Performance of discrete feedback adjustment schemes with dead band, under stationary versus nonstationary stochastic disturbance

Discrete dead-band adjustment schemes are often analyzed assuming that the disturbance may be approximately represented by a nonstationary integrated moving average (IMA) model. Sometimes, however, stationary autoregressive moving average (ARMA) models have been used for the same purpose. This article shows (a) that the IMA model leads to a much easier analysis, (b) that almost exactly the same average adjustment intervals (AAI's) and mean squared deviations (MSD's) are obtained under both disturbance models in the region of interest of the action limits, (c) that for wider action limits the ARMA disturbance overestimates the AAI and underestimates the MSD with respect to the results provided by the IMA disturbance, and (d) that the IMA disturbance model is robust against model misspecification but the ARMA model is not.