On Quantization and Other Bounded Non-Linearities in First Order Discrete Multi-Variable 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 non-linearities such as measurement quantization or deadzone at the implement stage. Explicit upper bands on the transient error induced by the nonlinearity are obtained and their validity illustrated by nemerical 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, non-oscillating responses and small interaction effects, it also ensures that peak transient errors due to the non-linearity are less than the error involved in approximating the non-linearity by a unity grain matrix. For example, if the nonlinearity is measurement quantization, the peak transient effects of the quantization will be bounded by the quantization error itself at fast sampling rates, and will not be amplified by system dynamics.