Design the following controllers

a$)$ A lead controller that gains $30$ in phase at $=1\mathrm{.}3$ and at the same time minimizes gain in amplitude over all frequencies.

b$)$ A lead controller that gains $40$ in phase $=1\mathrm{.}3$ and at the same time minimizes gain in amplitude over all frequencies.

c$)$ A lead controller that gains $50$ in phase at $=1\mathrm{.}6$ and at the same time minimizes gain in amplitude over all frequencies.

d$)$ A lead controller that gains $25$ in phase at $=0\mathrm{.}75$ and at the same time minimizes gain in amplitude over all frequencies.

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