<s>
Because	O
it	O
only	O
looks	O
at	O
the	O
Nyquist	B-Application
plot	I-Application
of	O
the	O
open	O
loop	O
systems	O
,	O
it	O
can	O
be	O
applied	O
without	O
explicitly	O
computing	O
the	O
poles	O
and	O
zeros	O
of	O
either	O
the	O
closed-loop	O
or	O
open-loop	O
system	O
(	O
although	O
the	O
number	O
of	O
each	O
type	O
of	O
right-half-plane	O
singularities	O
must	O
be	O
known	O
)	O
.	O
</s>
<s>
In	O
contrast	O
to	O
Bode	B-Algorithm
plots	I-Algorithm
,	O
it	O
can	O
handle	O
transfer	O
functions	O
with	O
right	O
half-plane	O
singularities	O
.	O
</s>
<s>
Nevertheless	O
,	O
there	O
are	O
generalizations	O
of	O
the	O
Nyquist	O
criterion	O
(	O
and	O
plot	O
)	O
for	O
non-linear	O
systems	O
,	O
such	O
as	O
the	O
circle	O
criterion	O
and	O
the	O
scaled	O
relative	O
graph	O
of	O
a	O
nonlinear	B-Architecture
operator	I-Architecture
.	O
</s>
<s>
Techniques	O
like	O
Bode	B-Algorithm
plots	I-Algorithm
,	O
while	O
less	O
general	O
,	O
are	O
sometimes	O
a	O
more	O
useful	O
design	O
tool	O
.	O
</s>
<s>
A	O
Nyquist	B-Application
plot	I-Application
is	O
a	O
parametric	O
plot	O
of	O
a	O
frequency	O
response	O
used	O
in	O
automatic	O
control	O
and	O
signal	O
processing	O
.	O
</s>
<s>
The	O
most	O
common	O
use	O
of	O
Nyquist	B-Application
plots	I-Application
is	O
for	O
assessing	O
the	O
stability	O
of	O
a	O
system	O
with	O
feedback	O
.	O
</s>
<s>
The	O
Nyquist	B-Application
plot	I-Application
is	O
named	O
after	O
Harry	O
Nyquist	O
,	O
a	O
former	O
engineer	O
at	O
Bell	O
Laboratories	O
.	O
</s>
<s>
Assessment	O
of	O
the	O
stability	O
of	O
a	O
closed-loop	O
negative	O
feedback	O
system	O
is	O
done	O
by	O
applying	O
the	O
Nyquist	O
stability	O
criterion	O
to	O
the	O
Nyquist	B-Application
plot	I-Application
of	O
the	O
open-loop	O
system	O
(	O
i.e.	O
</s>
<s>
The	O
Nyquist	B-Application
plot	I-Application
can	O
provide	O
some	O
information	O
about	O
the	O
shape	O
of	O
the	O
transfer	O
function	O
.	O
</s>
<s>
When	O
drawn	O
by	O
hand	O
,	O
a	O
cartoon	O
version	O
of	O
the	O
Nyquist	B-Application
plot	I-Application
is	O
sometimes	O
used	O
,	O
which	O
shows	O
the	O
linearity	O
of	O
the	O
curve	O
,	O
but	O
where	O
coordinates	O
are	O
distorted	O
to	O
show	O
more	O
detail	O
in	O
regions	O
of	O
interest	O
.	O
</s>
<s>
Conclusions	O
can	O
also	O
be	O
reached	O
by	O
examining	O
the	O
open	O
loop	O
transfer	O
function	O
(	O
OLTF	O
)	O
,	O
using	O
its	O
Bode	B-Algorithm
plots	I-Algorithm
or	O
,	O
as	O
here	O
,	O
its	O
polar	O
plot	O
using	O
the	O
Nyquist	O
criterion	O
,	O
as	O
follows	O
.	O
</s>
<s>
The	O
Nyquist	B-Application
plot	I-Application
of	O
,	O
which	O
is	O
the	O
contour	O
will	O
encircle	O
the	O
point	O
of	O
the	O
plane	O
times	O
,	O
where	O
by	O
Cauchy	O
's	O
argument	O
principle	O
.	O
</s>
<s>
If	O
instead	O
,	O
the	O
contour	O
is	O
mapped	O
through	O
the	O
open-loop	O
transfer	O
function	O
,	O
the	O
result	O
is	O
the	O
Nyquist	B-Application
Plot	I-Application
of	O
.	O
</s>
<s>
We	O
now	O
note	O
that	O
gives	O
us	O
the	O
image	O
of	O
our	O
contour	O
under	O
,	O
which	O
is	O
to	O
say	O
our	O
Nyquist	B-Application
plot	I-Application
.	O
</s>
<s>
In	O
fact	O
,	O
we	O
find	O
that	O
the	O
above	O
integral	O
corresponds	O
precisely	O
to	O
the	O
number	O
of	O
times	O
the	O
Nyquist	B-Application
plot	I-Application
encircles	O
the	O
point	O
clockwise	O
.	O
</s>
<s>
If	O
the	O
open-loop	O
transfer	O
function	O
has	O
a	O
zero	O
pole	O
of	O
multiplicity	O
,	O
then	O
the	O
Nyquist	B-Application
plot	I-Application
has	O
a	O
discontinuity	O
at	O
.	O
</s>
<s>
If	O
the	O
open-loop	O
transfer	O
function	O
is	O
stable	O
,	O
then	O
the	O
closed-loop	O
system	O
is	O
unstable	O
,	O
if	O
and	O
only	O
if	O
,	O
the	O
Nyquist	B-Application
plot	I-Application
encircle	O
the	O
point	O
−1	O
at	O
least	O
once	O
.	O
</s>
