Integration of process design and controller design for chemical processes using model-based methodology

Abstract

In this paper, a novel systematic model-based methodology for performing integrated process design and controller design (IPDC) for chemical processes is presented. The methodology uses a decomposition method to solve the IPDC typically formulated as a mathematical programming (optimization with constraints) problem. Accordingly the optimization problem is decomposed into four sub-problems: (i) pre-analysis, (ii) design analysis, (iii) controller design analysis, and (iv) final selection and verification, which are relatively easier to solve. The methodology makes use of thermodynamic-process insights and the reverse design approach to arrive at the final process design–controller design decisions. The developed methodology is illustrated through the design of: (a) a single reactor, (b) a single separator, and (c) a reactor–separator-recycle system and shown to provide effective solutions that satisfy design, control and cost criteria. The advantage of the proposed methodology is that it is systematic, makes use of thermodynamic-process knowledge and provides valuable insights to the solution of IPDC problems in chemical engineering practice.

Introduction

Traditionally, process design and controller design are two separate problems that are dealt with sequentially. The process is designed first to achieve the design objectives, and then, the operability and control aspects are analyzed and resolved to obtain the controller design. This traditional-sequential approach is often inadequate since many process control challenges arise because of poor design of the process and may lead to overdesign of the process, dynamic constraint violations, and may not guarantee robust performance (Malcom, Polam, Zhang, Ogunnaike, & Linninger, 2007). Another drawback has to do with how process design decisions influence the controllability of the process. To assure that design decisions give the optimum economic and the best control performance, controller design issues need to be considered simultaneously with the process design issues. The research area of combining process design and controller design considerations is referred here as integrated process design and controller design (IPDC). One way to achieve IPDC is to identify variables together with their target values that have roles in process design (where the optimal values of a set of design variables are obtained to match specification on a set of process variables) and controller design (where the same set of design variables serve as the actuators or manipulated variables and the same set of process variables become the controlled variables). Also, the optimal design values become the set points for the controlled and manipulated variables. Using model analysis, controllability issues are incorporated to pair the identified actuators with the corresponding controlled variables. The integrated design problem is therefore reduced to identifying the dual purpose design-actuator variables, the process-controlled variables, their sensitivities, their target-set-point values, and their pairing.

The importance of an integrated process-controller design approach, considering operability together with the economic issues, has been widely recognized (Allgor and Barton, 1999, Bansal et al., 2000, Bansal et al., 2003, Kookos and Perkins, 2001, Luyben, 2004, Meeuse and Grievink, 2004, Patel et al., 2008, Ricardez Sandoval et al., 2008, Schweiger and Floudas, 1997). The objective has been to obtain a profitable and operable process, and control structure in a systematic manner. The IPDC has advantage over the traditional-sequential method because the controllability issues are resolved together with the optimal process design issues. Meeuse and Grievink (2004) used the Thermodynamic Controllability Assessment (TCA) technique to incorporate controllability issues into the design problem. The IPDC problem, however, involved multi-criteria optimization and needed trade-off between conflicting design and control objectives. For example, the process design issues point to design of smaller process units in order to minimize the capital and operating costs, while, process control issues point to larger process units in order to smooth out disturbances (Luyben, 2004).

A number of methodologies have been proposed for solving IPDC problems (Sakizlis et al., 2004, Seferlis and Georgiadis, 2004). In these methodologies, a mixed-integer nonlinear optimization problem (MINLP) is formulated and solved with standard MINLP solvers. The continuous variables are associated with design variables (flowrates, heat duties) and process variables (temperatures, pressures, compositions), while binary (decision) variables deal with flowsheet structure and controller structure. When an MINLP problem represents an IPDC, the process model considers only steady-state conditions, while a MIDO (mixed-integer dynamic optimization) problem represents an IPDC where steady state as well as dynamic behaviour is considered.

A number of algorithms have been developed to solve the MIDO problem. From an optimization point of view, the solution approaches for MIDO problems can be divided into simultaneous and sequential methods, where the original MIDO problem is reformulated into a mixed-integer nonlinear program (MINLP) problem (Sakizlis et al., 2004). The former method, also called complete discretization approach, transforms the original MIDO problem into a finite dimensional nonlinear program (NLP) by discretization of the state and control variables. Avraam, Shah, and Pantelides (1999), Flores-Tlacuahuac and Biegler (2007) and Mohideen, Perkins, and Pistikopoulos (1996) applied this complete discretization approach and solved the resulting MINLP problem using outer approximation (OA) and generalized Benders decomposition (GBD) frameworks. However, this method typically generates a very large number of variables and equations, yielding large NLPs that may be difficult to solve reliably (Exler et al., 2008, Patel et al., 2008), depending on the complexity of the process models.

As regards the sequential method, also called control vector parameterization approach, only control variables are discretized. The MIDO algorithm is decomposed into a sequence of primal problems (nonconvex DOs) and relaxed master problems (Bansal et al., 2003, Mohideen et al., 1997, Schweiger and Floudas, 1997, Sharif et al., 1998). Because of nonconvexity of the constraints in DO problems, such solution methods are possibly excluding large portions of the feasible region within which an optimal solution may occur, leading to the suboptimal solutions (Chachuat, Singer, & Barton, 2005).

In order to overcome convergence to the suboptimal solution in DO or MIDO problems, stochastic and deterministic global optimization (GO) methods have also been proposed. Regarding stochastic GO methods, a number of works have shown that the region of global solutions can be located with relative efficiency (Banga et al., 2003, Moles et al., 2003, Sendin et al., 2004), but they tend to be computationally expensive and have difficulties with highly constrained problems. Most importantly, their major drawback is that global optimality cannot be guaranteed. While deterministic GO methods can guarantee that the optimal performance has been found (Esposito & Floudas, 2000), however their applicability is limited only to problems with medium complexity (Moles et al., 2003).

The objective of this paper is to present an alternative systematic model-based IPDC approach that is simple to apply, easy to visualize and efficient to solve. Here, the IPDC problem is solved by the so-called reverse approach (reverse design algorithm) by decomposing it into four sequential hierarchical sub-problems: (i) pre-analysis, (ii) design analysis, (iii) controller design analysis, and (iv) final selection and verification (Hamid & Gani, 2008). Using thermodynamic and process insights, a bounded search space is first identified. This feasible solution space is further reduced to satisfy the process design and controller design constraints in sub-problems 2 and 3, respectively, until in the final sub-problem all feasible candidates are ordered according to the defined performance criteria (objective function). The final selected design is verified through rigorous simulation. In the pre-analysis sub-problem, the concepts of attainable region (AR) and driving force (DF) are used to locate the optimal process-controller design solution (see Section 2.4) in terms of optimal condition of operation from design and control viewpoints. While other optimization methods may or may not be able to find the optimal solution, depending on the performance of their search algorithms and computational demand, the use of AR and DF concepts is simple and able to find at least near-optimal designs (if not optimal) to IPDC problems.

This paper is organized as follows. First the new model-based IPDC methodology together with the decomposition into sub-problems and the methods used within the sub-problems are introduced in Section 2. Then, in Section 3, the application of the IPDC methodology in solving process design–controller design problems related to of a single reactor, a single separator, and a reactor–separator-recycle system are presented and discussed. Finally, future perspectives and conclusions are presented.