Test: Control Systems - 1 - Electrical Engineering (EE) MCQ

The traffic lamp will glow according to the set timing and sequence and is time-dependent. The sequence and time are controlled by relays that work on the pre-programmed time. It does not depend upon the rush of the road.
Hence the correct answer is an option (a).

Given:
G(s) = 2
H(s) = 0.5 and R(s) = 10V
Output voltage:
= (2/1+2x 0.5) x 15 = 15V
Error voltage:
= (1/1+2x 0.5) x 15 = 7.5V
Hence the correct answer is option (c).

Given: x is the displacement in the above diagram. The Laplace transform of x is X(s). The differential equations governing the system are the balanced force equation at these nodes.
Here,
F is the opposite force due to mass.
F =
f is the opposite force due to friction
F =
k is the ideal elastic spring element that has negligible mass and friction. The force generated by the spring is directly proportional to the displacement of the body.
F = Kx
So, the force equation can be represented as:

Hence, the correct answer is an option (c).

According to Mason's Gain formula, the transfer function can be calculated as:
T(s) = C(s)/R(s)

Where,
Pk is the forward path gain
∆ is the loop gain, which is calculated as:
∆ = 1-∑(All loop gain) + ∑(Gain product of two non-touch in gloops) - ∑(Gain product of three non-touching loops)
∆k is calculated bye liminating all loops touching Pk
Here, the loop gain is defined as the product of the branch gain that is traversing a forward path.
Hence, the correct answer is an option (b).
The Mason's gain formula is used to find the overall transfer function of a signal graph.

The transfer function of a loop is G/(1+GH)
We will first simplify the above block diagram into the simple system. Let's calculate the transfer function of the first loop.
TF = [1/ (40s+2)] / [1 + 2/ (40s+2)] = 1/ (40s +4)
Now, two blocks are left in cascade. The equivalent block is the product of these two blocks, as given below:
C(s)/R(s) = 4. (1/ (40s +4)) = 1/ (10s + 1)
The Laplace transform of the step input is 1/s. It means R(s) = 1/s.
C(s) = [1/ (10s + 1)]. R(s)
C(s) = [1/ s (10s + 1)
Taking the inverse Laplace of the above equation, we get:
1-e^-t⁄10

The standard transfer function can be written as:


The given equation is: 81/ (s² + 16s + 81)
Comparing the values, we get:

Thus, the undamped natural frequency is 9, and the damping ratio is 0.889.
The Peak time can be calculated as:

Hence, the correct answer is an option (a).

The given transfer function is:
G(s) = (s + 4)/ (ks² + s + 4)
The characteristic equation ks² + s + 4 = 0
Dividing the equation by k, we get:
S² +s/k + 4/k = 0

Hence, the correct answer is an option (b).

The given transfer function is: G(s) = 25/ (s² + 6s + 25)
Comparing the value of the given transfer function with the standard equation


we know

Hence, the correct answer is option (c).

The zeroes can be calculated by equating the numerator to zero:
5 (s + 2) = 0
5s + 10 = 0
5s = -10
s = -2
The poles can be calculated by equating the denominator to zero:
s² + 3s + 2 = 0
s² + 2s + s + 2 = 0
s (s + 2) + 1 (s + 2) = 0
(s + 1) (s + 2) = 0
s = -1, -2
Hence, the correct answer is an option (a).

Centroid is defined as a common point where all the asymptotes intersect on the real axis. The value of centroid is always real. But, it can be located either on the positive or negative real axis.

The phase margin can be calculated as 180 +
Where,
∅ is the phase of G(jw) at the gain cross over frequency.
So, phase margin = 180 + (-115)
= 180 - 115
= 65 degrees
Hence, the correct answer is an option (d).

The given open-loop transfer function is: G(s) = 1 / s(s + 1) (2s + 1)

The imaginary part of the system at phase cross over frequency is zero. Hence, we will equate the imaginary part to zero, as shown below:

It means that the phase cross-over frequency to the system is 0.707 Radians/s.
Hence, the correct answer is an option (c).

The Bode plot is defined as the frequency response plot of the sinusoidal transfer function of a system. The two graphs of the Bode plot are the plot of magnitude and phase angle. Thus, it is in the frequency domain.

The Nyquist plot is considered as the extension of the polar plot. The variation of frequency from infinity to -infinity results in the plot, known as the Nyquist plot. Hence, the Nyquist criterion is in the frequency domain.

Hence, the correct answer is an option (b).

The formula to calculate the damping ratio using the phase margin is:
Damping Ratio = tan∅√cos ∅⁄2
= ((tan45√cos45))⁄2
= 0. 42
Hence, the correct answer is an option (b).

The PID is the combination of proportional, integral, and derivate control modes. Such a combination makes it the most powerful controller.

Hence, the correct answer is an option (c).