Control Systems Flashcards

What is the primary purpose of a feedback control system?

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.

For a unity-feedback closed-loop system with forward transfer function G(s), the closed-loop transfer function T(s) is:

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)).

A first-order system reaches what percentage of its final value at exactly one time constant (τ)?

Answer: 63.2%

A first-order system follows an exponential step response y(t) = 1 − e^(−t/τ), which evaluates to 1 − e^(−1) ≈ 63.2% at t = τ.

Steady-state error in a feedback control system is defined as:

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 → ∞).

Which system type can track a unit step reference with zero steady-state error without a proportional controller alone?

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.

A system is considered BIBO stable if and only if:

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.

The Laplace transform of the unit impulse function δ(t) is:

Answer: 1

By definition, the Laplace transform of δ(t) is ∫₀^∞ δ(t)e^(−st)dt = 1, making the impulse function the identity element in the Laplace domain.