Backshift operator

For more effective notation it is necessary to introduce the backshift operator B ... 

Therefore, the backshift operator furnishes easy notation for processes dependent on the past. 

Irrespective of the situation, process system identification is focused on determining the values for Gp and G/ as accurately as possible. Since most of the applications assume that the controller is digital, the system identification methods considered here will focus on the discrete time implementation of system identification. For this reason, the models for each of the blocks will be assumed to be linear, rational functions of the backshift operator Such models are most often referred to as transfer functions. The most general plant model is the prediction error model, which has the following form ... 

The dependence of the -functions on the backshift operator is made explicit in this formulation. The backshift operator has not been considered in any of the other transfer functions in order to keep the notation simple. 

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