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A first order system and its response to a unit step input are shown in figure below. The system parameters are____________
  • a)
    a=5 and k=12
  • b)
    a=10 and k=5
  • c)
    a=5 and k=10
  • d)
    a=8 and k=9
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A first order system and its response to a unit step input are shown i...
First Order System and Unit Step Response

The given figure represents a first-order system and its response to a unit step input. In order to determine the system parameters, we need to analyze the response curve and compare it with the general form of a first-order system's step response.

First Order System

A first-order system is a linear time-invariant system that can be represented by a first-order ordinary differential equation (ODE). The transfer function of a first-order system can be expressed as:

G(s) = k / (τs + 1)

Where k is the system gain and τ is the time constant. The time constant determines the speed of the system's response.

Unit Step Response

The unit step response of a first-order system is a characteristic curve that shows how the system responds to a step input. It starts at zero and gradually approaches the final value with a certain time constant.

Analysis of the Response Curve

By analyzing the given response curve, we can observe the following key points:

1. Steady-state value: The response curve approaches a final value after a certain time. In this case, the steady-state value is approximately 5.

2. Time constant: The time it takes for the response to reach approximately 63.2% of the steady-state value is known as the time constant. By estimating the time it takes for the response to reach 63.2% of the steady-state value, we can determine the time constant.

Determining the System Parameters

Based on the analysis of the response curve, we can conclude the following system parameters:

a) a=5 and k=12: This option does not match the steady-state value observed in the response curve.

b) a=10 and k=5: This option does not match the steady-state value observed in the response curve.

c) a=5 and k=10: This option matches the steady-state value observed in the response curve.

d) a=8 and k=9: This option does not match the steady-state value observed in the response curve.

Therefore, the correct answer is option 'C' (a=5 and k=10) as it matches the observed steady-state value in the response curve.
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A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a=5 and k=12b)a=10 and k=5c)a=5 and k=10d)a=8 and k=9Correct answer is option 'C'. Can you explain this answer?
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A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a=5 and k=12b)a=10 and k=5c)a=5 and k=10d)a=8 and k=9Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a=5 and k=12b)a=10 and k=5c)a=5 and k=10d)a=8 and k=9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a=5 and k=12b)a=10 and k=5c)a=5 and k=10d)a=8 and k=9Correct answer is option 'C'. Can you explain this answer?.
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