BEE Control System Principles 2 β Questions and Answers
Question 1: Which of the following best describes the steady-state error of a Type 1 system subjected to a ramp input?
- Zero
- A finite constant (Correct answer)
- Infinite
- Oscillatory
Correct answer: A finite constant
A Type 1 system has one integrator, which eliminates steady-state error for step inputs but produces a finite constant error for ramp inputs.
Question 2: In a second-order control system, if the poles are located at -3 Β± j4, what is the damping ratio?
- 0.6 (Correct answer)
- 0.75
- 0.5
- 0.8
Correct answer: 0.6
The poles are at Ο Β± jΟ_d where Ο = 3 and Ο_d = 4, giving Ο_n = 5 and ΞΆ = Ο/Ο_n = 3/5 = 0.6.
Question 3: What is the primary function of a lead compensator in a control system?
- Reduce steady-state error
- Improve transient response and increase phase margin (Correct answer)
- Attenuate high-frequency noise
- Increase system type number
Correct answer: Improve transient response and increase phase margin
A lead compensator adds positive phase at crossover frequency, increasing phase margin and improving transient response speed.
Question 4: For a unity feedback system with open-loop transfer function G(s) = K/[s(s+2)(s+5)], what happens to closed-loop stability as K increases beyond a critical value?
- System becomes more stable
- System becomes unstable (Correct answer)
- Damping ratio increases
- Steady-state error decreases without limit
Correct answer: System becomes unstable
As K increases, root locus poles migrate into the right-half plane, causing instability; the Routh criterion confirms a finite gain margin.
Question 5: Which parameter is directly read from the Bode magnitude plot at the gain crossover frequency?
- Phase margin
- Gain margin
- Bandwidth
- The magnitude is 0 dB by definition (Correct answer)
Correct answer: The magnitude is 0 dB by definition
The gain crossover frequency is defined as the frequency where the open-loop magnitude equals 0 dB (unity gain).
Question 6: In state-space representation, what does the matrix C represent in the equation y = Cx + Du?
- System dynamics matrix
- Input distribution matrix
- Output matrix relating states to outputs (Correct answer)
- Feedthrough matrix
Correct answer: Output matrix relating states to outputs
The C matrix (observation matrix) maps the state vector x to the system output y.
Question 7: A PD controller applied to a second-order plant primarily has what effect on the closed-loop system?
- Increases steady-state error
- Adds a zero that increases damping ratio (Correct answer)
- Reduces bandwidth
- Introduces an integrator
Correct answer: Adds a zero that increases damping ratio
The derivative term of the PD controller adds a zero to the open-loop transfer function, which increases damping and reduces overshoot.
BEE Control System Principles 2
Which of the following best describes the steady-state error of a Type 1 system subjected to a ramp input?