Active Constraint Regions Research Articles

Decentralized control using selectors for optimal steady-state operation with changing active constraints

We study the optimal steady-state operation of processes where the active constraints change. The aim of this work is to eliminate or reduce the need for a real-time optimization layer, moving the optimization into the control layer by switching between appropriately selected controlled variables (CVs) in a simple way. The challenge is that the best CVs, or more precisely the reduced cost gradients associated with the unconstrained degrees of freedom, change with the active constraints. This work proposes a framework based on decentralized control that operates optimally in all active constraint regions, with region switching mediated by selectors. A key point is that the nullspace associated with the unconstrained cost gradient needs to be selected in accordance with the constraint directions so that selectors can be used. A main benefit is that the number of SISO controllers that need to be designed is only equal to the number of process inputs plus constraints. The main assumptions are that the unconstrained cost gradient is available online and that the number of constraints does not exceed the number of process inputs. The optimality and ease of implementation are illustrated in a simulated toy example with linear constraints and a quadratic cost function. In addition, the proposed framework is successfully applied to the nonlinear Williams–Otto reactor case study.

Comparison of Simple Feedback Control Structures for Constrained Optimal Operation

Optimal operation of systems subject to constraints can be challenging, especially when the set of active constraints changes during operation due to disturbances. The use of traditional model-based real-time optimization strategies has limitations related to model-plant mismatch and computational effort, and therefore the use of simple feedback strategies in lower layers is a good alternative to avoid these issues on fast timescales. This work aims to evaluate the viability of region-based control structures using selectors and the use of a primal-dual feedback optimizing control framework on this kind of problem, through the study of two process systems with changing active constraints. While region-based strategies focus on the effective control in specific active constraint regions, the primal-dual approach allows for control in all possible regions, with the introduction of intermediate variables that estimate the Lagrange multiplier values. In the first case study, the traditional region-based strategy could not handle all constraint regions, and an additional logical switching was necessary to account for the remaining region. The implementation of primal-dual feedback optimizing control was flexible enough to control the system in all regions without the need for additional logic. The second case study presents more constraints than the first and increased nonlinearities, which makes finding controlled variables for the unconstrained degrees of freedom challenging. The primal-dual control framework was able to drive the system to the optimum in all considered regions. Therefore, this framework is deemed as a promising control structure for optimal operation in the presence of changing active constraints.

Optimal operation of oil and gas production using simple feedback control structures

The purpose of this paper is to describe the control challenges related to optimal operation of oil and gas production wells, and show that optimal operation can be achieved using simple feedback control structures. In particular, we find that conventional feedback control structures can efficiently handle changes in active constraint regions using simple logics such as split-range and selectors. This eliminates the need for complex models to be used in the optimization problem, and in addition eliminates the need to solve numerical optimization problems online. Thus, by using only simple feedback controllers that have been used widely in the oil and gas industry, it has a higher chance of implementation. We demonstrate the use of simple feedback controllers on two application examples; 1) a gas-lift optimization simulation study with a network of six gas-lifted wells, 2) an experimental study of optimal control of electrical submersible pump (ESP) lifted oil wells tested on a large-scale experimental test facility with a full scale ESP and live viscous crude oil.

Online Process Optimization with Active Constraint Set Changes using Simple Control Structures

The purpose of this paper is to show that online process optimization can be achieved using simple control structures without the need for solving numerical optimization problems online. In particular, we show that changes in active constraint regions can be handled using simple logics such as selectors, without needing to identify the exact location of the active constraint regions a priori, nor using a detailed model online. Good case studies are used to clearly demonstrate how optimal operation can be achieved with changes in active constraint regions using simple feedback control structures.

Optimal Operation with Changing Active Constraint Regions using Classical Advanced Control

With ”classical advanced control” we mean the control structures that are commonly used in industry for multivariable control. These have been in use for at least 50 years, but surprisingly there is little literature published on how to design such structures in a systematic manner. We present a design procedure to assure optimal operation when active constraint changes occur. In this paper, we focus on input saturation. We suggest to use a priority list of constraints as an important first step of the presented design procedure. We also discuss how to handle input saturation using split range control, valve position control (input resetting), and selectors. As a case study, we consider optimal operation and a priority list of constraints for a cooler with temperature and flow control, and evaluate alternative classical advanced control implementations that maintain optimality.

