Control Systems and Dynamics Flashcards
7 cards from real ME or MEng Master of Engineering practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Control Systems and Dynamics flashcards as text
For a second-order system to be classified as underdamped, the damping ratio ζ must satisfy:
Answer: 0 < ζ < 1
An underdamped system has 0 < ζ < 1, producing an oscillatory transient response that decays exponentially to the steady-state value.
What is the natural frequency ωn of a simple spring-mass system with mass m and spring constant k?
Answer: √(k/m)
From the equation of motion mẍ + kx = 0, the natural frequency is ωn = √(k/m) rad/s.
Using the 2% criterion, the settling time Ts of a second-order system is approximately:
Answer: 4/(ζωn)
The 2% settling time is approximated as Ts ≈ 4/(ζωn), derived from the time constant of the exponential decay envelope.
By standard definition, rise time is the time for the step response to travel from:
Answer: 10% to 90% of its final value
Rise time is conventionally defined as the time for the response to increase from 10% to 90% of its final steady-state value.
Critical damping in a mass-spring-damper system occurs when:
Answer: The damping ratio ζ equals 1
Critical damping (ζ = 1) gives the fastest return to equilibrium without oscillation, representing the boundary between underdamped and overdamped responses.
The impulse response h(t) of a linear system is related to its transfer function H(s) by:
Answer: h(t) is the inverse Laplace transform of H(s)
Since the Laplace transform of the unit impulse δ(t) is 1, the output transform equals H(s)·1 = H(s), so h(t) = L⁻¹{H(s)}.
Convolution in the time domain corresponds to which operation in the Laplace domain?
Answer: Multiplication of transforms
The convolution theorem states that time-domain convolution of two signals corresponds to multiplication of their Laplace transforms in the s-domain.