model predictive formulation for control of open-loop unstable cascade systems

Cascade control is commonly used in the operation of chemical processes to reject disturbances that have a rapid effect on a secondary measured state, before the primary measured variable is affected. In this paper, we develop a state estimation-based model predictive control approach that has the same general philosophy of cascade control (taking advantage of secondary measurements to aid disturbance rejection), with the additional advantage of the constraint handling capability of model predictive control (MPC). State estimation is achieved by using a Kalman filter and appending modeled disturbances as augmented states to the original system model. The example application is an open-loop unstable jacketed exothermic chemical reactor, where the jacket temperature is used as a secondary measurement in order to infer disturbances in jacket feed temperature and/or reactor feed flow rate. The MPC-based cascade strategy yields significantly better performance than classical cascade control when operating close to constraints on the jacket flow rate.     

Use of bifurcation analysis for development of nonlinear models for control applications

Nonlinear system identification poses challenging questions because a closed general theory is not available for this field. Particularly, nonlinear models based on neural networks (NN) may present incompatible general dynamic process behavior, leading to improper closed-loop responses, even when they allow for satisfactory one step ahead prediction of process dynamics, as required by traditional validation methods. It is shown here that performing detailed bifurcation and stability analysis may be very helpful for the adequate development and implementation of nonlinear models and model based controllers. The study of many parameters that are defined a priori during the training of the NN shows that the spurious dynamic behavior is related mostly to the use of incomplete data sets during the learning process. This is an indication that, for each kind of process, the number, range and distribution of the data points in the operation region of interest are of paramount importance for proper training of the nonlinear model. Strategies to improve the quality of the training procedure are provided and analyzed both theoretically and experimentally, using the solution polymerization of styrene in a tubular reactor as a case study.     

Integrated multi‐echelon supply chain design with inventories under uncertainty: MINLP models,computational strategies

We address in this article a problem that is of significance to the chemical industry, namely, the optimal design of a multi‐echelon supply chain and the associated inventory systems in the presence of uncertain customer demands. By using the guaranteed service approach to model the multi‐echelon stochastic inventory system, we develop an optimization model to simultaneously determine the transportation, inventory, and network structure of a multi‐echelon supply chain. The model is an MINLP with a nonconvex objective function including bilinear, trilinear, and square root terms. By exploiting the properties of the basic model, we reformulate this problem as a separable concave minimization program. A spatial decomposition algorithm based on the integration of Lagrangean relaxation and piecewise linear approximation is proposed to obtain near global optimal solutions with reasonable computational expense. Examples for specialty chemicals and industrial gas supply chains with up to 15 plants, 100 potential distribution centers, and 200 markets are presented. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

DYNAMIC PERFORMANCE-BASED DESIGN FOR PLANTWIDE CONTROL STRUCTURE

This article presents a plantwide control structure design using dynamic performance-based optimization. The controlled and manipulated variable sets were obtained heuristically. The main plantwide control structures were established via dynamic optimization and the rest established via heuristic rules. The optimization problem was formulated as dynamic mixed integer nonlinear programming with objective function of measuring the control performance (ITAE of CVs) and the cost of manipulated variables (ITAE of MVs). The integer matrix in the formulation represents the plantwide control structure explicitly. The Tennessee Eastman (TE) process was selected to illustrate the proposed design procedure. The obtained control structures were evaluated via dynamic simulation in the face of various disturbances and set-point changing. The results were then compared with the control structure proposed by Luyben et al. (1999 Luyben , W. L. , Tyreus , B. D. , and Luyben , M. L. ( 1999 ). Plantwide Process Control , McGraw-Hill , New York . [Google Scholar]).     

Assessing plant design with regard to MPC performance

Model Predictive Control is ubiquitous in the chemical industry and offers great advantages over traditional controllers. Notwithstanding, new plants are being projected without taking into account how design choices affect the MPC’s ability to deliver better control and optimization. Thus a methodology to determine if a certain design option favours or hinders MPC performance would be desirable. This paper presents the economic MPC optimization index whose intended use is to provide a procedure to compare different designs for a given process, assessing how well they can be controlled and optimised by a zone constrained MPC. The index quantifies the economic benefits available and how well the plant performs under MPC control given the plant’s controllability properties, requirements and restrictions. The index provides a monetization measure of expected control performance.This approach assumes the availability of a linear state-space model valid within the control zone defined by the upper and lower bounds of each controlled and manipulated variable. We have used a model derived from simulation step tests as a practical way to use the method. The impact of model uncertainty on the methodology is discussed. An analysis of the effects of disturbances on the index illustrates how they may reduce profitability by restricting the ability of a MPC to reach dynamic equilibrium near process restrictions, which in turn increases product quality giveaway and costs. A case of study consisting of four alternative designs for a realistically sized crude oil atmospheric distillation plant is provided in order to demonstrate the applicability of the index.