On quantisation and other bounded nonlinearities in first-order discrete multivariable control

Recent work on the use of discrete first-order approximate models of plant dynamics in multi-variable process control is extended to consider the effect on transient performance of nonhinearities, such as measurement quantisation or dead-zone at the implementation stage. Explicit upper bounds on the transient error induced by the nonlinearity are obtained and their validity illustrated by numerical examples. In particular, at fast sampling rates, it is seen that, not only does the first-order controller produce a closed-loop system with rapid, nonoscillating responses and small interaction effects, but it also ensures that peak transient errors owing to the nonlinearity are less than the error involved in approximating the nonlinearity by a unity gain matrix. For example, if the nonlinearity is measurement quantisation, the peak transient effects of the quantisation will be bounded by the quantisation error itself at fast sampling rates, and will not be amplified by system dynamics.