Control Systems Theory Flashcards
7 cards from real BEE 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 Theory flashcards as text
The controllability matrix for a system with matrices A and B is formed as [B, AB, A²B, ...]. A system is controllable if this matrix has:
Answer: Rank equal to the order n of the system
A system is controllable (Kalman's criterion) if and only if the controllability matrix [B AB A²B ... Aⁿ⁻¹B] has full rank n.
In a discrete-time control system with sampling period T, the z-transform variable z and the Laplace variable s are related by:
Answer: z = e^(sT)
The mapping between continuous and discrete domains is z = e^(sT), which maps the left-half s-plane to the interior of the unit circle in the z-plane.
A system exhibiting limit cycle behavior is best classified as:
Answer: Nonlinear, with a sustained oscillation at a fixed amplitude and frequency
Limit cycles are self-sustained oscillations characteristic of nonlinear systems, with fixed amplitude and frequency independent of initial conditions within a region.
Which of the following actions does a lead compensator primarily perform on the Bode plot?
Answer: Adds phase lead near the crossover frequency to improve phase margin
A lead compensator contributes positive phase (phase lead) near the crossover frequency, improving phase margin and transient response speed.
For an underdamped second-order system, the percent overshoot depends only on:
Answer: The damping ratio ζ
Percent overshoot = exp(−πζ/√(1−ζ²)) × 100%, which depends solely on the damping ratio ζ.
The sensitivity function S(s) = 1/[1 + G(s)H(s)] in a feedback control system quantifies:
Answer: How much the closed-loop transfer function changes relative to changes in the plant
The sensitivity function S(s) measures the relative change in closed-loop transfer function due to relative changes in the plant G(s), with small |S| indicating robustness.
In the Ziegler-Nichols ultimate gain tuning method, the controller is first set to proportional-only mode and the gain is increased until:
Answer: The system output exhibits sustained oscillations
In the Ziegler-Nichols method, the ultimate gain Ku is found by increasing K until the system oscillates at constant amplitude (marginally stable), then the ultimate period Tu is recorded.