Correlation of process nonlinearity with closed-loop disturbance rejection

In this work, correlations between control-relevant nonlinearity and the achievable performance of a variety of control structures are investigated for two processes. Each process' degree of open-loop nonlinearity is assessed using a numerical nonlinearity measure and then compared to the performance results for a set of controllers of varying complexity in disturbance rejection. The results for an experimental quadruple-tank process indicate an extremely low degree of control-relevant nonlinearity, agreeing with the open-loop nonlinearity assessment and the mild performance specification. Given tunings optimized for low-frequency output disturbance rejection, a bioreactor model demonstrates a mild degree of control-relevant nonlinearity when output disturbances are considered and a relatively high degree of control-relevant nonlinearity for input disturbance rejection. The bioreactor thus demonstrates the need to assess properly control-relevant nonlinearity in terms of desired performance and to consider the effects of controller tuning on the nonlinearity of the closed-loop operators.