Classroom Assignment $-1$

Maximum Marks: $10$ marks

Time: $40$min.

Attempt All question

In a temperature control unit a temperature measurement system whose output and input is related with the transfer function

$G(s)=\frac{y(s)}{x(s)}=\frac{10s+1}{2s+1}$

A unit step change is introduced in this system.

A$.$ Determine the value of response $y(t).$

B$.$ Sketch the response function and

$(2\mathrm{.}5$ Marks$)$

$(1$ Mark$)$

C$.$ Find ultimate, steady state and initial value of the response. $(1\mathrm{.}5$ Marks$)$

$2.$ In a pressure control system input pressure $(x)$ is related with an equation, $\frac{d2x}{d{t}^2}+6*\frac{dx}{dt}+9x=6,x(0)=x^{\text{'}}(0)=0$

Where pressure is in atm and time $t$ is in minute.

a$)$ Find the pressure as a function of time.

b$)$ Find the pressure at $1$ minute,

$(3$ Marks$)$

$(2$ Marks$)$