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hapter 6
Chapter 6
Stability
(c) 2010 Farrokh Sharifi
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View Full Document bjectives
Objectives
o learn:
To learn:
How to determine the stability of a LTI system
using RouthHurwitz criterion
How to determine system parameters to yeild
stability
(c) 2010 Farrokh Sharifi
troduction
ection 6 1)
Introduction
(section 6.1)
•
ontrol Design Requirements:
Control Design Requirements:
 Transient Response
tability (in this chapter)
 Stability (in this chapter)
 Steadystate Errors (next chapter)
• Transient response and Steadystate Error are
eaningless for an unstable system
meaningless for an unstable system.
• This chapter investigates stability for linear time
variant (LTI) systems
(c) 2010 Farrokh Sharifi
invariant (LTI) systems.
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Introduction
• What is stability?
y
• System total response:
)
()
t
c
t
c
t
• If
results in
then the LTI system is
forced
natural
ct
t
natural
unstable.
• If
results in
then the LTI system is
b
l
t
0
natural
stable.
• If
results in
remaining constant or
scillating then the LTI system is marginally stable
t
natural
(c) 2010 Farrokh Sharifi
oscillating, then the LTI system is marginally stable.
troduction
Introduction
• If the input is unbounded, forced response could be
unbounded as well. (Hard to determine the stability)
ounded
put Bounded
utput (BIBO) Stability:
•
BoundedInput BoundedOutput (BIBO) Stability:

systemis
able
every
ounded
put yields a
A system is
stable
if every
bounded
input yields a
bounded
output. (stable systems)
 A system is
unstable
if every
bounded
input yields a
unbounded
output. (marginally stable and unstable
systems)
(c) 2010 Farrokh Sharifi
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Introduction
ow to determine if a system is stable?
How to determine if a system is stable?
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This note was uploaded on 02/20/2011 for the course MEC 709 taught by Professor Sharifi during the Fall '11 term at Ryerson.
 Fall '11
 Sharifi

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