A control system with a PD controller is shown in the figure. If the velocity error constant $${K_v} = 1000$$ and the damping ratio $$\zeta = 0.5,$$ then the values of $${K_P}$$ and $${K_D}$$ are

The asymptotic Bode plot of a transfer function is shown in the figure. the transfer function G(s) corresponding to this bode plot is

The transfer function of a plant is $$$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$ The second-order approximation of T (s) using dominant pole concept is:

A unity feedback control system has an open-loop transfer function $$$G\left(s\right)=\frac K{s\left(s^2+7s+12\right)}$$$ The gain K for which s = −1 + j1 will lie on the root locus of this system is: