An open loop control system results in a response of $${e^{ - 2t}}\left( {\sin 5t + \cos 5t} \right)$$ for a unit impulse input. The DC gain of the control system is __________.

The transfer function $${{{V_2}\left( s \right)} \over {{V_1}\left( s \right)}}$$ of the circuit shown below is

Errors associated with each respective subsystem $$\,{G_1},\,{G_2}$$ and $${G_3}$$ are $${\varepsilon _1},\,\,{\varepsilon _2}$$ and $${\varepsilon _3}$$. The error associated with the output is :

For a tachometer if $$\theta \left( t \right)$$ is the rotor displacement is radians, $$e\left( t \right)$$ is the output voltage and $${K_t}$$ is the tachometer constant in V/rad/sec, then the transfer function $${{E\left( s \right)} \over {\theta \left( s \right)}},$$ will be

Feedback control systems are

A linear time-invariant system initially at rest, when subjected to a unit-step input, gives a response $$y\left( t \right) = t{e^{ - t}},\,\,t > 0.$$ The transfer function of the system is:

The impulse response of an initially relaxed linear system is $${e^{ - 2t}}u\left( t \right).$$ To produce a response of $${te^{ - 2t}}u\left( t \right),$$ the input must be equal to

For a system having transfer function $$G\left( s \right) = {{ - s + 1} \over {s + 1}},$$ a unit step input is applied at time $$t=0.$$ The value of the response of the system at $$t=1.5$$ sec (round off to three decimal places) is __________.

Let a causal $$LTI$$ system be characterized by the following differential equation, with initial rest condition
$${{{d^2}y} \over {d{t^2}}} + 7{{dy} \over {dt}} + 10y\left( t \right) = 4x\left( t \right) + 5{{dx\left( t \right)} \over {dt}}\,\,$$

Where, $$x(t)$$ and $$y(t)$$ are the input and output respectively. The impulse response of the system is ($$u(t)$$ is the unit step function)

The transfer function of the system described by $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} = {{du} \over {dt}} + 2u$$ with $$u$$ as input and $$y$$ as output is