Control Systems...

Consider a stable system with the transfer function

\(G\left( s \right) = \frac{{{s^p} + {b_1}\;{s^{p - 1}} + \ldots {b_p}}}{{{s^q} + {a_1}{s^{q - 1}} + \ldots {a_q}}}\)

Where b₁,…..,b_p  and a₁,…..,a_q are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to -60 dB/decade as ω → ∞. A possible pair of values for p and q is:

The open loop transfer function of a unity feedback system is given by \(G\left( s \right) = \frac{{\pi {e^{ - 0.25s}}}}{s}\). In G(s) plane, the Nyquist plot of G(s) passes through the negative real axis at the point

A unity feedback control system has an open-loop transfer function,

\(G\left( s \right)H\left( s \right) = \frac{K}{{s\left( {s + 2} \right)\left( {s + 4} \right)}}\)

What is the value of K so that the gain margin of the system becomes 20 dB?

A unit step input is applied to a unity feedback control system having open-loop transfer function,

\(G\left( s \right)H\left( s \right) = \frac{K}{{s\left( {1 + sT} \right)}}\)

The specification is such that the maximum overshoot is 20% and the resonant frequency is ω_r = 6 rad/sec. The values of K and T are