# Controller design

#### dEEP6ix

I need to design a lead/lag controller for the following 3rd order close loop transfer function using the root locus method:

(11.35)(1.62)
-------------------------------
(s^2 + 1.84 s + 11.35)(s + 1.62)

The design requirement is just to reduce the settling time from the orginal 2.85s to 1.2s for a unit step input. I have tried adding a lead controller hoping to improve the transient response of the system. However, I soon discovered that I was just varying the gain, zero and pole in a trial and error method and it is getting me nowhere.

I have tried looking for information in control textbook but most of the examples are on 2nd order system. Those examples on higher order systems are always approximated to 2nd order systems which could not be done in the above transfer function.

Is there any systematic approach to zero/pole placement for higher order systems? Should I use a lag compensator instead? Any help is greatly appreciated.

http://www.freeimagehosting.net/image.php?72420b1ba8.jpg

http://www.freeimagehosting.net/image.php?6b83e7173f.jpg

Last edited:
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#### CEL

I need to design a lead/lag controller for the following 3rd order close loop transfer function using the root locus method:

(11.35)(1.62)
-------------------------------
(s^2 + 1.84 s + 11.35)(s + 1.62)

The design requirement is just to reduce the settling time from the orginal 2.85s to 1.2s for a unit step input. I have tried adding a lead controller hoping to improve the transient response of the system. However, I soon discovered that I was just varying the gain, zero and pole in a trial and error method and it is getting me nowhere.

I have tried looking for information in control textbook but most of the examples are on 2nd order system. Those examples on higher order systems are always approximated to 2nd order systems which could not be done in the above transfer function.

Is there any systematic approach to zero/pole placement for higher order systems? Should I use a lag compensator instead? Any help is greatly appreciated.

http://www.freeimagehosting.net/image.php?72420b1ba8.jpg

http://www.freeimagehosting.net/image.php?6b83e7173f.jpg
A lag compensator will only improve your steady-state response (reduction of ss error). For improving transient response you need a lead compensator.
Since you want a 1.2s settling time, you can calculate the real part of your dominant poles.
Normally yoou would want the damping coefficient to remain constant. Now you can calculate the desired position of your dominant poles. Since you want those poles to belong to the root-locus, you want that the angles from them to the open loop poles and zeros (including plant and compensator) to be an odd multiple of 180.
Place the zero of the compensator over the real pole of the plant and calculate the position of the pole of the compensator in order to achieve the angle condition.

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