Section 1 - Control Systems Fundamentals

Question 1

The main advantage of a closed-loop control system over an open-loop system is:

A. Simpler construction and lower cost

B. Reduced sensitivity to disturbances and parameter variations

C. Faster response in all cases

D. No need for a controller

Question 2

The transfer function of a linear time-invariant system is defined as:

A. Ratio of output to input in the time domain at steady state

B. Ratio of the Laplace transform of the output to the Laplace transform of the input with zero initial conditions

C. Ratio of the derivative of output to the derivative of input

D. Ratio of steady-state error to input

Question 3

The order of a control system is defined as:

A. The highest power of s in the numerator of the transfer function

B. The highest power of s in the denominator (characteristic polynomial) of the transfer function

C. The number of feedback loops in the system

D. The number of poles minus the number of zeros

Question 4

The type of a control system is determined by:

A. The number of open-loop poles at the origin (s = 0)

B. The highest power of s in the transfer function denominator

C. The number of zeros at the origin

D. The gain of the system at DC

Question 5

The steady-state error of a Type-1 system for a unit step input is:

A. Zero

B. 1

C. 1 / (1 + Kp)

D. Infinite

Question 6

The steady-state error of a Type-0 system for a unit ramp input is:

A. Zero

B. Finite non-zero constant

C. Infinite

D. Unity

Question 7

Mason's gain formula is used to determine:

A. The stability of the system directly

B. The overall transfer function from a signal flow graph

C. The frequency response from a Bode plot

D. The transient response of the system

Question 8

The characteristic equation of a closed-loop system with unity feedback and open-loop transfer function G(s) is:

A. G(s) = 0

B. 1 + G(s) = 0

C. G(s) = 1

D. 1 - G(s) = 0

Question 9

For a stable linear time-invariant system, all poles of the closed-loop transfer function must lie:

A. On the imaginary axis of the s-plane

B. In the left half of the s-plane

C. In the right half of the s-plane

D. At the origin

Question 10

The Routh-Hurwitz criterion is used to determine:

A. The transient response of a system

B. The absolute stability of a system without solving the characteristic equation

C. The frequency response of a system

D. The gain margin only

Question 11

For a second-order underdamped system, the damping ratio zeta lies in the range:

A. zeta < 0

B. 0 < zeta < 1

C. zeta = 1

D. zeta > 1

Question 12

A second-order system with damping ratio zeta = 1 is called:

A. Undamped

B. Underdamped

C. Critically damped

D. Overdamped

Question 13

For a standard second-order underdamped system with natural frequency omega_n and damping ratio zeta, the damped frequency of oscillation is:

A. omega_n

B. omega_n * sqrt(1 - zeta^2)

C. omega_n * zeta

D. omega_n / zeta

Question 14

The peak overshoot of a second-order underdamped system depends on:

A. Only the natural frequency

B. Only the damping ratio

C. Both natural frequency and damping ratio

D. Only the input magnitude

Question 15

The rise time of a second-order underdamped system generally decreases when:

A. The damping ratio is increased

B. The natural frequency is increased

C. The input magnitude is decreased

D. The system order is increased

Question 16

The root locus of a control system shows the paths of:

A. Open-loop poles as a function of frequency

B. Closed-loop poles as a system parameter (typically gain K) varies from 0 to infinity

C. Zeros of the open-loop transfer function

D. Steady-state errors versus gain

Question 17

The number of asymptotes of the root locus is equal to:

A. Number of open-loop zeros

B. Number of open-loop poles minus number of open-loop zeros

C. Number of closed-loop poles

D. Order of the system minus one

Question 18

The Nyquist stability criterion relates the stability of a closed-loop system to:

A. The Bode plot only

B. The number of encirclements of the point (-1, j0) by the open-loop frequency response plot

C. The root locus branches only

D. The gain crossover frequency only

Question 19

Gain margin of a stable minimum-phase system is:

A. The additional gain (in dB) that can be added before the system becomes unstable

B. The phase lag added at the gain crossover frequency

C. The steady-state gain of the system

D. The peak of the magnitude response

Question 20

Phase margin of a stable minimum-phase system is:

A. The additional phase lag (at the gain crossover frequency) that can be added before the system becomes unstable

B. The gain (in dB) at the phase crossover frequency

C. The peak overshoot

D. The natural frequency

Question 21

In a Bode magnitude plot, a simple pole contributes a slope of:

A. +20 dB/decade

B. -20 dB/decade

C. +40 dB/decade

D. -40 dB/decade

Question 22

In a Bode magnitude plot, a simple zero contributes a slope of: