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**QUESTION (2/2)**

1)What are some alternatives to iterative design in control theory?

1)

**I have a certain plant transfer function PTF(s) that is higher order than two and non-unity numerator.**

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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.**

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