A Robustness Study of Process Control Loops Designed Using Exact Linearization

Exact linearization is often applied to control nonlinear processes. This method requires not only the knowledge of the model structure but also the accurate parameter values. If the real parameter values of the controlled process are different from the nominal values used for the exact linearization, the resulting system may not be linear or may have different gains and time constants as expected. A simple procedure is suggested that allows first the parameter grid based characterisation of the composition of the uncertain nonlinear system and its linearizing feedback for the nominal parameters and then the design of a $H_\infty$ controller. The approach is illustrated by simple examples including 1st order systems and the nonlinear Van der Pol oscillator.