Control Systems Theory Flashcards

A system has the characteristic equation s³ + 6s² + 11s + 6 = 0. Using the Routh-Hurwitz criterion, how many roots lie in the right-half s-plane?

Answer: 0

All Routh array elements are positive (1, 6, 11, 6 → row 2: 6, 6; row 3: 10, 0; row 4: 6), so no sign changes and all roots are in the left-half plane.

The steady-state error of a Type 1 system to a ramp input is:

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.

On a Bode plot, what is the slope (in dB/decade) introduced by each additional open-loop pole?

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.

Which of the following best describes the principle of superposition as it applies to linear control systems?

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.

The transfer function of an ideal PD controller is:

Answer: Kp(1 + Td·s)

A PD controller adds proportional and derivative action, yielding the transfer function Kp(1 + Td·s).

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.

Answer: 10

A gain margin of 20 dB corresponds to a factor of 10 (since 20 dB = 20·log₁₀(10)), meaning gain can be multiplied tenfold before instability.

In state-space representation, the matrix that relates the current state and input to the output is called the:

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.