# Homework Help: Alternative Methods vs Iterative Design — Control Theory

Tags:
1. Apr 5, 2016

### ltkach2015

QUESTION (2/2)

1)

2)
I have a certain plant transfer function PTF(s) that is higher order than two and non-unity numerator.
I want certain characteristics such as a certain damping ratio (zeta).
So I want approximate it as second order (specially second order underdamped approximation)
I introduce controller whose transfer function is K(s) in the feed-foward direction, and a unity gain in (-) feedback
PTF(s) has open loop zeros which will become closed loop zeros (and a part of the denominator of the closed loop transfer function). So, I want to cancel the closed loop zeros with the higher order closed loop poles.
I impose the "Angle Design Criteria" in-conjuction with the second order approximation constraint, therefore I determine that the system would need a phase lead angle (e.g. -75.89 degrees)
This implies that the difference of controller's pole angles and zero angles is negative.
There must exist either only: one zero and no poles, or some combination that yields a negative angle.

So I introduce lag compensator which will increase the order of my system and introduce another closed loop zero
case1) K(s) = (s+z1); no poles, so I using angle criteria I can determine the zero location
or
case2) K(s) = (s+z2)/(s+p2); I set the zero arbitrarily, and determine pole location from angle criteria

So my OLTF = K(s)*PTF(s); (OLTF denotes open loop transfer function)

both cases may not satisfy the second order approximation constraints.

How can I analytically solve for pole and zero location that satisfy angle criteria and second order approximation constraints? (given the compensator chosen) Thank you.

Last edited: Apr 5, 2016
2. Apr 11, 2016