Calculating Dynamic Disturbance Rejection Measures

A number of indicators for the determination of the disturbance rejection capability of a system have been proposed in the literature in the last two decades. These tools are useful for evaluating early stage process designs and screening regulatory control structures, since they are based on minimal modelling requirements. We study the evaluation of disturbance rejection measures proposed by Wolff and Skogestad. If acceptable values for these disturbance rejection measures are not achieved, no controller can achieve satisfactory control. Previoius publications have only shown how to evaluate these measures at steady state. In this paper, it is shown how to obtain upper and lower bounds for these disturbance rejection measures also as a function of frequency. Theupper and lower bounds can be made arbitrarily accurate at the expense of increasing the size of the optimization.