Question $1)$ A grid$-$connected inverter is inputted by a constant power source $($e$.$g$.$ PV power with MPPT$).$ There are two controllers to control its capacitor voltage and inductor current.

Remark: taking the lecture note example as a reference

a$)$ Draw out the corresponding small$-$signal control block diagram. $(5$ marks$)$

b$)$ Determine the small$-$signal model and transfer function of each control diagram. $(10$ marks$)$

c$)$ Calculate the loop gain equation of the overall control system. $(5$ marks$)$