C.K. Pithawalla College of
Engineering & Technology
Subject :Control Engineering
Branch :- Mechanical
Division
Sem
Group
Enrol. No.
Roll No
:- B
:- 5th
:- B1(1)
:- 130090119003, 06, 07,
10, 01, 09
:- 131903, 06, 07, 10, 01, 09
Presentation Topic
Concept of Stability
Stability of Control Systems
Relative Stability
Concept of Stability
Concept of Stability
Concept of Stability
The first ball shown in the image
below, indicates stability while second
indicates instability.
Types of Control Systems
According to Stability
 According to stability of the system,
the control systems can be classified
in to three different categories shown
below :
1) Stable System
2) Unstable System
3) Marginally Stable System
1. Stable System
A system is said to be stable if for a
bounded input, the response of the
system is bounded.
In the absence of an input, a stable
system approaches infinity
irrespective of the initial conditions.
The above condition is known as the
Bounded input Bounded output (BiBo)
condition.
1. Stable System
By bounded input we mean, that the
values of x(t) within certain limits e.g.
0-230 V.
If the input itself is not bounded, we
cannot blame the system for giving an
unbounded output.
It is important to note that every
working system is stable.
2. Unstable System
A system is said to be unstable if for a
bounded input, the system produces
an output which goes on increasing
without any bounds and the designer
has no control over it.
An unstable system whose response
grows without bounds can cause
damage to the system, adjacent
property and also to human life.
2. Unstable System
As engineering students, we must
have all used bread boards and
designed basic circuits on them.
Heating up of IC’s and eventually
burning off is a result of the system
becoming unstable.
One will not find an unstable system
in working condition.
3.
Marginally Stable System
A system is said to be marginally stable if
the output of the system does not go down
to zero or does it go on increasing.
The output of a marginally stable system
oscillates in a finite range.
In all the diagram shown in next slide,
the input is kept the same.
Hence the response naturally depends on
the system.
Stability of A System
Relative Stability
In a practical system it is not merely
sufficient to know whether the system is
stable.
It is also Important to know the relative
stability of that system.
Relative stability is a measure of how fast
the transients dies out in the system.
Relative stability is related to the settling
time.
Relative Stability
Settling time is inversely proportional
to the real negative part of the roots.
This simply means farther the pole
from the origin (LHP), shorter is the
settling time.
In short, a system having poles far
away from the jw-axis is more stable
than a system having poles close to
the jw-axis.
Thank You