Version 1.0, August 31, 2001, Copyright, Hugh Jack 1993-2001

5.3 BLOCK DIAGRAMS AND TRANSFER FUNCTIONS

· Block diagrams are the primary tool for showing process and control system models.

· In a block diagram each block has one input and one output.

· A transfer function provides functions that are a ratio of block output to block input.

· Consider the block diagram seen before, but with transfer functions (ratio of output to input) shown for the controller and process.

· Both of the transfer functions are ratios of inputs to outputs,

· These transfer functions (ratios) are rarely a simple multiplication, and so we need to use an alternate representation called a `transform'.

· In this case we will use a backshift transform, hence the `B' in the representation.

· equations for the block diagram below,

· Recall the techniques for block diagram manipulation.

5.3.1 The Backward-Shift `B' Operator