Test: Control Systems - 3 - Electrical Engineering (EE) MCQ

The phase margin can be calculated as: 180 + ∅

Where,

∅ is the phase of G(jω) at the gain cross over frequency.

We will first find the magnitude of the given system, as shown below:

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

The frequency at which the two asymptotes in the Bode plot meet is termed as corner frequency.

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

The given plot is of the type 1/ (ST1 + 1)(ST2 + 1)

The above transfer function has order 2 and type 0.

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

The Phase margin can be calculated as:

The gain margin (GM) = 20 log (1 / |G(s)H(s)|)

At, s = jω

We get: (GM) = 60dB

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

The error the rate of 1.2% per second c neb calculated as:

e = 1.2% x 2 = 1.2/100 x 2 = 2.4%

Now, let's calculate the Pout (controller output) = 4 (2.4%+ KD x 1.2%) + Po

= 4 (2.4 / 100 + 0.4 x 1.2 /100) + 50/100

= 4 x 2.88/100 + 50/100

= 11.52/100 + 50/100

= 61.52/100

= 61.52%

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

Lag compensator does not suppress steady state performance. Instead, it improves steady state performance.

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

Phase lead is responsible for improving the damping and reducing the system's steady-state error.

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

The sum of Eigenvalue of a given matrix is generally called the trace of that matrix. The trace of a matrix is the sum of the diagonal elements of a matrix.

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

We know,

Here,

The product of matrix A and B is,

Thus, the rank of the system is 2.

The determinant of the system is non-zero. Hence, the system is controllable.

Now, we will check for stability.

SI - A = 0

The above matrix can be written in the form of an equation:

s² + 3s -6 = 0

Now, we will find the roots using Routh's array table, as shown below:

There are two sign changes in the first column. Thus, the system is unstable.

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

The given transfer function is:

(1 +aTs) / (1 + Ts)

We will first calculate the poles and zeroes of the given transfer function.

Here,

Zero = -1/aT

Pole = -1/T

The pole in the given system is nearer to the jω axis (origin). The 0 will be far from the axis, such that the value of a < 1. It means that the value lies between 0 and 1.

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

The Proportional Derivative controller is preferred to handle fast process load changes.

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

The given equation for the feedback control system is s³ + 4s² + (K + 5)s + K = 0

The above equation can also be written as:

s³ + 5s² + Ks + 6s + K = 0

s³ + 5s² + 6s + K(s + 1) = 0

s (s² + 5s + 6) + K(s + 1) = 0

1 + K(s + 1) / [s (s² + 5s + 6)] = 0

1 + K(s + 1) / s (s² + 2s + 3s + 6) = 0

1 + K(s + 1) / s (s + 2)(s + 3) = 0

Now, we will calculate the value of centroid, which is equal to:

σ= / (P - Z)

Here, the number of poles and zeroes are 3 and 1.

σ= [(0 - 2 - 3) + 1] / (3 - 1)

σ=(-4)⁄2

σ=-2

Hence, the correct answer is option (b).

The formula to calculate a number of zeroes at infinity is P - Z. Here, P and Z are the number of poles and zeroes in a given transfer function.

We know that poles are calculated by equating the denominator to zero, and zeroes are calculated by equating the numerator to zero. So, for the above given transfer function, we get:

P = 3

Z = 1

So, the number of zeroes at infinity = 3 - 1 = 2

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

The two blocks in the above diagram are in cascade. So, the equivalent block will be the product of these two blocks.

G(s) = k (s - 2) /(s +1) (s^2 + 9s + 16)

Now, H(s) = 1, as shown in the above block diagram. The characteristic equation will be: 1 + G(s) H(s)

C(s) = 1 + [k (s - 2) / (s + 1) (s^2 + 9s + 16)] = 0

= s^3 + 10s^2 + 25s + 16 + ks - 2k

= s^3 + 10s^2 + s (25 + k) + 16 - 2k

For the above equation, we need to find the roots by creating the Routh's array table.

The table is given below:

For stability,

16 - 2k > 0

16 > 2k

8 > k or k < 8

10 (25 + k) - (16 -2k) /10 > 0

250 + 10k -16 + 2k > 0

12k + 234 > 0

12k > -234

k > -19.5

From the two values of k, we can say that it lies between -19.5 < k < 8

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

For the above equation, we need to find the roots by creating the Routh's array table. The given equation is:s³ + Ks² + 5s + 10

The table is given below:

 

For the system to be critically stable, we will put (5K -10)/K = 0

5K - 10 = 0

5K = 10

K = 2

The value of K for which the system is said to be critically stable is 2.

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