If $L=100H,CF=1000F,R_{\text{l}\text{o}\text{a}\text{d}}=10,$RESR$=1,$ compute the magnitude and phase bode plots for the transfer function of this system from two decades below the resonant frequency of the filter to two decades above the resonant frequency of the filter. If the post$-$compensation crossover frequency $f_c=\frac{{}_c}{2}=1\mathrm{.}5kHz,$ pick the one best type of compensator from the following choices and then justify your answer with a short discussion of the properties of the Bode plots that led you to this decision.

a$)$ Type $1$ compensator $\frac{u(s)}{v_{\text{e}\text{r}\text{r}\text{o}\text{r}}(s)}=K_{PWM}\frac{{}_{\text{I}}}{s}$

b$)$ Type $2$ compensator $\frac{u(s)}{v_{\text{e}\text{r}\text{r}\text{o}\text{r}}(s)}=K_{PWM}\frac{{}_{\text{I}}}{s}\frac{s+{}_z}{s+{}_p}$

c$)$ Type $3$ compensator $\frac{u(s)}{v_{\text{e}\text{r}\text{r}\text{o}\text{r}}(s)}=K_{PWM}\frac{{}_{\text{I}}}{s}\frac{(s+{}_{z1})(s+{}_{z2})}{(s+{}_{p1})(s+{}_{p2})}$