Chapter 6
Stability
(c) 2010 Farrokh Sharifi
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Objectives
To learn:
d
i
h
bili
f
How to determine the stability of a LTI system
using RouthHurwitz criterion
How to determine system parameters to yeild
stability
(c) 2010 Farrokh Sharifi
Introduction
(section 6 1)
Introduction
(section 6.1)
• Control Design Requirements:
Control Design Requirements:

Transient Response
 Stability (in this chapter)

Stability (in this chapter)

Steadystate Errors (next chapter)
•
Transient response and Steadystate Error are
meaningless for an unstable system
meaningless for an unstable system.
•
This chapter investigates stability for linear time
invariant (LTI) systems
(c) 2010 Farrokh Sharifi
invariant (LTI) systems.
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Introduction
•
What is stability?
•
System total response:
( )
( )
( )
c t
c
t
c
t
• If
results in
then the LTI system is
forced
natural
t
( )
natural
c
t
unstable.
• If
results in
then the LTI system is
t bl
t
( )
0
natural
c
t
stable.
• If
results in
remaining constant or
oscillating then the LTI system is marginally stable
t
( )
natural
c
t
(c) 2010 Farrokh Sharifi
oscillating, then the LTI system is marginally stable.