BEE Control Systems Theory 2 ā Questions and Answers
Question 1: A system has the characteristic equation sĀ³ + 6sĀ² + 11s + 6 = 0. Using the Routh-Hurwitz criterion, how many roots lie in the right-half s-plane?
- 0 (Correct answer)
- 1
- 2
- 3
Correct answer: 0
All Routh array elements are positive (1, 6, 11, 6 ā row 2: 6, 6; row 3: 10, 0; row 4: 6), so no sign changes and all roots are in the left-half plane.
Question 2: The steady-state error of a Type 1 system to a ramp input is:
- Zero
- A finite nonzero constant (Correct answer)
- Infinite
- Dependent on system gain only
Correct answer: A finite nonzero constant
A Type 1 system has one open-loop integrator, so it tracks step inputs perfectly but produces a finite steady-state error proportional to ramp rate divided by velocity constant Kv.
Question 3: On a Bode plot, what is the slope (in dB/decade) introduced by each additional open-loop pole?
- +20 dB/decade
- -20 dB/decade (Correct answer)
- +40 dB/decade
- -40 dB/decade
Correct answer: -20 dB/decade
Each real open-loop pole adds a -20 dB/decade slope change to the magnitude Bode plot above its break frequency.
Question 4: Which of the following best describes the principle of superposition as it applies to linear control systems?
- The output for a sum of inputs equals the sum of individual outputs (Correct answer)
- The gain is constant at all frequencies
- The system is stable for all bounded inputs
- Phase shift is zero for all sinusoidal inputs
Correct answer: The output for a sum of inputs equals the sum of individual outputs
Superposition states that for linear systems, the response to a linear combination of inputs equals the same linear combination of individual responses.
Question 5: The transfer function of an ideal PD controller is:
- Kp(1 + TdĀ·s) (Correct answer)
- Kp/(1 + TiĀ·s)
- Kp(1 + 1/(TiĀ·s) + TdĀ·s)
- Kp/(TiĀ·s)
Correct answer: Kp(1 + TdĀ·s)
A PD controller adds proportional and derivative action, yielding the transfer function Kp(1 + TdĀ·s).
Question 6: If the gain margin of a system is 20 dB, the actual gain can be increased by a factor of _____ before the system becomes unstable.
- 10 (Correct answer)
- 20
- 100
- 200
Correct answer: 10
A gain margin of 20 dB corresponds to a factor of 10 (since 20 dB = 20Ā·logāā(10)), meaning gain can be multiplied tenfold before instability.
Question 7: In state-space representation, the matrix that relates the current state and input to the output is called the:
- State matrix A
- Input matrix B
- Output matrix C and feedthrough matrix D (Correct answer)
- Transition matrix Ī¦
Correct answer: Output matrix C and feedthrough matrix D
The output equation y = Cx + Du uses the output matrix C and feedthrough (direct transmission) matrix D to compute outputs from states and inputs.
BEE Control Systems Theory 2
A system has the characteristic equation sĀ³ + 6sĀ² + 11s + 6 = 0.
Using the Routh-Hurwitz criterion, how many roots lie in the right-half s-plane?