GATE EC Control Systems questions

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Identify the feedback structure before forming the transfer function. Check the characteristic equation and stability conditions before calculating steady-state behaviour.

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SubjectTopicYearType

For the system described by the state equation

x=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0.5 & 1 & 2 \end{array}\right] x+\left[\begin{array}{l} 0 \\ 0 \\ 1 \end{array}\right] u

If the control signal

u

is given by

u=[-0.5-3-5]

x+v

, then the eigenvalues of the closed-loop system will be

Consider the points

s_{1}=-3+j 4

and

s_{2}=-3-j 2

in the

s

-plane. Then, for a system with the open-loop Transfer function

G(s) H(s)=\frac{K}{(s+1)^{4}}

If the closed-loop transfer function

T(s)

of a unity negative feedback system is given by

\mathrm{T}(\mathrm{s})=\frac{a_{n -1} \mathrm{~s}+a_{n}}{\mathrm{~s}^{n}+n_{1} s^{n-1}+\ldots+a_{n-1} s+a_{n}}

then the steady state error for a unit ramp input is

In a shunt-shunt negative feedback amplifier, as compared to the basic amplifier

From a measurement of the rise time of the output pulse of an amplifier whose input is a small amplitude square wave, one can estimate the following parameter of the amplifier

In a synchro error detector, the output voltage is proportional to

[\omega(t)]^n

, where

\omega(t)

is the rotor velocity and

n

equals

The transfer function of a system is

\frac{2 s^2+6 s+5}{(s+1)^2(s+2)}

The characteristic equation of the system is

The Nyquist plot of a phase transfer function

g(j \omega) H(j \omega)

of a system encloses the

(-1,0)

point. The gain margin of the system is

The transfer function of a phase lead controller is

\frac{1+3 \mathrm{Ts}}{1+\mathrm{Ts}}

. The maximum value of phase provided by this controller is

Consider a feedback control system with loop transfer function

\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}(1+0.5 s)}{s(1+s)(1+2 s)}

The type of the closed loop system is

In the Bode-plot of a unity feedback control system, the value of phase of

G(j \omega)

at the gain cross over frequency is

-125^{\circ}

. The phase margin of the system is

Consider a unity feedback control system with open-loop transfer function

\mathrm{G} (s)=\frac{\mathrm{K}}{s(s+1)}

. The steady state error of the system due to a unit step input is

The transfer function of a tachometer is of the form

The number of roots of

s^3+5 s^2+7 s+3=0

in the left half of the

s

-plane is

The unit impulse response of a linear time-invariant system is the unit step function

u(t)

. For

t>0

, the response of the system to an excitation

e^{-a t} u(t), a>0

will be

The Laplace Transform of

e \alpha t \cos (\alpha \; t)

is equal to

A certain linear time invariant system has the state and the output equations given below …

In the signal flow graph of the figure is

\text{y/ x}

equals

The inverse Laplace transform of the function

\frac{s+5}{(s+1)(s+3)}

Non-minimum phase transfer function is defined as the transfer function.