Control system miscellaneous Easy Questions and Answers | Page - 14

Control system miscellaneous

The correct sequence of steps needed to improve system stability is

1. insert derivative action, use negative feedback reduce gain
1. reduce gain, use negative feedback, insert derivation action
1. reduce gain, insert derivation action, use negative feedback
1. use negative feedback, reduce gain, insert derivation action

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Since all the coefficients in all the three polynomials are positive, it is required to construct Hurwitz table for further checking.
1. s⁴ + 7s³ + 17s² + 17s + 6
This is seen to be a Hurwitz polynomial as all the terms in the first column have the same sign.

2. s⁴ + 11s³ + 41s² + 61s + 30
This also is a Hurwitz polynomial

3. s⁴ + s³ + 2s² + 3s + 2
This is not a Hurwitz polynomial

Correct Option: D

Since all the coefficients in all the three polynomials are positive, it is required to construct Hurwitz table for further checking.
1. s⁴ + 7s³ + 17s² + 17s + 6
This is seen to be a Hurwitz polynomial as all the terms in the first column have the same sign.

2. s⁴ + 11s³ + 41s² + 61s + 30
This also is a Hurwitz polynomial

3. s⁴ + s³ + 2s² + 3s + 2
This is not a Hurwitz polynomial

What is the unit step response of a unity feedback control system having forward path transfer
function G(s) = 80
s(s + 18)

1. Overdamped
1. Critically damped
1. Underdamped
1. Undamped oscillatory

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T(s) = G(s) = 80
1 + G(s) s² + 18s + 80

C(s) = 80
R(s) s² + 18s + 80

Here , 2ξω_n = 18
and ω_n = √80
∴ ξ = 18 = 1.006
2√80

Since, ξ > 1, the system is overdamped.

Correct Option: D

T(s) = G(s) = 80
1 + G(s) s² + 18s + 80

C(s) = 80
R(s) s² + 18s + 80

Here , 2ξω_n = 18
and ω_n = √80
∴ ξ = 18 = 1.006
2√80

Since, ξ > 1, the system is overdamped.

The unstable system is

1. G(s) H(s) = K ; K > 0
  (T₁s + 1)(T₂s + 1)
1. G(s) H(s) = K(s + 1) ; K > 91
  s²(s + 4)(s + 5)
1. G(s) H(s) = K(s + 2) ; K > 2
  (s + 1)(s - 3)
1. G(s) H(s) = K ; -1 < K < 2
  (Ts + 1)³

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Characteristic equation is
s⁴ + 9s³ + 20s² + Ks + K = 0
Routh table is as shown below.

For stability, 0 < K < 99.

Correct Option: B

Characteristic equation is
s⁴ + 9s³ + 20s² + Ks + K = 0
Routh table is as shown below.

For stability, 0 < K < 99.

The forward-path transfer function of a unity feedback system is
G(s) = K(s² - 4)
s³ + 3

For the system to be stable the range of K is

1. K > -1
1. K < 3
  4
1. -1 < K < 3
  4
1. marginal stable

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Closed loop transfer function

T(s) = K(s² - 4)
(K + 1)s² + (3 - 4K)

The system can be only marginally stable.

Correct Option: D

Closed loop transfer function

T(s) = K(s² - 4)
(K + 1)s² + (3 - 4K)

The system can be only marginally stable.

The open-loop transfer function of a unity feedback control system is
G(s) = K(s + 2)
(s + 1)(s - 7)

For K > 6, the stability characteristic of the openloop and closed-loop configurations of the system are respectively

1. stable and unstable
1. stable and stable
1. unstable and stable
1. unstable and unstable

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In open-loop system, there is a pole in RHP. So system is unstable.
In closed loop system
T(s) = K(s + 2)
s² + (K - 6)s + 2K - 7

For stability K > 6, 2K – 7 > 0
⇒ K > 6
So for K > 6, system is stable.

Correct Option: C

In open-loop system, there is a pole in RHP. So system is unstable.
In closed loop system
T(s) = K(s + 2)
s² + (K - 6)s + 2K - 7

For stability K > 6, 2K – 7 > 0
⇒ K > 6
So for K > 6, system is stable.