Optimal design of dynamic systems under uncertainty

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Abstract
Fundamental developments of a unified process design framework for obtaining integrated process and control systems design, which are economically optimal and can cope with parametric uncertainty and process disturbances, are described. Based on a dynamic mathematical model describing the process, including path constraints, interior and end‐point constraints, a model that describes uncertain parameters and time‐varying disturbances (for example, a probability distributions or lower/upper bounds), and a set of process design and control alternatives (together with a set of control objectives and types of controllers), the problem is posed as a mixed‐integer stochastic optimal control formulation. An iterative decomposition algorithm proposed alternates between the solution of a multiperiod “design” subproblem, determining the process structure and design together with a suitable control structure (and its design characteristics) to satisfy a set of “critical” parameters/periods (for uncertainty disturbance) over time, and a time‐varying feasibility analysis step, which identifies a new set of critical parameters for fixed design and control. Two examples are detailed, a mixing‐tank problem to show the analytical steps of the procedure, and a ternary distillation design problem (featuring a rigorous tray‐by‐tray distillation model) to demonstrate the potential of the novel approach to reach solutions with significant cost savings over sequential techniques.