Design the following controllers

a$)$ A lag controller that loses between $10$ db and $11$ db in amplitude and less than $5$ in phase at $=3.$

b$)$ A lag controller that loses between $19$ db and $20$ db in amplitude and less than $10$ in phase at $=3.$

c$)$ A lag controller with $=\frac{1}{4}$ losing more than $11db$ in amplitude at $=5$ and the smallest possible parameter $T.($Hint: it is an acceptable strategy to look for $T$ by trail and error. $)$

d$)$ A lag controller with $=\frac{1}{7}$ losing more than $16$ db in amplitude at $=5$ and the smallest possible parameter $T.($Hint: it is an acceptable strategy to look for $T$ by trail and error. $)$

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