On the efficiency and robustness of discrete proportional-integral control schemes

Feedback control schemes have been widely used in process industries for many years. They are also increasingly being used in the discrete-parts manufacturing-industry in recent years. Proportional-integral (PI) schemes are especially popular, primarily because of their simple structure and ease of implementation. This article studies the efficiency and robustness properties of discrete PI schemes under some commonly encountered situations. For process disturbance, we consider the stationary ARMA (1, 1) model and the nonstationary ARIMA (1, 1, 1) model. Process dynamics is studied under a first-order dynamic model, including the special case of pure gain. The efficiency of PI schemes is compared with that of minimum mean squared error (MMSE) schemes under these models. The PI schemes are seen to be quite efficient over a broad range of the parameter space. Furthermore, the PI schemes are much more robust than MMSE schemes to model misspecifications, especially the presence of first-order nonstationarity. The results here provide additional justification for the use of discrete PI schemes.