Control System – Concepts of Stability MCQ

21. Which of the following transfer functions is/are minimum phase transfer function(s)?

1. $\frac{1}{(s-1)}$
2. $\frac{s-1}{(s+3)(s+4)}$
3. $\frac{(s+2)}{(s+3)(s-4)}$

Select the correct answer using the code given below:

1. i and iii
2. i only
3. ii and iii
4. None of these

22. If the poles of a system lie on the imaginary axis, the system will be

1. Stable
2. Conditionally stable
3. Marginally stable
4. Unstable

23. Which one of the following is the correct statement?

A non-minimum phase network is one whose transfer function has

1. zeros in the left-hand plane and poles in the right-hand plane.
2. zeros and poles in the left-hand plane.
3. zeros in the right-hand plane and poles in the left-hand plane.
4. arbitrary distribution of zeros and poles in the s-plane.

24. The open-loop transfer function of a unity feedback control system is given by G(s) = Ke^-Ts, where K and T are constants and these are greater than zero. The stability of closed-loop system depends on which of the following?

1. Both K and T
2. K only
3. Neither on K nor on T
4. T only

25. The characteristic equation of a system is given as

s³ + 25s² + 10s + 50 = 0.

What is the number of roots in the right half of s-plane and on the jω axis, respectively?

1. 1, 1
2. 0, 0
3. 1, 2
4. 2, 1

26. The transfer function of a system is $\frac{(1-s)}{(1+s)}$.

The system is then which one of the following?

1. Non-minimum phase system
2. Minimum phase system
3. Low-pass system
4. Second-order system

27. Which one of the following is the correct statement?

A minimum phase transfer function has

1. poles in the right half of s-plane
2. zeros in the right half of s-plane
3. poles in the left half of s-plane and zeros the right half of s-plane
4. no poles or zeros in the right half of s-plane or on the jω-axis excluding the origin

28. An electromechanical closed-loop control system has the transfer function

$\frac{C(s)}{R(s)}=\frac{k}{s(s^2+s+1)(s+4)+k}$

Which one of the following is correct?

1. The system is stable for all positive values of k.
2. The system is unstable for all values of k.
3. The system is stable for values of k between 0 and 3.36.
4. The system is stable for values of k between 1.6 and 2.45.

29. Consider the following equation:

2s⁴ + s³ + 3s² + 5s + 10 = 0

How many roots does this equation have in the right half of s-plane?

1. Two
2. One
3. Four
4. Three

30. A control system is defined in s-domain. Following points regarding the poles of the transfer function obtained from the characteristic equation were noted:

1. Poles with positive real part denote stable system
2. Complex poles always occur in pairs
3. A pole s = -σ (σ > 0) means that the transient response contains exponential decay.

Which of the above are correct?

1. i and iii
2. i and ii
3. i, ii and iii
4. ii and iii

31. The characteristic equation of a system is given by

3s⁴ + 10s³ + 5s² +2 = 0.

This system is

1. marginally stable
2. stable
3. unstable
4. neither (a), (b) nor (c)