As aircraft speed varies, which strategy adjusts controller parameters?
AIntegral reset
BGain scheduling
CPole cancellation
DOutput scaling
Answer: B. Gain scheduling. Gain scheduling selects controller parameters for different operating conditions, such as aircraft speed.
Integral windup occurs under what condition?
AIntegrator accumulates during saturation
BDerivative gain becomes zero
CSensor feedback is unity
DPlant poles move left
Answer: A. Integrator accumulates during saturation. When the actuator saturates, the integrator may continue accumulating error and demand excessive control action.
Which anti-windup method feeds actuator mismatch back to the integrator?
ABack-calculation
BPole cancellation
CDead-zone control
DLead compensation
Answer: A. Back-calculation. Back-calculation uses the difference between commanded and applied actuator signals to limit integrator accumulation.
Which limitation commonly affects ideal derivative action?
ARemoves all steady-state error
BAmplifies high-frequency noise
CReduces sensor bandwidth
DEliminates actuator saturation
Answer: B. Amplifies high-frequency noise. Differentiation emphasizes rapid signal changes, including high-frequency measurement noise.
PID derivative kick can follow which event?
AConstant plant output
BSlow sensor drift
CStep change in setpoint
DZero proportional gain
Answer: C. Step change in setpoint. Differentiating the error can create a large impulse-like response when the setpoint changes abruptly.
Why is practical derivative action filtered?
AIncrease integral windup
BMove every pole to zero
CLimit high-frequency noise gain
DRemove reference tracking
Answer: C. Limit high-frequency noise gain. A derivative filter rolls off high-frequency gain while retaining useful phase lead over a chosen band.
In frequency response, a pure delay adds which phase effect?
AConstant gain increase
BFrequency-dependent phase lag
CPositive phase at all frequencies
DA zero-frequency pole
Answer: B. Frequency-dependent phase lag. A delay e^(-sT) has unit magnitude and phase lag that grows with frequency.
How much can loop gain increase before instability?
AOutput rise before overshoot
BSensor error at steady state
CGain increase before instability
DTime to reach the setpoint
Answer: C. Gain increase before instability. Gain margin indicates how much loop gain can increase before the closed loop reaches instability.
What does phase margin quantify?
AExtra phase lag before instability
BOutput amplitude at resonance
CController integral time
DPlant input disturbance size
Answer: A. Extra phase lag before instability. Phase margin indicates how much additional phase lag can occur before the stability boundary is reached.
Which angle condition must root-locus points satisfy?
AEven multiple of 90 degrees
BZero degrees at every pole
COdd multiple of 180 degrees
DExactly 45 degrees always
Answer: C. Odd multiple of 180 degrees. For positive gain, the sum of pole angles minus zero angles is an odd multiple of 180 degrees.
At a root-locus point, what must open-loop magnitude equal?
AClosed-loop magnitude equals zero
BFeedback magnitude equals gain
CPlant phase equals zero
DMagnitude equals reciprocal gain
Answer: D. Magnitude equals reciprocal gain. At a root-locus point, the open-loop magnitude must equal 1/K for the selected gain K.
What internal behavior can unstable pole-zero cancellation conceal?
AA guaranteed stable response
BHidden unstable mode
CZero sensor noise
DInfinite phase margin
Answer: B. Hidden unstable mode. Canceling an unstable pole in an input-output transfer function can hide an unstable internal mode; it does not guarantee internal stability.
In a Routh array, what does a complete zero row indicate?
ANo closed-loop poles
BAll roots at zero
CSymmetric roots about origin
DOnly stable real roots
Answer: C. Symmetric roots about origin. A complete zero row indicates roots symmetric about the origin; an auxiliary polynomial helps continue the array.
For the final-value theorem, where must poles of sY(s) lie?
ALeft half-plane
BFinite final value always
CEvery pole is at origin
DOnly for sinusoidal inputs
Answer: A. Left half-plane. The theorem requires all poles of sY(s) to lie in the open left half-plane, with no invalid axis poles.
Discrete-time poles must lie where for asymptotic stability?
AOutside unit circle
BOn positive real axis
CAnywhere in left half-plane
DInside unit circle
Answer: D. Inside unit circle. For a discrete-time linear system, asymptotic stability requires poles strictly inside the unit circle.
Nyquist encirclements of −1 are interpreted using which pole count?
AOpen-loop unstable poles
BReference signal zeros
CSensor bandwidth peaks
DPlant time constants
Answer: A. Open-loop unstable poles. The Nyquist relation combines encirclements of −1 with the number of open-loop right-half-plane poles to determine closed-loop stability.
Laplace-domain representation of a pure delay T is what?
As plus T
BOne over sT
CT times s squared
De^(−sT)
Answer: D. e^(−sT). A pure delay of T seconds is represented by e^(−sT) in the Laplace domain.
Each additional first-order pole adds which high-frequency magnitude-slope change?
APlus 20 dB per decade
BMinus 20 dB per decade
CMinus 3 dB per decade
DPlus 90 dB per decade
Answer: B. Minus 20 dB per decade. Each first-order pole contributes an additional -20 dB per decade to the asymptotic magnitude slope.
Far above a first-order pole’s corner frequency, its phase approaches what?
APlus 90 degrees
BMinus 90 degrees
CMinus 180 degrees
DZero degrees
Answer: B. Minus 90 degrees. A first-order pole approaches a -90 degree phase contribution well above its corner frequency.
Aliasing may result when what sampling condition occurs?
AExcessive damping
BHigh loop gain only
CLow actuator torque
DSampling too slowly
Answer: D. Sampling too slowly. If sampling is too slow relative to signal frequency, distinct components can appear as false lower frequencies.
Lead compensation places which element at the lower break frequency?
APole closer to origin
BBoth at origin
CZero closer to origin
DZero at infinity only
Answer: C. Zero closer to origin. A lead network has its zero at a lower break frequency than its pole, producing positive phase over a band.
Which element lies closer to the origin in a lag compensator?
AZero closer to origin
BBoth at infinity
CPole on imaginary axis
DPole closer to origin
Answer: D. Pole closer to origin. A lag network places its pole closer to the origin than its zero, increasing low-frequency gain relative to high-frequency gain.
Two-degree-of-freedom control separates which objectives?
AReference tracking and disturbance rejection
BRise time and pole count
CSensor gain and actuator size
DSampling and quantization only
Answer: A. Reference tracking and disturbance rejection. Two-degree-of-freedom structures allow separate shaping of command tracking and feedback disturbance response.
Setpoint weighting can reduce which transient after a command change?
ASteady-state disturbances always
BSensor noise to zero
CPlant model order
DOvershoot after command changes
Answer: D. Overshoot after command changes. Setpoint weighting can soften the controller response to reference changes without changing the feedback disturbance path.
Physical actuator saturation means the control signal does what?
AControl effort hits a limit
BTransfer function loses poles
CSensor becomes open loop
DReference input turns into noise
Answer: A. Control effort hits a limit. Actuator saturation limits the actual control signal, so the plant receives less action than the controller requests.