Chemical Engineering - Process Control and Instrumentation - Discussion
Discussion Forum : Process Control and Instrumentation - Section 2 (Q.No. 23)
23.
The initial value (t=0) of the unit step response of the transfer function [(s + 1)/(2s + 1)] is
Discussion:
6 comments Page 1 of 1.
Hitesh Pawade said:
8 years ago
@Deepti right.
y(s)={(1/s)* [(s + 1)/(2s + 1)] }.
=1/s*[s/(2s+1) +1/(2s+1)].
=1/(2s+1) + 1/s*(2s+1).
=1/(2s+1) + 1/s -2/(2s+1) ...(Partial Fraction).
y(s) = 1/s - 1/(2s+1).
taking inverse laplace.
y(t)=u(t) - e^(t/2)/2.
t=0.
Y(0) = u(0) - e^0/2.
Y(0) = 1-1/2.
y(0) = 1/2.
[B].
y(s)={(1/s)* [(s + 1)/(2s + 1)] }.
=1/s*[s/(2s+1) +1/(2s+1)].
=1/(2s+1) + 1/s*(2s+1).
=1/(2s+1) + 1/s -2/(2s+1) ...(Partial Fraction).
y(s) = 1/s - 1/(2s+1).
taking inverse laplace.
y(t)=u(t) - e^(t/2)/2.
t=0.
Y(0) = u(0) - e^0/2.
Y(0) = 1-1/2.
y(0) = 1/2.
[B].
(2)
Udaykiran said:
1 decade ago
Option B.
For a unit step response X(s) = 1/s.
Y(s)/X(s)= [(s + 1)/(2s + 1)] becomes,
Y(s)={(1/s)* [(s + 1)/(2s + 1)] }.
Now apply final value value theorem i.e.,
lt y(t) = lt sY(s)
t->0 s->(1/0).
On RHS,
Yes will get cancelled now apply limits. So the answer is 1/2.
Therefore the opt is B.
For a unit step response X(s) = 1/s.
Y(s)/X(s)= [(s + 1)/(2s + 1)] becomes,
Y(s)={(1/s)* [(s + 1)/(2s + 1)] }.
Now apply final value value theorem i.e.,
lt y(t) = lt sY(s)
t->0 s->(1/0).
On RHS,
Yes will get cancelled now apply limits. So the answer is 1/2.
Therefore the opt is B.
(1)
Babar munir said:
1 decade ago
I have not understand what are you saying please tell me the whole procedure?
Deepti said:
1 decade ago
One can also take inverse Laplace transform.
Kel said:
9 years ago
Great answer @Udaykiran. This helps greatly to simplify the solution, especially in time constrained situations.
Bhavin trada said:
8 years ago
@Udaykiran.
Why you have applied final value theorem? we are asked for an initial value.
Why you have applied final value theorem? we are asked for an initial value.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers