Time-Response-EE

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is $$ \begin{array}{|l|c|c|c|c|c|} \hlin...

When a unit ramp input is applied to the unity feedback system having closed loop transfer function $${{C\left( s \right)} \over {R\left( s \right)}} = {{Ks + b} \over {{s^2} + as + b}},\,\left( {a > 0,\,b > 0,\,K > 0} \...

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...

The unit step response of a system with the transfer function $$G\left( s \right) = {{1 - 2s} \over {1 + s}}$$ is given by which one of the following waveforms?

The closed-loop transfer function of a system is $$T\left( s \right) = {4 \over {\left( {{s^2} + 0.4s + 4} \right)}}.$$ The steady state error due to unit step input is ________

The response $$h(t)$$ of a linear time invariant system to an impulse $$\delta \left( t \right),$$ under initially relaxed condition is $$h\left( t \right) = \,{e^{ - t}} + {e^{ - 2t}}.$$ The response of this system for...

For the system $${2 \over {\left( {s + 1} \right)}},$$ the approximate time taken for a step response to reach $$98$$% of its final value is

For the system $$\frac2{\left(s+1\right)}$$, the approximate time taken for a step response to reach 98% of its final value is

The transfer function of a system is given as $${{100} \over {{s^2} + 20s + 100}}.$$ The system is

A function $$y(t)$$ satisfies the following differential equation : $${{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$ Where $$\delta \left( t \right)$$ is the delta function. Assuming ze...

The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}$$ The steady state value of the output of the system for a unit impulse input applied at time instant $...

The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12.5{e^{ - 6t}}\,\sin 8t,\,\,t \ge 0.$$ The steady-state value of the unit step response of the system...

A control system with certain excitation is governed by the following mathematical equation $$${{{d^2}x} \over {d{t^2}}} + {1 \over 2}{{dx} \over {dt}} + {1 \over {18}}x = 10 + 5{e^{ - 4t}} + 2{e^{ - 5t}}$$$ The natural...

A control system is defined by the following mathematical relationship $$${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - 2t}}} \right)$$$ The response of the system as $$\,t \to \infty $$ is

A unity feedback system has open loop transfer function $$G(s).$$ The steady-state error is zero for

A unity feedback system has open-loop transfer function $$G\left( s \right) = {{25} \over {s\left( {s + 6} \right)}}.$$ The peak overshoot in the step-input response of the system is approximately equal to

A first order system is initially at rest and excited by a step input at time $$t=0.$$ Its output becomes $$1.1$$ $$V$$ is in $$4$$ seconds and eventually reaches a steady state value of $$2V$$. Determine its time

For a feedback control system of type $$2,$$ the steady state error for a ramp input is

The closed - loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}} = {1 \over {\left( {1 + s} \right)}}$$ For the input $$\,r\left( t \right)\,\, = \,\,\sin \,t,$$ the s...

The unit impulse response of a system is given as $$c\left( t \right) = - 4{e^{ - t}} + 6{e^{ - 2t}}.\,\,\,$$ The step response of the same system for $$\,t \ge 0$$ is equal to

Consider the unit step response of a unity feedback control system whose open loop transfer function is $$G\left( s \right) = {1 \over {s\left( {s + 1} \right)}}.$$ The maximum overshoot is equal to

The closed loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}}\, = \,\,{{2\left( {s - 1} \right)} \over {\left( {s + 2} \right)\left( {s + 1} \right)}}$$ for a unit st...

The steady state error due to a step input for type $$1$$ system is ______________.