A normal vector approach for integrated process and control design with uncertain model parameters and disturbances

Abstract:
In this work the normal vector method for robust design is extended to the simultaneous treatment of parametric uncertainty and disturbances. The normal vector method ensures that desired dynamic properties hold despite model and process uncertainty by maintaining a minimal distance between the operating point and so-called critical manifolds where the process behavior changes qualitatively. In this paper, unknown exogeneous disturbances and uncertain model and process parameters are considered simultaneously for the first time in the context of the normal vector method. In order to implement this simultaneous problem formulation, the augmented systems presented in [J. Gerhard, W. Marquardt, and M. Mönnigmann, Normal vectors on critical manifolds for robust design of transient processes in the presence of fast disturbances, SIAM J. Appl. Dyn. Syst. (2) (2008)] have to be modified to include uncertain model parameters in addition to time-varying exogeneous disturbance. A generalized formulation of the robust optimization problem is given including normal vector constraints on critical manifolds of steady states and of bounds on the state transient. Finally a case study for a continuous mixed-suspension mixed-product removal (MSMPR) crystallization process is presented.

Keywords:
grazing bifurcation, robustness, robust stability, robust optimization, robust performance, disturbances, normal vector, crystallization process.

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