Abstract :
The polynomial system approach has been widely used to formulate the LQG controller for industrial processes. The plant is usually represented as an ARMA-type model using the forward shift operator, z. The model is based on a time interval necessary for data processing and analogue-to-digital and digital-to-analogue conversions. The controller is thus applied discretely in contrast to continuous controller where the system input is continuously processed. The performance of the discrete controller can be improved and made closer to the continuous one by reducing the sample time. Numerical problems are, however, associated with fast sampling rates. When the sampling period is shortened, the ARMA model exhibits numerical ill-behaviour. Various problems resulting from this approach are listed. In order to overcome the limitations associated with the backward shift operator, a difference type discrete operator is used. This operator is employed here to formulate an LQG control law which is numerically more reliable than its counterpart in the z domain. It is shown that the discrete controller approaches the continuous one when the sampling period tends to zero. The controller is derived for the general system. Ship rolling motions are considered as an illustrative example
