ME-314 Control Systems
Lecture 6
• Modeling in the Frequency Domain
– Block Diagrams
• Block Diagrams are used to describe the
component parts of a system.
• They offer an alternative to dealing directly with
equations.
• All block diagrams are made up of three
fundamental elements:
‒ Block
‒ Summer
‒ Junction (or pickoff point)
‒ A block is used to indicate a proportional relationship
between two Laplace-transformed signals. The
proportionality function (actually the transfer function
or transmittance), relates incoming and outgoing
signals and is indicated within the block.
– A summer is used to show addition or subtraction of
signals. A summer can have any number of incoming
signals, but only one outgoing signal. The algebraic
signs to be used in the summation are indicated next
to the arrowhead for each incoming signal.
– A junction or a pickoff point indicates that the same
signal has to go several places.
• Block Diagram Reduction
‒ Rearranging system block diagrams to effect
simplification or special structures is termed block
diagram algebra.
‒ Since the block diagrams represent Laplacetransformed system equations, manipulating a
block diagram is equivalent to algebraic
manipulation of original equations.
‒ For a single input, single output block diagram,
reduction means simplifying the block diagram to
the point where it is a single block, displaying the
transfer function relating the output to the input.
• Basic Simplification Rules of Thumb
‒ Cascade or Series
‒ Tandem or Parallel
‒ Feedback Configuration
In feedback configuration above, signs of the
feedback signal are reversed when written inside
the block after the simplification is effected.
• Other Useful Block Diagram Equivalence
(i) Moving a block to the left past a summing junction
(j) Moving a block to the right past a summing junction
• Example 1
• Example 2
• Reading Assignment
– Reference Book 2 / Chapter 1 / Topic 1.13.
– Text Book / Chapter 5 / Topic 5.2