# MATLAB Questions and Answers – Time Response of Control Systems – 2

This set of MATLAB Objective Questions & Answers focuses on “Time Response of Control Systems – 2”.

1. The steady state error of the system with a forward path transfer function G(s)=13(s-1)/(s-1) and with a parabolic input is _______
a) Infinite
b) 0
c) -Infinite
d) Undefined

Explanation: The given system has no poles at s=0. This means that for a parabolic input, the parabolic error constant is 0. Hence, the steady state error will go to infinity. Thus option Infinite is correct only.

2. For a step response of the system 1/s2+1, the maximum overshoot is __________
a) 1
b) 0
c) Infinite
d) 2

Explanation: For a step response of a second ordered system, the maximum overshoot depends only upon its damping ratio. Since the given system is a second ordered system, the maximum overshoot is a function of its damping ratio. But here, the damping ratio is 0 so the system has a maximum overshoot of 1.

3. What is the gain of the system derived from the following code?

`tf[1,100]`

a) 1/100
b) s/100
c) 1/100s
d) Error

Explanation: The input to the tf command should be within parentheses. Here we’ve used [] which leads to an error. If the input was within parentheses, the gain is .01 which is a static gain.
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4. What is the output of the following code?

`step(impulse(1,[1 0]))`

a) A ramp function
b) A parabolic function
c) A step function
d) Error

Explanation: The input to the step command should be the poles and zeros of the transfer function. This way of giving input is not possible since the impulse command generates a graph and we are really giving a graph as an input to the command which leads to an error. Although, the impulse command generates a step function and the step response of a step function is a ramp function- here there will be an error.

5. What is the output of the following code?

```r.DampingRatio = 0;
overshoot = getOvershoot(r);```

a) 100
b) 0
c) 1
d) Error

Explanation: To use the getOvershoot command, we need to instantiate the sdp.requirements.DampingRatio class. Since the class is not instantiated, the command won’t be discovered by MATLAB and it will give an error.

6. Which of the following command gives the step response characteristics of a control system?
a) stepinf()
b) stepinfo()
c) stepinfo[]
d) step()

Explanation: The stepinfo command is pre-defined in MATLAB to get the step response characteristics of a control system. The input is to be given within parentheses and not []. The step() command gives the output graph of the step response and it doesn’t reveal the characteristics explicitly.

7. Which of the following command generates the impulse response of a system which has more zeros than poles?
a) impulse()
b) impulse[]
c) impulse{}
d) No such command

Explanation: There isn’t any command defined in MATLAB which will compute the response of a system having more zeros than poles. Such a system is unstable at higher frequencies.

8. Which of the following command generates the transfer function of a system?
a) tf()
b) tf[]
c) tf{}
d) No such command

Explanation: The command to get the transfer function of a system is tf. The input to the command should be within parentheses. Hence, option tf() is correct only.

9. What is the output of the following code?

`step([1],[1 0 0])`

a) A parabola
b) A ramp function
c) A step function
d) An impulse function

Explanation: We observe that the given input vectors suggest that the transfer function is actually 1/s2. This means that the transfer function is a ramp function. The step response of a ramp function is a parabola. Hence, a parabola is correct.

10. The time constant of a system is ________
a) equal to the damping constant
b) inverse of the damping constant
c) twice the damping constant
d) half of the damping constant

Explanation: The time constant of a system is inverse of the damping constant. It is defined so and hence the rest of the options are incorrect.

11. If the natural frequency of a system increases, the rise time ________
a) Increases
b) Decreases
c) Doubles
d) Halves

Explanation: The rise time of a system is inversely proportional to the natural frequency of a system. Hence, if it increases, the rise time decreases.

12. The settling time is a measure of _________
a) The speed of reaching stead state
b) The speed of reaching maximum overshoot
c) The speed of reaching second overshoot
d) Nothing

Explanation: The settling time is a measure of the time required by the system to reach approximately 5% of it’s steady state value. Hence, it is a measure of how fast the system reaches it’s steady state value.

13. If the poles of a system transfer function are equal and imaginary, the system is ________
a) Undamped
b) Critically damped
c) Overdamped
d) Negatively damped

Explanation: Since the poles are equal and imaginary, the damping factor is 0 and hence the damping ratio is 0. Thus, the system is absolutely undamped and option Undamped is correct only.

14. For negative damping, the system is unstable.
a) True
b) False

Explanation: Negative damping implies that the response of the system grows in magnitude and it is unbounded in time. Hence, the system output is unstable and the system is also unstable.

15. An undamped system is stable.
a) True
b) False

Explanation: An undamped system is marginally stable or marginally unstable- it cannot be defined as stable. This is because it results in a response which is sustained by oscillatory in nature. Hence, the statement is false.

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