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The identical first order system have been cascaded non-interactively. The unit step response of the systems will be:
- a)Overdamped
- b)Underdamped
- c)Undamped
- d)Critically damped
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The identical first order system have been cascaded non-interactively....
Answer: d
Explanation: Since both the systems that is the first order systems are cascaded non-interactively, the overall unit step response will be critically damped.
Explanation: Since both the systems that is the first order systems are cascaded non-interactively, the overall unit step response will be critically damped.
Most Upvoted Answer
The identical first order system have been cascaded non-interactively....
Explanation:
When two identical first-order systems are cascaded, the overall transfer function becomes the product of the individual transfer functions. Let the transfer function of each system be:
G(s) = K/(1+Ts)
The overall transfer function becomes:
G(s) = [K/(1+Ts)]*[K/(1+Ts)] = K^2/(1+2Ts+s^2)
The characteristics of the step response of this second-order system depend on the value of the damping ratio, ζ = T/(2√K).
If ζ < 1,="" the="" system="" is="" underdamped="" and="" has="" oscillatory="" />
If ζ = 1, the system is critically damped and has no oscillations.
If ζ > 1, the system is overdamped and takes longer to reach steady state.
In this case, since the systems are identical, ζ = T/(2√K) is the same for both systems, and therefore the overall system is also critically damped. Thus, the unit step response of the system will have no overshoot and will reach steady state in the shortest possible time.
When two identical first-order systems are cascaded, the overall transfer function becomes the product of the individual transfer functions. Let the transfer function of each system be:
G(s) = K/(1+Ts)
The overall transfer function becomes:
G(s) = [K/(1+Ts)]*[K/(1+Ts)] = K^2/(1+2Ts+s^2)
The characteristics of the step response of this second-order system depend on the value of the damping ratio, ζ = T/(2√K).
If ζ < 1,="" the="" system="" is="" underdamped="" and="" has="" oscillatory="" />
If ζ = 1, the system is critically damped and has no oscillations.
If ζ > 1, the system is overdamped and takes longer to reach steady state.
In this case, since the systems are identical, ζ = T/(2√K) is the same for both systems, and therefore the overall system is also critically damped. Thus, the unit step response of the system will have no overshoot and will reach steady state in the shortest possible time.
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The identical first order system have been cascaded non-interactively. The unit step response of the systems will be:a)Overdampedb)Underdampedc)Undampedd)Critically dampedCorrect answer is option 'D'. Can you explain this answer?
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