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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:
∴
Forward paths are:
Loops are:
The unit impulse response of a system is h(t) = e^{2t}, _{t} 0_{.}
For this system, the steadystate value of the output for unit step input is equal to
and
∴
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
The openloop transfer function of a feedback control system is given by G(s)
Find the range of the values of T for stability.
The characteristic equation of the system is
s^{2} + s(2 — T) + 1 = 0
Routh's array becomes:
The system will be stable if
∴
If the openloop transfer function of a feedback system is given by
G(s) H(s) = , then the controid of the asymptotes will be
Poles = 0, —2, —1 + 2j, —1 —2j
Total number of pole, P = 4
Total number of zero, Z = 0
∴ P — Z = 4
∴
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
For inner loop:
let
For outer loop:
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?
Because of concept of dominant pole. Here P_{1} and P_{2} are dominant pole and P_{3} and P_{4} are
insignificant poles.
Match ListI (Type of compensator) with ListII (Polar plot) and select the correct answer using the code given below the lists:
ListI
1.Phase lead
2. Phase lag
3. Leadlag
A B C
(a)123
(b) 132
(c) 213
(d) 231
For the given network, the maximum phase lead _{4m} of V_{o} with respect to V_{1} is
In the Bodeplot of a unity feedback control system, the value of phase of G(j@) at the gain
crossover frequency is —125°. The phase margin of the system is
φ at ωg C = —125°
Phasemargin (PM) = 180°+ φ
= 180°— 125°
= 55°
The Nyquist plot for the function is
The condition for stability is given by
The openloop transfer function of unity feedback system is G(s) = . Thes (s + 2) (s + 10)range of k for which closedloop system is stable.
It is type1 and order —3 system so the Nyquist plot is
For stability:
(a)
For the system shown below the statespace equation is X = A x + B u. The matrix A is
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