How much positive phase can we realistically expect from a C

How much positive phase can we realistically expect from a CT PID controller C(S) = K(T_ZS + 1)^N/S(T_pS + 1) with N=2: About 150deg. About 50deg. About 180deg. About 90 degree None of the above.

Solution

Ans) About 90 deg

with N=2 there is double pole at s=-1/Tz which gives +180 deg phase and also there is pole at origin s=0 which

gives -90 deg phase and also there is a pole at s=-1/Tp For maximum poitive phase we can eliminate this by making Tp=0 so its contribution is 0 then

Now net phase is +180-90= +90 deg