Control System

Q:   The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

• A:  Both the criteria provide information relative to the stable gain range of the system.
• B:  The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems.
• C:  The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion.
• D:  The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

Q:   Consider p(s)=s³+a₂s²+a₁s+a₀ with all real coefficients. It is known that its derivative p(s) has no real roots. The number of real roots of p(s) is

• A:  0
• B:  1
• C:  2
• D:  3

Q:   For a unity feedback control system with the forward path transfer function
G(s)=K/s(s+2)
The peak resonant magnitude Mr of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is

Q:   The open loop transfer function G(s)=(s+1)sp(s+2)(s+3) where p is an integer, is connected in unity feedback configuration as shown in the figure. Given that the steady state error is zero for unit and 6 for unit ramp input, the value of the parameter p is_________.

Q:   Which one of the following options correctly describes the location of the roots of the equation s⁴+s²+1=0 on the plane?

• A:  Four left half plane (LHP) roots
• B:  One right half plane (RHP) root, one LHP root and two roots on the imaginary axis
• C:  Two RHP roots and two LHP roots
• D:  All four roots are on the imaginary axis

Q:   A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

• A:  encircles the s-plane point (−1 + j 0) in the counterclockwise direction as many times as the number of right-half s-plane poles.
• B:  encircles the s-plane point (0 − j 1) in the clockwise direction as many times as the number of right-half s-plane poles.
• C:  encircles the s-plane point (−1 + j 0) in the counterclockwise direction as many times as the number of left-half s-plane poles.
• D:  encircles the s-plane point (−1 + j 0) in the counterclockwise direction as many times as the number of right-half s-plane zeros.

Q:   The response of the system G(s)=(s−2)/(s+1)(s+3) to the unit step input u(t) is y(t). The value at t =0+ is ________

Q:   Negative feedback in a closed-loop control system DOES NOT

• A:  reduce the overall gain
• B:  reduce bandwidth
• C:  improve disturbance rejection
• D:  reduce sensitivity to parameter variation

Q:   The open-loop transfer function of a plant in a unity feedback configuration is given as G(s) =K(s+4)/(s+8)(s2−9) . The value of the gain K (>0) for which the point (–1 + j 2) lies on the root locus is _____.

Q:   The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.