Systematic top-down economic plantwide control of the cumene process

Plantwide control system design for economic operation over a wide through range (design throughput to maximum throughput) encompassing multiple active constraint regions, is studied for the cumene process. A unique feature of the process is that it recycles the heavy side-product to extinction. A novel top-down control system synthesis approach, where the control objectives for maximum throughput operation are first obtained using steady state optimization followed by control loop pairings with highest priority to economic objectives, is applied. The control structure thus obtained is unconventional with tight active constraint control requiring ‘long’ level loops that maintain the reflux drum and bottom sump levels of a column using the two process fresh feeds. This structure for maximum throughput operation is adapted for economic operation at lower throughputs. Rigorous dynamic simulations show that the structure provides acceptable process regulation for large disturbances despite the long level loops over the entire throughput range. More importantly, no back-off from the active hard equipment capacity constraints also ensure that the loss in throughput from the maximum achievable is negligible. This work is amongst the first reports illustrating the application of the top-down plantwide control system design approach for superior economic performance with robust process stabilization.

External Reset Feedback for Constrained Economic Process Operation

Efficiency and sustainability considerations increasingly require control systems to drive process operation as close as possible to optimally active process constraints. Because the active constraint set is changeable, override control structures are employed to transfer the control of important control objectives from one controller to another and to manage the transition between the different constraint regions. Reset windup problems can occur when these controllers have integral action with large swings (bumps) in controller output as control is transferred from one controller to another. This work considers the Shinskey–Buckley external reset feedback control structure in override control applications for a smooth transition between active constraint regions. Three example processes with increasing levels of complexity are used to quantitatively demonstrate the significant improvement in dynamic control and consequent process economic performance (compared to internal reset). The quantitative results...

Active constraint regions for a natural gas liquefaction process

Optimal operation of liquefaction processes is little studied in the open literature. In particular, the issue of how optimal operation changes with disturbances has received very little attention. This paper addresses optimal operation of a simple natural gas liquefaction process – the PRICO process. The focus is on how the active process constraints change with disturbances. It is shown that the feasible part of the disturbance space can be divided into five regions with different sets of active constraints. We also suggest control structures for the process, and find that as little as two control structures may be needed despite of the fact that there are five regions. It is suggested to use compressor speed to control the margin to surge at minimum, and to keep the turbine outlet stream at saturation at all times.

DESIGN OF A CONTROL STRUCTURE FOR MASS EXCHANGER NETWORKS

This work aims to present a design for optimal operation of mass exchange networks (MENs) with minimum total annual cost (TAC) and optimal split-range control. The proposed strategy consists of five main steps. First, MENs are formulated as mixed-integer nonlinear programming (MINLP) with minimized TAC. Second, a network flexibility test is performed to ensure feasibility for a large number of uncertain parameters that are generated randomly within the operating ranges. Next, parametric programming is used to find the active constraint regions, and integer linear programming (ILP) is used to formulate an optimal split-range control structure. Then, the optimal operations of the control structure are verified with the preliminary dynamic behaviors. Finally, the common equipment design data are presented. The validation of the proposed method of designing an optimal split-range control structure for MEN is performed by three case studies from El-Halwagi and Manousiouthakis's work (1989, 1990). The results do not guarantee global optimization, but are checked through flexibility and dynamics tests. They demonstrate that the obtained control structures can keep all mass fraction targets at the desired values, even with the saturation of some manipulated variables when MENs are disturbed by reductions of 10, 20, and 30% of the mass fractions of rich streams and lean streams.

Active Constraint Regions for Optimal Operation of Distillation Columns

When designing the control structure of distillation columns, with optimal operation in mind, it is important to know how the active set of constraints changes with disturbances. This issue has received little attention in the literature. This paper applies a procedure presented in an earlier paper, to find how the active constraints for distillation columns change with variations in energy cost and feed flow rate. The production of the most valuable product is maximized by keeping its purity on the minimum allowed, that is, by keeping the valuable product on spec. This is the avoid product giveaway rule, which means that the purity specification of the valuable product is always an active constraint. We find that this rule generally holds for distillation for the common case when the price of the on-spec product is independent of purity. The paper includes three case studies: a single distillation column with constant product prices, a single column where the price of the most valuable product is dependent on purity, and two distillation columns in series. In all three case studies, there is a bottleneck, corresponding to a feed flow rate above which the column(s) cannot operate without breaking constraints.

Active Constraint Regions for Optimal Operation of Chemical Processes

Whendesigning the control structure ofa chemical plant,withoptimaloperationand control inmind,it is important to know how the active set of constraints changes with disturbances.The generation of optimal active constraints regions using optimization generally is very time-consuming, and this paper discusses how to use process knowledge to minimize the need for numerical calculations—that is, minimize the number of optimization problems that must be solved. We consider the case of two disturbances, as this can be nicely represented graphically. In this paper, we study economically optimal operation of a reactorseparatorrecycle process and show how the set of active constraints changes with feed flow rate and energy cost as disturbances.Wealsoidentifytheeconomicalandphysicalbottleneckoftheprocess.Forthiscasestudyprocess,we find fivedistinct regions with different active sets. This illustrates that, even for simple cases, the map of active constraint regions can be quite complex.