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QUESTION: 1

Determine C/R for the system given in figure below. Then put G_{3} = G_{1} G_{2} H_{2}. Now the new

transfer function will be:

Solution:

∴

QUESTION: 2

The signal-flow graph shown in figure below has:

Solution:

Forward paths are:

Loops are:

*Answer can only contain numeric values

QUESTION: 3

The unit impulse response of a system is h(t) = e^{-2t}, _{t} 0_{.}

For this system, the steady-state value of the output for unit step input is equal to

Solution:

and

∴

QUESTION: 4

A control system has input r(t) and output c(t). If the input is first passed through a block

whose transfer function is a^{-2s} and then applied to the system, the modified output will be

Solution:

QUESTION: 5

The open-loop transfer function of a feedback control system is given by G(s)

Find the range of the values of T for stability.

Solution:

The characteristic equation of the system is

s^{2} + s(2 — T) + 1 = 0

Routh's array becomes:

The system will be stable if

∴

QUESTION: 6

If the open-loop transfer function of a feedback system is given by

G(s) H(s) = , then the controid of the asymptotes will be

Solution:

Poles = 0, —2, —1 + 2j, —1 —2j

Total number of pole, P = 4

Total number of zero, Z = 0

∴ P — Z = 4

∴

QUESTION: 7

For the block diagram shown in figure below, the limiting value of k for stability of the inner loop is found to be X < k < Y. The overall system will be stable if and only if

Solution:

For inner loop:

let

For outer loop:

QUESTION: 8

The closed loop transfer function of a control system has the following poles and zeros

Poles Zeros

P_{1} = 0.5 Z_{1} = –7

P_{2} = –1.0 Z_{2} = 9

P_{3} = –5

P_{4} = —10

The closed loop response can be closely approximated by considering which of the following?

Solution:

Because of concept of dominant pole. Here P_{1} and **P**** _{2}** are dominant pole and

insignificant poles.

QUESTION: 9

Match List-I (Type of compensator) with List-II (Polar plot) and select the correct answer using the code given below the lists:

**List-I **

1.Phase lead

2. Phase lag

3. Lead-lag

A B C

(a)123

(b) 132

(c) 213

(d) 231

Solution:

QUESTION: 10

For the given network, the maximum phase lead _{4m} of V_{o} with respect to V_{1} is

Solution:

QUESTION: 11

In the Bode-plot of a unity feedback control system, the value of phase of G(j@) at the gain

cross-over frequency is —125°. The phase margin of the system is

Solution:

φ at ωg C = —125°

Phase-margin (PM) = 180°+ φ

= 180°— 125°

= 55°

QUESTION: 12

The Nyquist plot for the function is

The condition for stability is given by

Solution:

QUESTION: 13

The open-loop transfer function of unity feedback system is G(s) = . Thes (s + 2) (s + 10)range of k for which closed-loop system is stable.

Solution:

It is type-1 and order —3 system so the Nyquist plot is

For stability:

QUESTION: 14

The Bode plot for minimum phase transfer function is:

Solution:

(a)

- In option (a) Bode plot represents - Minimum phase transfer function
- In option (b) Bode plot represents - Non-minimum phase transfer function
- In option (c) Bode plot represents - All pass transfer function

QUESTION: 15

For the system shown below the state-space equation is X = A x + B u. The matrix A is

Solution:

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