# Control Systems Control Systems
| Control Systems |
Q.1
Solution of the variables x1 and x2 for the following equations is to be obtained by employing the Newton-Raphson iterative method.
equation (i)    10x2 sinx1 - 0.8 = 0
equation (ii)    10x2 - 10x2 cosx1 - 0.6 = 0
Assuming the initial valued x1 = 0.0 and x2 = 1.0, the jacobian matrix is
A. B. C. D. Answer : Option B
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Q.2
A unity feedback control system has an open-loop transfer function . The gain K for which s = +j will lie on the root locus of this system is
A. 4
B. 5.5
C. 6.5
D. 10
Answer : Option D
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Q.3
A two loop position control system is shown below The gain k of the Tacho-generator influences mainly the
A. Peak overshoot
B. Natural frequency of oscillation
C. Phase shift of the closed loop transfer function at very low frequencies (ω → 0)
D. Phase shift of the closed loop transfer function at very low frequencies (ω → ∞)
Answer : Option A
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Q.4
A second-order real system has the following properties:
a) the damping ratio ς = 0.5 and undamped natural frequency ω=10 rad/s
b) the steady state value of the output, to a unit step input, is 1.02.
The transfer function of the system is
A. B. C. D. Answer : Option B
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Q.5
A closed loop system has the characteristic equation given by s3 + Ks2 +(K + 2)s + 3 = 0 For this system to be stable, which one of the following conditions should be satisfied?
A. 0 < K < 0.5
B. 0.5 < K < 1
C. 0 < K < 1
D. K > 1
Answer : Option D
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Q.6
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
A. All the poles of the system must lie on the left side of the B. Zeros of the system can lie anywhere in the s-plane
C. All the poles must lie within ƖsƖ  = 1
D.
All the roots of the characteristic equation must be located on the left side of the axis.
Answer : Option C
Explaination / Solution:

For a system to be casual, the R.O.C of system transfer function H(s) h which is rational should be in the right half plane and to the right of the right most pole.
For the stability of LTI system. All poles of the system should lie in the left half of S -plane and no repeated pole should be on imaginary axis. Hence,
options (A), (B), (D) satisfies an LTI system stability and causality both.
But, Option (C) is not true for the stable system as,  ƖsƖ =1 have one pole in right hand plane also.

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Q.7
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
A. All the poles of the system must lie on the left side of the jω axis
B. Zeros of the system can lie anywhere in the s-plane
C. All the poles must lie within |s| = 1
D. All the roots of the characteristic equation must be located on the left side of the jω axis
Answer : Option C
Explaination / Solution:
No Explaination.

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Q.8
The characteristic equation of a closed-loop system is s(s + 1)(s + 3) + k(s + 2) = 0, k > 0. Which of the following statements is true?
A. Its roots are always real
B. It cannot have a breakaway point in the range −1 < Re[s] <0
C. Two of its roots tend to infinity along the asymptotes Re[𝑠] = −1
D. It may have complex roots in the right half plane.
Answer : Option C
Explaination / Solution:
No Explaination.

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Q.9
The signal flow graph of a system is shown below: The state variable representation of the system can be
A. B. C. D. Answer : Option D
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Q.10
The second order dynamic system has the matrices P, Q and R as follows: The system has the following controllability and observability properties:
A. Controllable and observable
B. Not controllable but observable
C. Controllable but not observable
D. Not controllable and not observable
Answer : Option C
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