41. Find the locations of any two roots of the characteristic equation F(s) = s4 + 2s3 + 11s2 + 18s + 18 = 0.
42. The unit step response of the above system is given by
43. If the closed-loop transfer function of a control system is given as $$T\left( s \right) = \frac{{s - 5}}{{\left( {s + 2} \right)\left( {s + 3} \right)}},$$ then it is
44. The pole-zero plot is shown here when the DC gain is equal to 20. The system transfer function is . . . . . . . .
45. In the case of a second order system described by the differential equation, $$\frac{{J{d^2}{\theta _0}}}{{d{t^2}}} + F\frac{{d{\theta _0}}}{{dt}} + k{\theta _0} = k{\theta _i}$$
(where θ1 and θ0 are input and output shaft angles), the natural frequency is given by:
(where θ1 and θ0 are input and output shaft angles), the natural frequency is given by:
46. For a lead compensator, whose transfer function is given by $$K\frac{{s + a}}{{s + b}};\,a,\,b \geqslant 0$$
47. The magnitude and phase relationship between the sinusoidal input and the steady-state output of a system is called as:
48. Consider the following for a variable reluctance stepper motor used in system:
1. The stator torque acting on the rotor is a function of angular misalignment between stator and rotor teeth.
2. There are two positions of zero torque: $$\theta = {0^ \circ },\,\frac{{{{180}^ \circ }}}{{\text{T}}}$$ (T = number of rotor teeth)
3. Both the torque zero positions are stable.
4. As the stator is excited, the rotor is pulled into the nearest minimum reluctance position.
Of these statements
1. The stator torque acting on the rotor is a function of angular misalignment between stator and rotor teeth.
2. There are two positions of zero torque: $$\theta = {0^ \circ },\,\frac{{{{180}^ \circ }}}{{\text{T}}}$$ (T = number of rotor teeth)
3. Both the torque zero positions are stable.
4. As the stator is excited, the rotor is pulled into the nearest minimum reluctance position.
Of these statements
49. Consider the following statements:
The Gain margin and Phase margin of an unstable system may respectively be:
1. Positive, negative
2. Negative, positive
3. Negative, negative
Which of the above statements is/are correct?
The Gain margin and Phase margin of an unstable system may respectively be:
1. Positive, negative
2. Negative, positive
3. Negative, negative
Which of the above statements is/are correct?
50. A system's open loop transfer function is given by $$G\left( s \right) = \frac{K}{{s\left( {s + 2} \right)\left( {s + 4} \right)}}.$$ If system is having a unity negative feedback, which of the following is true for such system to be stable?
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