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When the unit step response of a unity feedback control system having forward path transfer function G (s) =80/s(s+18)?
  • a)
    Overdamped
  • b)
    Critically damped
  • c)
    Under damped
  • d)
    Un Damped oscillatory
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
When the unit step response of a unity feedback control system having ...
Answer: a
Explanation: The open loop transfer function is first converted into the closed loop as unity feedback is used and then value of damping factor is calculated.
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When the unit step response of a unity feedback control system having ...
Unity Feedback Control System:
In a unity feedback control system, the output of the system is fed back to the input with a gain of 1. It is represented by the following block diagram:

```
+--------+
| |
---->| G(s) |---+
| | | |
| +--------+ |
| |
+------------------+
```

Transfer Function:
The transfer function of the forward path in the given system is G(s) = 80/s(s+18). The transfer function represents the relationship between the Laplace transform of the input and the Laplace transform of the output of a system.

Unit Step Response:
The unit step response of a system is the output of the system when the input is a unit step function, also known as a Heaviside function. The unit step function is defined as follows:

```
{ 0, t < />
u(t) = { 1, t >= 0
```

Types of System Response:
The type of response of a control system can be determined by analyzing the poles of its transfer function. The poles of the transfer function are the values of 's' for which the denominator of the transfer function becomes zero.

The different types of system response based on pole locations are as follows:

1. Overdamped: When all the poles of the transfer function have negative real parts.
2. Critically damped: When the poles of the transfer function are real and repeated.
3. Underdamped: When the poles of the transfer function have negative real parts and complex conjugate imaginary parts.
4. Undamped oscillatory: When the poles of the transfer function have purely imaginary parts.

Analysis:
The transfer function G(s) = 80/s(s+18) has two poles at s = 0 and s = -18.

1. Pole at s = 0: This pole represents a pure integrator in the system. It causes the output to keep increasing without any damping effect.

2. Pole at s = -18: This pole represents a negative feedback term in the system. It introduces damping and helps in stabilizing the system.

The presence of the pole at s = -18 indicates that the system is overdamped. In an overdamped system, the response gradually approaches the steady-state value without any oscillations. The higher the damping, the slower the response.

Conclusion:
Therefore, the unit step response of the given unity feedback control system with the transfer function G(s) = 80/s(s+18) is overdamped.
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When the unit step response of a unity feedback control system having forward path transfer function G (s) =80/s(s+18)?a)Overdampedb)Critically dampedc)Under dampedd)Un Damped oscillatoryCorrect answer is option 'A'. Can you explain this answer?
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