Christopher L.E. Swartz

A computational framework for dynamic operability assessment

Abstract The interrelationship between a plant design and its closed-loop performance has led to an awareness that dynamic operability issues need to be considered at the plant design stage. This in turn motivates the need for systematic procedures whereby the operability of competing plant designs may be assessed. Particularly useful would be a measure of inherent plant operability, independent of controller type or tuning. A procedure for computing a measure of this type is presented in this paper. It utilizes Q-parametrization as a representation of feedback controllers which permits operability assessment to be posed as a convex optimization problem; the solution of which represents the best achievable performance for any linear feedback controller. The formulation of the method is presented and its application demonstrated through example problems.

Robust decision making for hybrid process supply chain systems via model predictive control

Abstract Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.

On the effects of constraints, economics and uncertain disturbances on dynamic operability assessment

It is desirable in chemical process design to select a design which is not only economically competitive but which would also yield satisfactory closed-loop performance. Dynamic operability reflects the ability with which a plant can be controlled and is typically assessed on the basis of the response to specific setpoint or disturbance changes. In this paper, dynamic operability in the face of arbitrary step-like disturbances within a specified range is considered. It is furthermore recognized that the best achievable closed-loop performance is dependent on the proximity of the operating point to the process constraints, which is in turn determined by the process economics and the expected disturbance range. These effects are included in a procedure which extends the operability assessment framework proposed by Swartz (1994). The application of the method is demonstrated on a simple single-input-single-output (SISO) process.

Design for dynamic performance: Application to an air separation unit

The significant effect that the design of a plant can have on its dynamic performance has led to methodologies for systemic analysis of the interaction between design and control, and for inclusion of dynamic performance considerations in plant design. In this paper, an optimization-based approach is presented for identifying design characteristics that limit plant agility in the face of production demand and electricity price changes. Responding optimally to such variation could have a significant impact on plant economics and operational efficiency. The problem formulation is described, and its efficacy demonstrated through application to a case study based on an industrial nitrogen production plant. Conclusions are drawn, and avenues for future research identified.

A mixed-integer formulation for back-off under constrained predictive control

The steady-state economic optimum in chemical process plants generally lies at the intersection of constraints. However, in order to maintain feasible operation in the face of disturbances, the steady-state operating point needs to be moved some distance from the constraints into the feasible region. The optimal back-off is a function of the plant dynamics, the type and magnitude of the expected disturbances, and the plant control system. This paper considers calculation of the optimal back-off with regulation under constrained predictive control. The resulting optimization problem is multilevel in nature, and is formulated and solved as a mixed-integer quadratic or linear programming problem for which global optimality is guaranteed. Case studies comprising CSTRs in series and a fluid catalytic cracking unit illustrate the application of the strategy.

Simultaneous Solution Strategies for Inclusion of Input Saturation in the Optimal Design of Dynamically Operable Plants

Recent work has considered the inclusion of input saturation in optimization-based integrated plant and control system design. Two mathematical formulations have been derived which allow saturation to be included within a simultaneous optimization framework; these are mixed-integer and bilinear formulations. The MIP formulation applied within an integrated design and control framework was found to be computationally intensive. This paper reviews these formulations and proposes an alternative solution strategy that uses an interior point approach to handle the complementarity constraints present in the bilinear formulation. A solution algorithm is presented and applied to an example problem.

Flexible maintenance within a continuous-time state-task network framework

Abstract Preventative maintenance is common in industry and aids in sustaining reliable process operations. If maintenance is executed within the production schedule, it imposes restrictions on the shared resources of the manufacturing facility. In multipurpose batch plants, these restrictions can affect many product pathways and have a significant impact on plant profitability. The combined optimization of process maintenance and production scheduling should therefore exploit the inherent flexibility of such plants and provide solutions with the highest profitability. This paper presents a mathematical model capable of addressing the combined scheduling of maintenance and production tasks within a continuous-time state-task network based framework. Multiple maintenance types are addressed within the framework. The proposed formulation is illustrated on an adaptation of a well cited literature problem, and the benefit of combined maintenance and production scheduling highlighted.

A regional convexity test for global optimization: Application to the phase equilibrium problem

This paper introduces a new method for testing the convexity of a function in an n-rectangular region of its domain which may be used in conjunction with a branch and bound global optimization algorithm to improve its convergence rate. The method makes use of interval analysis techniques together with a determinant test based on Schur complements. Its enhancement of a global optimization algorithm is demonstrated on a set of phase equilibrium problems which are formulated as nonconvex Gibbs energy minimization problems where the Gibbs energy function is modelled using the NRTL equation.

Flexibility analysis of process supply chain networks

Abstract One of the key fundamentals for organizations to remain competitive in the present economic climate is to effectively manage their supply chains under uncertainty. The notion of supply chain flexibility attempts to characterize the ability of a supply chain to perform satisfactorily in the face of uncertainty. However, limited quantitative analysis is available. In this work, we utilize a flexibility analysis framework developed within the context of process operations and design to characterize supply chain flexibility. This framework also provides a quantitative mapping to various types of flexibility discussed in the operations research and management science literature. Two case studies are included to illustrate the application of this framework for analyzing the flexibility of existing supply chain processes, as well as utilizing it in supply chain design.

An algorithm for hierarchical supervisory control

Abstract A scheme for implementing hierarchical steady-state control objectives is presented in this paper. These objectives are implemented through a supervisory controller which provides setpoints to a standard regulatory control system. The setpoints are calculated through a sequence of optimization subproblems structured in such a way that objectives of any assigned priority are not compromised in favor of objectives of lower priority. The given procedure has a useful property that feasibility of the first subproblem guarantees feasibility of all the remaining subproblems. The supervisory control structure includes a feedback mechanism to compensate for unmodeled disturbances. The performance of the proposed scheme is demonstrated through example problems. The relatively small dimension of the optimization subproblems, the structure of the proposed scheme as a supervisory system independent of the regulatory control system and the simplicity of the calculation procedure should make this method attractive for industrial implementation.