Consider the following standard first order plus time delay $($FOPTD$)$ model for the

bio$-$lubricant production process in QUESTION $3.$

tilde$(G{)}_{(s)}=\frac{7e^{-8s}}{3s+1}$

a$.$ Derive an expression for a controller with time delay compensation using the

direct synthesis approach with FOPTD desired response. Discuss the nature of

the resulting controller.

$[14$ marks$]$

b$.$ Design an internal model controller $($IMC$)$ for the process using the Pade

approximation model. Discuss the nature of the resulting controller. Given:

$e^{-s}$~$=\frac{1-\frac{}{4}s}{1+\frac{}{4}s}$Consider the following standard first order plus time delay $($FOPTD$)$ model for the

bio$-$lubricant production process in QUESTION $3.$

$$

$()=78$

$3+1$

a$.$ Derive an expression for a controller with time delay compensation using the

direct synthesis approach with FOPTD desired response. Discuss the nature of

the resulting controller.

$[14$ marks$]$

b$.$ Design an internal model controller $($IMC$)$ for the process using the Pade

approximation model. Discuss the nature of the resulting controller. Given:

$\backslash$cong

$1$

$4$

$1+$

$4$

$[11$ marks$]$