Parametrically robust control-integrated design of nonlinear systems

Abstract:
An approach is presented which allows to incorporate constraints on the system dynamics into the optimization based design of nonlinear systems. In this approach, boundaries in the parameter space of the nonlinear system are taken into account, at which desired dynamics characteristics of the system are lost. These boundaries can be defined, for example, by a critical value of the real part of the leading eigenvalue of the linearized system, or by a restriction of eigenvalues to an angular sector in the complex plane. We stress that even though linearizations may be involved when defining the boundaries of interest, the boundaries themselves apply to the nonlinear system. Parametric robustness is guaranteed by staying off the boundaries at a user specified distance in the parameter space. This ensures that the desired dynamics characteristics will be met despite of parametric uncertainty or parameter drift. The proposed method can be applied both to system and controller parameters, thus allowing for an optimization based integrated system and controller design. We illustrate the approach by an application to a simple model of a continuous fermentation process.

Keywords:
Nonlinear systems design, robustness, stability, optimization.

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