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Two linear time-invariant systems with transfer functions
have unit step responses y1(t) and y2(t) , respectively. Which of the following statements is/are true?
- a)y1(t) and y2(t) have the same percentage peak overshoot.
- b)y1(t) and y2(t) have the same steady-state value.
- c)y1(t) and y2(t) have the same 2% settling time.
- d)y1(t) and y2(t) have the same damped frequency of oscillation.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two linear time-invariant systems with transfer functionshave unit st...
Given transfer functions of two linear time invariant system.
For transfer function G1(s) :
Characteristic equation of G1 (s) is,
1 + G1 (s) = 0
s2 + s + 1 = 0 … (i)
Standard characteristic equation for second order system is given by,
On comparing equation (i) and (ii),
Maximum Peak Overshoot (MPO) is given by,
Settling time for 2% tolerance band is given by,
Damped frequency of oscillation is given by,
Steady state value of y1 (t) is,
Apply final value theorem,
For transfer function G2(s) :
Characteristic equation of G2 (s) is,1 + G2 (s) = 0
Standard characteristic equation for second order system is given by,
Comparing equations (iii) and (iv),
Maximum Peak Overshoot (MPO) is given by,
Settling time for 2% tolerance band is given by,
Damped frequency of oscillation is given by
Steady state value of y2(t) is,
Apply final value theorem,
So, y1(t) and y2 (t) have the same percentage overshoot.
Hence, the correct option is (A).
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Community Answer
Two linear time-invariant systems with transfer functionshave unit st...
Given transfer functions of two linear time invariant system.
For transfer function G1(s) :
Characteristic equation of G1 (s) is,
1 + G1 (s) = 0
s2 + s + 1 = 0 … (i)
Standard characteristic equation for second order system is given by,
On comparing equation (i) and (ii),
Maximum Peak Overshoot (MPO) is given by,
Settling time for 2% tolerance band is given by,
Damped frequency of oscillation is given by,
Steady state value of y1 (t) is,
Apply final value theorem,
For transfer function G2(s) :
Characteristic equation of G2 (s) is,1 + G2 (s) = 0
Standard characteristic equation for second order system is given by,
Comparing equations (iii) and (iv),
Maximum Peak Overshoot (MPO) is given by,
Settling time for 2% tolerance band is given by,
Damped frequency of oscillation is given by
Steady state value of y2(t) is,
Apply final value theorem,
So, y1(t) and y2 (t) have the same percentage overshoot.
Hence, the correct option is (A).
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Two linear time-invariant systems with transfer functionshave unit step responses y1(t) and y2(t) , respectively. Which of the following statements is/are true?a)y1(t) and y2(t) have the same percentage peak overshoot.b)y1(t) and y2(t) have the same steady-state value.c)y1(t) and y2(t) have the same 2% settling time.d)y1(t) and y2(t) have the same damped frequency of oscillation.Correct answer is option 'A'. Can you explain this answer?
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