Control Systems...

The transfer function of a system is represented by the equation

\(\ddot y\left( t \right) - 3\dot y\left( t \right) - 4y\left( t \right) = \ddot u\left( t \right) + 2\dot u\left( t \right) + 2u\left( t \right),\)

Which of the following statements is/are true?

Match List-I (Transfer function of the system) with List-II (Type and order of the system) and select the correct answer using the codes given below the Lists:

A unity feedback system has open loop transfer function \(G\left( s \right) = \frac{{K\left( {s + 1.1} \right)\left( {s + 2.2} \right)}}{{s\left( {s + 3.3} \right)\left( {s + 4.4} \right)}}.\) For K = 0 the closed-loop poles are

An open loop control system results in a response of 1 – e^-3t (sin 4t + cos 4t) for a unit impulse. The DC gain of the open loop control system for a unity feedback is _______

A control system whose ramp input response is 3(1 – e^-2t) is cascaded to another control block whose step response is e^-4t. What is the transfer function of the cascaded combination?

A system is represented by the differential equation

ÿ(t) + 6ẏ(t) + 5y(t) = u(t)

Which of the following is/are true for a unit step response?

The response y(t) of a linear system to an excitation x(t) = e^-3t u(t) is y(t) = (2t + 1) e^-2t u(t). Poles and zeros will be at