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

In this work the normal vector method is extended to the simultaneous treatment of parametric uncertainty and disturbances. This method ensures that desired dynamic properties hold despite parametric uncertainty by maintaining a minimal distance between the operating point and so-called critical manifolds where the process behavior changes qualitatively. Here, unknown exogeneous disturbances and uncertain model and process parameters are considered simultaneously. To address this simultaneous problem formulation, the augmented systems developed for only parameterized disturbances in previous works have to be modified and extended. A generalized formulation of the robust optimization problem results, which includes normal vector constraints on critical manifolds of steady states and of bounds on the state transient. The numerical methods are further developed to prepare for the treatment of high-dimensional problems. Illustrative case studies considering the design of a continuous mixed-suspension mixed-product removal crystallization process and the Tennessee Eastman process are presented.