V. Bansal

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.

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.

The interactions of design and control: double-effect distillation

Abstract A general, rigorous dynamic model is described for studying the interactions of design and control in a double-effect distillation system. Two approaches are adopted. In the first, the steady-state process design and the control system are optimized sequentially ; potential operability bottlenecks are identified and the economic advantage of double-effect systems over conventional single column systems is demonstrated. In the second approach, the process design and the control system are optimized simultaneously leading to a more economically beneficial system than that obtained using the sequential approach.

Flexibility analysis and design of dynamic processes with stochastic parameters

In this paper, we present theoretical developments for the analysis and design of linear dynamic process systems in the presence of uncertain parameters, described by Gaussian probability distribution functions. The concept of the stochastic flexibility index, as a metric for quantifying the ability of a process to maintain feasible operation in the face of stochastic uncertainties, is first extended to linear dynamic models. A detailed procedure for evaluating the stochastic flexibility over time, is then outlined. This procedure fully exploits the mathematical properties of the system to enable derivation of analytical expressions describing the dynamic feasible region. These expressions are then used as constraints in a single-stage design formulation for the determination of an economically optimal process design that meets a desired stochastic flexibility target over the entire time horizon of interest. With this formulation, the trade-offs between cost and target flexibility can be investigated. A numerical example is used to demonstrate the potential of the techniques.

Optimal design and control of an industrial distillation system

Abstract In this paper, an industrial distillation system, designed in a traditional manner without considering the interactions of design and control, is introduced and shown to be severely ill-conditioned. Through rigorous modelling and sensitivity analyses, a new control scheme is first proposed for overcoming the operational difficulties. A simultaneous optimization approach is then implemented to highlight the economic and operability benefits that could have been obtained if design and control interactions had been systematically considered in the first place.

Using mathematical programming to compute singlular multivariate normal probablities

This paper describes two new, mathematical programming-based approaches for evaluating general, one- and two-sidedp-variate normal probabilities where the variance-covariance matrix (of arbitrary structure) is singular with rankr(r<pand r and p can be of unlimited dimensions. In both cases, principal components are used to transform the original, ill-definedp-dimensional integral into a well-definedrdimensional integral over a convex polyhedron. The first algorithm that is presented uses linear programming coupled with a Gauss-Legendre quadrature scheme to compute this integral, while the second algorithm uses multi-parametric programming techniques in order to significantly reduce the number of optimization problems that need to be solved. The application of the algorithms is demonstrated and aspects of computational performance are discussed through a number of examples, ranging from a practical problem that arises in chemical engineering to larger, numerical examples.

A unified framework for the flexibility analysis and design of non-linear systems via parametric programming

Publisher Summary This chapter discusses a new framework based on parametric programming that unifies the solution of the various flexibility analyses and design optimization problems that arise for linear, convex, and nonconvex systems with deterministic or stochastic uncertainties and provides new information on the dependence of a systems flexibility on the values of the design variables. For systems with stochastic parameters described by any kind of continuous probability distribution, the procedures for evaluating the stochastic flexibility and the expected stochastic flexibility metrics are identical for both linear and nonlinear models once the parametric feasibility function expressions have been generated. The use of these expressions is, especially significant for nonlinear systems because they remove all nonlinearity from the intermediate optimization subproblems, something that would not be possible using nonparametric approaches. By considering the subproblems as multiparametric linear programs, the number of problems that needs to solved compared to existing approaches is drastically reduced, because it only increases linearly with the number of uncertain parameters as opposed to exponentially, and parametric information that allows the metrics to be evaluated for any structure and design through a series of function evaluations is obtained.