V$.25($a$)$ Develop a feedforward$-$feedback control system for a process with the following transfer functions;

$G_p(s)=\frac{(\frac{?}{\text{b}\text{a}\text{r}}(y))(s)}{(\frac{?}{\text{b}\text{a}\text{r}}(m))(s)}=\frac{s+1}{(s+2)(2s+3)},G_d(s)=\frac{(\frac{?}{\text{b}\text{a}\text{r}}(y))(s)}{(\frac{?}{\text{b}\text{a}\text{r}}(d))(s)}=\frac{5}{s+2}$

The following specifications are also given: $(1)$ use a PI controller for the feedback loop, and $(2)$ the feedforward system should have both disturbance rejection and set point tracking capabilities

$($b$)$ Show how you would tune the feedback PI controller.

$($c$)$ Derive the conditions that must be satisfied in order to have stable closed$-$loop response. Do these conditions depend on both feedforward and feedback characteristics?

V$.25($a$)$ Develop a feedforward$-$feedback control system for a process with the following transfer functions;

$G_p(s)=\frac{(\frac{?}{\text{b}\text{a}\text{r}}(y))(s)}{(\frac{?}{\text{b}\text{a}\text{r}}(m))(s)}=\frac{s+1}{(s+2)(2s+3)},G_d(s)=\frac{(\frac{?}{\text{b}\text{a}\text{r}}(y))(s)}{(\frac{?}{\text{b}\text{a}\text{r}}(d))(s)}=\frac{5}{s+2}$

The following specifications are also given: $(1)$ use a PI controller for the feedback loop, and $(2)$ the feedforward system should have both disturbance rejection and set point tracking capabilities

$($b$)$ Show how you would tune the feedback PI controller.

$($c$)$ Derive the conditions that must be satisfied in order to have stable closed$-$loop response. Do these conditions depend on both feedforward and feedback characteristics?