Root Locus - Why it is not possible to locate poles arbitrarilly?

[koochiee]

The root locus design method is used to locate poles at desired locations.
However, it is not possible to locate poles arbitrarily. Provide reasons for this statement.



K = 1/│G(s)H(s)│
K G(s)H(s) = (2k+1)π



I've formulated the answer for this as,
The root locus gives the path of the closed loop poles of the function for varying values of gain (K 0 to infinity). The reason for above statement is that, the values of poles (closed loop poles) are governed by the value of the gain.

Is this answer correct?

Thank you in advance for your help!

 

[Lancelot59]

Sounds right. To expand on that your poles follow a fixed path as the gain changes. Changing those base starting positions would mean changing your transfer function.

 

[koochiee]

Thank you very much for your answer Lancelot59! :)

 

[donpacino]

Typically you have a plant (your system), a feedback network, and a controller

as was already stated you cannot change your transfer function of the plant, so some of the poles are already in place.

root locus examines how adding an amplifier as a controller will change the closed loop poles of the system.
There is many ways you can arbitrarily place poles and zeros (kalman filters, low pass filter, high pass filters, band pass filters, notch filters, etc), however those can be complicated and possibly costly to implement. An amplifier is one component and relatively easy to implement.

Also using root locus to determine your optimal amplifier gain can make designing a control in other ways much easier.

 

[koochiee]

Thanks donpacino for the detailed answer.