A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has

If the closed-loop transfer function of a control system is given as T(s) = ^{$$\dfrac{s-5}{(s+2)(s+3)}$$}, then it is

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

G (s) = ^{$$\dfrac{k}{(s+1)(s+2)}$$}

The gain margin of the system in dB is given by

Despite the presence of negative feedback, control systems still have problems of instability because the

A system with transfer function G (s) = $$\dfrac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$$ Is excited by sin($\omega$t). The steady-state output of the system is zero at

The input-output transfer function of a plant H(x) = $$\dfrac{100}{s(s+10)^2}$$. The plant is placed in a unity negative feedback configuration as shown in the figure below.

The gain margin of the system under closed loop unity negative feedback is

Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

For the asymptotic Bode magnitude plot shown below, the system transfer function can be

The number of open right half plane of G (s) = ^{$ \dfrac{10}{s^5+2s^4+3s^3+6s^2+5s+3} $}

The state variable description of an LTI system is given by $ \left( \begin{array} x_1 \\ x_2 \\ x_3 \end{array} \right) $= $ \left( \begin{array} \ 0&a_1&0\\ 0&0&a_2\\ a_3&0&0 \end{array} \right) $$ \left( \begin{array} \ x_1\\ x_2\\ x_3 \end{array} \right) $+ $ \left( \begin{array} \ 0\\ 0\\ 1 \end{array} \right) u $ y = (1 0 0) $ \left( \begin{array} \ x_1\\ x_2\\ x_3 \end{array} \right) $ Where y is output and u is the input. The system is controllable for

The root locus of the system G (s) H(s) = $\dfrac{k}{s(s+2)(s+3)}$ has the break - away point located at

The input-output transfer function of a plant H(x) = $\dfrac{100}{s(s+10)^2}$. The plant is placed in a unity negative feedback configuration as shown in the figure below.

The signal flow graph that DOES NOT model the plant transfer function H(s) is

The feedback configuration and the pole-zero locations of are shown below. The root locus for negative values of k , i.e. for -$\infty$< k < 0, has breakaway / break-in points and angle of departure at pole P (with respect to the positive real axis) equal to

For the transfer function G (j$\omega$ ) = 5 + j$\omega$, the corresponding Nyquist plot for positive frequency has the form

A causal system having the transfer function H(s) = 1 /(s+2) is excited with 10u(t) . The time at which the output reaches 99% of its steady state value is

The transfer function of a compensator is given as

G_c(s) = ^{$\dfrac{s+a}{s+b}$}

G_c (s) is a lead compensator if

The gain margin for the system with open-loop transfer function G(s) H(s) = ^{$\dfrac{2(1+s)}{s^2}, \ is$}

A double integrator plant, ^{$G(s) = \dfrac{k}{s^2} \ H(s) = 1$} is to be compensated to achieve the damping ratio _^$\xi$ = 0.5, and an undamped natural, _{^{$\omega_n = 5\ rad/s$}}. Which one of the following compensator G_c(S) will be suitable?

Consider the system $\dfrac{dx}{dt}$= Ax + Bu with A = $ \left[ \begin{array} \ 1&0\\ 0&1 \end{array} \right] $ and B = $ \left[ \begin{array} \ p\\ q \end{array} \right] $

where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true?