Control Systems...

The closed loop transfer function of a unity feedback system is given as \(\frac{{10\left( {s + 1} \right)}}{{{s^2} + 20s + 10}}\). The steady state error to a unit ramp input is

The open loop transfer function of a unity feedback system is given by

\(\frac{1}{{s\left( {3s + 1} \right)}}{e^{ - 2Ts}},T > 0\)

It is shown that the phase angle of the loop transfer function at frequency ω₀ is 0. Which of the following equation is satisfied by ω₀

Consider a unity feedback closed-loop system whose open-loop transfer function is \(\frac{{2\left( {s + 8} \right)}}{{{s^2} + 7s - 8}}\)

The mapped contour of the Nyquist contour in the G(s) H(s) plane (where G(s) H(s) is the open-loop transfer function)

The transfer function of a system is given by \(G\left( s \right) = \frac{{{e^{ - \frac{s}{{500}}}}}}{{s + 500}}\)

The input to the system is x(t) = sin 100 πt.

In a periodic steady-state, the output of the system is found to be y(t) = A sin (100 πt - ϕ). The phase angle (ϕ) in degrees is _______ 

Given the following polynomial equation

s³ – s² + 3s + 1 = 0

The number of roots of the polynomial, which have real parts strictly less than 1, is_______

Given \(\rm G\left( s \right)H\left( s \right) = \frac{K}{{s\left( {s + 4} \right)\left( {{s^2} + 4s + 12} \right)}}\)is the open loop transfer function of a system. Then total number of complex break points is.

Consider the system \(\dot x\left( t \right) = \left[ {\begin{array}{*{20}{c}} 1&1\\ 0&1 \end{array}} \right]x\left( t \right) + \left[ {\begin{array}{*{20}{c}} {{b_1}}\\ {{b_2}} \end{array}} \right]u\left( t \right),c\left( t \right) = \left[ {\begin{array}{*{20}{c}} {{d_1}}&{{d_2}} \end{array}} \right]u\left( t \right)\). The conditions for complete state controlling and complete observability is

Obtain the complete time response of system given by,

\(\dot X\left( t \right) = \left[ {\begin{array}{*{20}{c}}0&1\\{ - 2}&0\end{array}} \right]X\left( t \right)\;where\;X\left( 0 \right) = \left[ {\begin{array}{*{20}{c}}1\\1\end{array}} \right]\)

And Y(t) = [1 - 1]X(t)