J.D. Perkins

On the design of robust two degree of freedom controllers

Abstract The aim of this paper is to introduce two methods of designing robust two degree of freedom (TDF) controllers. Both design procedures will be illustrated and evaluated on a high purity distillation column example. In the first approach the feedback controller and the prefilter are designed in a single step using an H ∞ optimization procedure. The second method optimizes the feedback controller and prefilter in two separate design stages. Roughly speaking, the feedback controller is designed to meet robust stability and disturbance rejection specifications, while the prefilter is used to improve the robust model matching properties of the closed loop system. The single step approach has the advantages that it is easy to use, and that the resulting controller degree is the same as that of the plant. The two stage approach offers greater design flexibility and it may produce robust stability and robust performance margins which are significantly bigger than those achievable with the single stage approach. Set against that, the two stage technique is more difficult to use and it produces controllers which may have an order which is significantly bigger than that of the plant.

Recent advances in optimization-based simultaneous process and control design

Abstract In this work, we first discuss recent advances towards the integration of process design, process control and process operability from the open literature and then we focus on techniques towards this endeavor that were developed within our group at Imperial College. While most of the approaches employ controllability measures to achieve this goal, our developments can be classified as a simultaneous process and control design methodology. Based on novel mixed integer dynamic optimization algorithms, our strategy features high fidelity process dynamic models, conventional PI control schemes, explicit consideration of structural process and control design aspects (such as number of trays, pairing of manipulated and controlled variables) through the introduction of 0–1 variables, and explicit consideration of time-varying disturbances and time-invariant uncertainties. The application of this strategy to a typical distillation system is discussed. In the second part of this chapter we present an extension of the process and control design framework that incorporates advanced model-based predictive controllers. Parametric programming is used for the controller derivation giving rise to a closed-form controller structure and removing the need for solving an optimization problem on-line. The resulting parametric controller is readily incorporated in the design optimization framework bringing about significant economic and operability benefits. The key features and advantages of this approach are highlighted via a simple binary distillation example.

Design of robust model-based controllers via parametric programming

In this paper a method is presented for deriving the explicit robust model-based optimal control law for constrained linear dynamic systems. The controller is derived off-line via parametric programming before any actual process implementation takes place. The proposed control scheme guarantees feasible operation in the presence of bounded input uncertainties by (i) explicitly incorporating in the controller design stage a set of feasibility constraints and (ii) minimizing the nominal performance, or the expectation of the performance over the uncertainty space. An extension of the method to problems involving target point tracking in the presence of persistent disturbances is also discussed. The general concept is illustrated with two examples.

New algorithms for mixed-integer dynamic optimization

Abstract Mixed-integer dynamic optimization (MIDO) problems arise in chemical engineering whenever discrete and continuous decisions are to be made for a system described by a transient model. Areas of application include integrated design and control, synthesis of reactor networks, reduction of kinetic mechanisms and optimization of hybrid systems. This article presents new formulations and algorithms for solving MIDO problems. The algorithms are based on decomposition into primal, dynamic optimization and master, mixed-integer linear programming sub-problems. They do not depend on the use of a particular primal dynamic optimization method and they do not require the solution of an intermediate adjoint problem for constructing the master problem, even when the integer variables appear explicitly in the differential–algebraic equation system. The practical potential of the algorithms is demonstrated with two distillation design and control optimization examples.

A mixed integer optimization formulation for the well scheduling problem on petroleum fields

In this paper, we present a novel mixed integer nonlinear (MINLP) model for the daily well scheduling in petroleum fields, where the nonlinear reservoir behaviour, the multiphase flow in wells and constraints from the surface facilities are simultaneously considered. Discrete decisions include the operational status of wells (open or closed), the allocation of wells to manifolds or separators and the allocation of flow lines to separators. Continuous decisions include the well oil rates and the allocation of gas-to-gas lift wells. A solution strategy is proposed involving (i) logic constraints, (ii) inclusion of piecewise linear approximations of each well model and (iii) an outer approximation based algorithm. A number of examples illustrate the applicability of the proposed model and solution strategy where an increase in oil production up to 10% is observed when the results of the proposed method are compared with typical heuristic rules widely applied in practice.

Simultaneous design and control optimisation under uncertainty

Abstract This paper demonstrates how the design and control of processes described by large-scale, complex, mixed-integer dynamic models can be simultaneously optimised in the face of time-varying disturbances and parametric uncertainties. A rigorously modelled distillation example is used for this purpose, where the number of trays, feed location, column diameter, surface areas of the heat exchangers and tuning parameters of the controllers are selected in order to minimise the total annualised cost of the system, while satisfying a large number of feasibility constraints.

Optimization as a tool for design/control integration

Abstract There is a long tradition of the use of optimization techniques to help solve process synthesis and design problems. Advances in optimization algorithms to handle problems involving integer variables, and problems involving dynamic systems with path constraints have recently been exploited to help address issues in the integration of process design and control. Methods, based on optimization, to assess controllability, to select control structures for a given process (the control system synthesis problem) and to develop integrated designs of process and control system for cases where dynamic performance is critical are presented in this paper.

An algorithmic method for the selection of multivariable process control structures

Abstract In process systems, the selection of suitable sets of manipulated and controlled variables and the design of their interconnection, known as the control structure selection problem, is an important structural optimisation problem. The operating performance of a plant depends on the control structure selected as well as the characteristics of the disturbances acting on the plant. The economic penalty associated with the variability of main process variables close to active constraints is used in this work in order to develop a quantitative measure for the ranking of alternative control structures. Based on this measure, a general methodology is presented for the generation of promising control structures where general centralised, linear time invariant, output feedback controllers are used to form the closed loop system. The special case of optimal static output feedback controllers is further investigated in this paper. Furthermore, the problem of selecting proper weights in forming quadratic integral performance indices in designing optimal multivariable controllers is addressed. The validity and usefulness of the method is demonstrated through a number of case studies.

Robust stability considerations in optimal design of dynamic systems under uncertainty

Abstract This paper presents a method for the incorporation of robust stability criteria in the design of dynamic systems under uncertainty. Process systems are modelled via dynamic mathematical models, variations include both uncertain parameters and time-varying disturbances, while control structure selection and controller design is considered as part of the design optimization problem. Stability criteria are included, based on the concept of the measure of a matrix, to maintain desired dynamic characteristics, in a multiperiod design formulation. A combined flexibility-stabiluty analysis step is also introduced to ensure feasible and stable operation of the dynamic system in the presence of parametric uncertainties and process disturbances. The potential of the proposed approach is illustrated with a ternary distillation column design and control problem (featuring a rigorous tray-by-tray model).

Interactions Between Process Design and Process Control

Abstract Techniques to consider aspects of process control during the early stages of process design are considered in this paper. A survey of existing theory and its application to process examples is given. Needs for further developments are identified.