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For the system in the given figure the characteristic equation is
Transfer function = .
Hence characteristic equation is .
In force voltage analogy force is analogous to voltage and velocity to current. Just as , force/velocity = mechanical impedance.
For the system in the given figure. The transfer function C(s)/R(s) is
Transfer function = (G_{1} + 1) G_{2} + 1 = G_{1} G_{2} + G_{2} + 1.
Whether a linear system is stable or unstable that it
Stability is a property of the system only.
For the system of the given figure the transfer function =
, E_{0}(s) = [I(s)][Z_{2}(s)] or .
In the given figure shows polezero plot. If steady state gain is 2 the transfer function G(s) is
The zero at  1 gives the term (s + 1) in the numerator.
The poles at ( 2 + j1) and ( 2  j1) give (s^{2} + 4s + 5) term is the denominator. Gain is 2.
If a system is to follow arbitrary inputs accurately the bandwidth should be
Arbitrary inputs require large bandwidth.
For the system of the given figure, the damping ratio of closed loop poles is
The standard form of characteristic equation is .
Therefore .
Assertion (A): Potentiometers can not be used as error detectors in position control systems.
Reason (R): The resolution of a potentiometer places an upper limit on its accuracy
Potentiometers are used as error detectors.
For a first order system having transfer function , the unit impulse response is
.
When input pulses are applied, the motor moves in steps.
In a two phase ac servomotor rotor resistance is R and rotor reactance is X. The speed curve will be linear if
In a two phase servomotor ∠ < 1 so that torque speed curve is almost linear.
In the given figure, the input frequency is such that R = X_{C}. Then
R = X_{C}, voltage drops across R and X_{C} are equal and at 90º with respect by each other. V_{0} lags V_{i} by 45º.
From the noise point of view, bandwidth should
If noise is to be eliminated, bandwidth cannot be large.
First column elements of Routh's tabulation are 3, 5, , 2. It means that there
Since there are two sign changes in the first column, hence two roots in right half plane.
When a unit step voltage drives a lag network the output
At t = 0 the capacitor behaves as a shortcircuit and output voltage is 0. At t = ∞ capacitor behaves as an opencircuit and V_{0} = V_{i}.
.
A system has its two poles on the negative real axis and one pair of poles lies on jω axis. The system is
Poles on j xaxis lead to oscillations.
.
In the given figure the input frequency is such that R << X_{c}, then
Voltage across capacitor lags by 90º.
To measure pressure, it is convenient to convert pressure into displacement and then use a displacement transducer.
A unity feedback system has open loop transfer function The closed loop transfer function is
.
In the given figure, of potentiometer V_{0} = V_{i} (R_{0}/R_{i}) only when
If R_{L} is not infinite, the voltage ratio of potentiometer depends on the value of R_{L}. This is called loading effect.
Assertion (A): The steady state response, of a stable, linear, time invariant system, to sinusoidal input depends on initial conditions.
Reason (R): Frequency response, in steady state, is obtained by replacing s in the transfer function by jω
Steady state response does not depend on initial conditions.
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