$(47\%)$ A process to be controlled has the transfer function

$G_P=\frac{1}{s^2+s+0\mathrm{.}25}$

The final control element has the transfer function

$G_v=\frac{1}{0\mathrm{.}5s+1}$

and the measurement element has the transfer function

$G_m=\frac{1}{0\mathrm{.}25s+1}$

a$)$ Please sketch a block diagram of the overall system, including the controller,

the final control element, the measurement element, and the process to be

controlled. Also include the setpoint; you do not need to include a

disturbance.

b$)$ Please characterize the damping behavior of the process to be controlled

$($defined by $G_P).$

c$)$ Please develop the overall transfer function from the setpoint $Y_{SP}$ to the

process variable $Y$; write this in terms of the $G$ s$.(47\%)$ A process to be controlled has the transfer function

$G_P=\frac{1}{s^2+s+0\mathrm{.}25}$

The final control element has the transfer function

$G_v=\frac{1}{0\mathrm{.}5s+1}$

and the measurement element has the transfer function

$G_m=\frac{1}{0\mathrm{.}25s+1}$

a$)$ Please sketch a block diagram of the overall system, including the controller,

the final control element, the measurement element, and the process to be

controlled. Also include the setpoint; you do not need to include a

disturbance.

b$)$ Please characterize the damping behavior of the process to be controlled

$($defined by $G_P).$

c$)$ Please develop the overall transfer function from the setpoint $Y_{SP}$ to the

process variable $Y$; write this in terms of the $G$ s$.$