The optimal control structure has been introduced as a design tool to measure the control-law nonlinearity of a given process design. In this context, control-law nonlinearity is the optimal degree of nonlinear compensation in the controller, a system property distinct from open-loop nonlinearity and determined by a performance objective and the region of operation as well as the nature of the open-loop system. This approach is extended to the analysis of multivariable systems with output feedback through the application of an extended Kalman filter. Coherence estimation is used as a practical method to measure continuous, open-loop multivariable system nonlinearity. The CSTR with van de Vusse kinetics, a system that features output feedback and a controllaw nonlinearity that changes with operating points, is analyzed. The optimal control structure approach with coherence estimation correctly indicates changes in the controllaw linearity between different operating points and changes as the regions of operation change around a particular operating point.
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