angle of departure in root locus

[garimella]

This is a elementary question on angle of departure of root locus.
As shown in the figure below, why is angle of s1 taken from real axis?

I did not find much of explanations in text books on this.

 

[KlausST]

Hi,

this is the usual way. from X-axis and usually counter clockwise.

like: cos(phi) for phi = 0 --> = 1 = real = real axis

Klaus

 

[garimella]

For all other poles, we are considering the inner angle. Only for the pole at origin, we are considering the external angle? Why? What is the logic?

 

[KlausST]

Hi,

Please tell where you see some difference...I don't see it.

Klaus

 

[garimella]

I have attached image with angles marked in blue. For pole at zero, why not consider the inner angle?. But for a pole at s=-5, inner angle is considered.

 

[garimella]

Should we consider direction of rotation of vector? Is that the logic?

 

[KlausST]

Hi,

I don´t know how your software treats vectors...

But from my school knowledge:
* a vector has no defined starting point
* a vector has no defined end point
* a vector has a defined length
* a vector has a defined direction - given as angle referenced to the x-axis.

Klaus

 

[garimella]

Hi KlausST

I was asking about the logic for not taking inner angle. Angles marked in blue are also with respect to x axis.

 

[KlausST]

Hi,

it seems I misunderstand....

What exactly do you mean with "inner angle"?

as already said in post#2 :
"... this is the usual way. from X-axis and usually counter clockwise. .."
One of your blue lines is from (negative) X-axis but clockwise..

I don´t know any "inner angle" when talking about vectors.


Klaus

 

[wwfeldman]

the standard for measuring angles is counterclockwise from the +x axis.

the angle marked for the pole at the origin, s1, is measured that way.
the blue line you added at that pole is not the correct way to measure the angle.

the pole at -1 -j is measured correctly - counterclockwise from the +x axis
since the start is not at the origin, we treat it as is the start is at the origin

the other poles and zeros on the x axis are alos measured that way -
since they are not at the origin, we treat it as if the origin was at the start
of the vector, measure counterclockwise from the +x axis

the angle theta for the pole at -1+j is also measured correctly,
using the same CCW from + x axis

i take it from your blue additions that "inner" means the acute angle
so that at the origin, the obtuse (outer?) angle is CCW from +x axis
and the acute angle (inner?) is CW from the -x axis

for those raised on digital clocks, counterclockwise is the direction
of rotating the +x axis about the origin toward the +y axis
and clockwise is the other rotational direction