BEE Control System Principles 5 — Questions and Answers
Question 1: In a block diagram, the signal flow from the output back to the summing junction is called:
- Feedforward path
- Forward path
- Feedback path (Correct answer)
- Error signal
Correct answer: Feedback path
The feedback path carries the measured output (or processed output) back to the summing junction to be compared with the reference input.
Question 2: For a unity-feedback system, the closed-loop transfer function T(s) = G(s)/[1+G(s)] has the sensitivity function S(s) equal to:
- G(s)/[1+G(s)]
- 1/[1+G(s)] (Correct answer)
- G(s)
- 1+G(s)
Correct answer: 1/[1+G(s)]
The sensitivity function S(s) = 1/[1+G(s)] quantifies how output changes in response to disturbances or plant perturbations.
Question 3: Which statement about a minimum-phase system is correct?
- All poles are in the right-half plane
- All zeros are in the left-half plane (Correct answer)
- The phase is always 0° at all frequencies
- It has no time delay
Correct answer: All zeros are in the left-half plane
A minimum-phase system has all its zeros located in the left-half plane (open), giving the minimum possible phase lag for a given magnitude response.
Question 4: State feedback control with full state feedback u = -Kx can place all closed-loop poles arbitrarily if and only if the system is:
- Observable
- Stable
- Controllable (Correct answer)
- Minimum phase
Correct answer: Controllable
Arbitrary pole placement via state feedback is possible if and only if the system is completely controllable (the controllability matrix has full rank).
Question 5: What is the bandwidth of a closed-loop system generally defined as?
- The frequency at which the open-loop gain equals 0 dB
- The frequency at which the closed-loop magnitude drops to -3 dB below its DC value (Correct answer)
- The resonant peak frequency
- The phase crossover frequency
Correct answer: The frequency at which the closed-loop magnitude drops to -3 dB below its DC value
Closed-loop bandwidth is defined as the frequency range over which the closed-loop magnitude stays within 3 dB of its low-frequency value.
Question 6: In signal flow graphs, Mason's gain formula is used to find:
- The number of feedback loops
- The overall transfer function from input to output (Correct answer)
- The system's stability margins
- The state transition matrix
Correct answer: The overall transfer function from input to output
Mason's gain formula computes the overall transfer function by summing path gains weighted by cofactors of the signal flow graph determinant.
Question 7: A PI controller introduces which of the following into the open-loop transfer function?
- An additional pole at the origin and a zero in the LHP (Correct answer)
- An additional zero at the origin and a pole in the LHP
- Two poles at the origin
- A pair of complex poles
Correct answer: An additional pole at the origin and a zero in the LHP
A PI controller C(s) = Kp + Ki/s = (Kp·s + Ki)/s adds a pole at s=0 (integrator) and a zero at s = -Ki/Kp in the left-half plane.
BEE Control System Principles 5
In a block diagram, the signal flow from the output back to the summing junction is called: