BME Control Systems 1 β Questions and Answers
Question 1: What is the primary purpose of a feedback control system?
- To amplify the input signal
- To compare the output with the desired value and reduce error (Correct answer)
- To eliminate all disturbances in the system
- To increase the system response time
Correct answer: To compare the output with the desired value and reduce error
A feedback control system continuously compares the actual output to the desired setpoint and uses the resulting error to adjust the input, minimizing deviations.
Question 2: For a unity-feedback closed-loop system with forward transfer function G(s), the closed-loop transfer function T(s) is:
- G(s) / (1 + G(s)) (Correct answer)
- G(s) / (1 - G(s))
- 1 / (1 + G(s))
- G(s) Β· H(s) / (1 + G(s)Β·H(s))
Correct answer: G(s) / (1 + G(s))
For unity feedback (H(s) = 1), the standard closed-loop formula G(s)H(s)/(1 + G(s)H(s)) reduces to G(s)/(1 + G(s)).
Question 3: A first-order system reaches what percentage of its final value at exactly one time constant (Ο)?
- 50.0%
- 86.5%
- 63.2% (Correct answer)
- 98.2%
Correct answer: 63.2%
A first-order system follows an exponential step response y(t) = 1 β e^(βt/Ο), which evaluates to 1 β e^(β1) β 63.2% at t = Ο.
Question 4: Steady-state error in a feedback control system is defined as:
- The maximum overshoot during the transient response
- The error at the moment the step input is applied
- The difference between desired and actual output as time approaches infinity (Correct answer)
- The time for the error to first reach zero
Correct answer: The difference between desired and actual output as time approaches infinity
Steady-state error is the residual difference between the reference input and the actual system output after all transients have died out (t β β).
Question 5: Which system type can track a unit step reference with zero steady-state error without a proportional controller alone?
- Type 0 system
- Type 1 system (Correct answer)
- Type 2 system
- All system types achieve zero steady-state error for step inputs
Correct answer: Type 1 system
A type-1 system contains one integrator in the open loop, which provides infinite DC gain and drives the steady-state error to zero for a step input.
Question 6: A system is considered BIBO stable if and only if:
- All closed-loop poles have positive real parts
- Every bounded input produces a bounded output (Correct answer)
- The open-loop gain is greater than one at all frequencies
- The steady-state error is finite for any input
Correct answer: Every bounded input produces a bounded output
BIBO (Bounded-Input Bounded-Output) stability requires that every bounded input signal produces a bounded output signal, which for LTI systems is equivalent to all closed-loop poles having negative real parts.
Question 7: The Laplace transform of the unit impulse function Ξ΄(t) is:
- 1/s
- s
- 1 (Correct answer)
- e^(βs)
Correct answer: 1
By definition, the Laplace transform of Ξ΄(t) is β«β^β Ξ΄(t)e^(βst)dt = 1, making the impulse function the identity element in the Laplace domain.
BME Control Systems 1
What is the primary purpose of a feedback control system?