In a standard second-order model, which frequency is associated with undamped oscillation?
ASteady-state error
BController output level
CSensor sampling interval
DUndamped oscillation frequency
Answer: D. Undamped oscillation frequency. Natural frequency is the oscillation frequency of an ideal undamped second-order system.
Damping ratio compares which two quantities?
AOutput to reference
BActual to critical damping
CGain to phase margin
DInput to disturbance
Answer: B. Actual to critical damping. Damping ratio expresses actual damping relative to critical damping.
When is a standard second-order system underdamped?
AEqual to one
BGreater than one
CBetween zero and one
DLess than zero
Answer: C. Between zero and one. For a standard second-order system, a damping ratio between zero and one gives an underdamped response.
Critical damping corresponds to which damping ratio?
AZero
BBetween zero and one
COne
DGreater than two
Answer: C. One. Critical damping corresponds to a damping ratio of one.
Overdamping is characterized by which condition?
ADamping ratio equals zero
BDamping ratio below zero
CDamping ratio equals one
DDamping ratio above one
Answer: D. Damping ratio above one. An overdamped system has a damping ratio greater than one and does not oscillate in its standard form.
Zero damping represents which ideal response condition?
AOne
BAbove one
CZero
DNegative one
Answer: C. Zero. Zero damping gives sustained oscillation in an ideal second-order model.
How is percent overshoot defined relative to the final value?
APeak above final value
BInitial value below zero
CRise time in seconds
DController output range
Answer: A. Peak above final value. Percent overshoot quantifies the response peak above its final value relative to the response change.
In a standard step response, what interval does rise time measure?
ATime to first disturbance
BController sampling period
CDuration of steady-state error
DRise between chosen response thresholds
Answer: D. Rise between chosen response thresholds. Rise time is measured between specified lower and upper response thresholds, such as 10–90% or 0–100%.
At what instant is peak time measured?
ATime to first input step
BTime for sensor calibration
CTime to first response peak
DTime to controller startup
Answer: C. Time to first response peak. Peak time is the time required to reach the first maximum of an oscillatory response.
When does settling time end?
AFirst crosses the setpoint
BStays within tolerance band
CReaches its first maximum
DReturns to zero input
Answer: B. Stays within tolerance band. Settling time is when the response enters and remains within a specified band around its final value.
Continuous-time poles must lie where for asymptotic stability?
ALeft half-plane
BRight half-plane
COutside the unit circle
DOn positive real axis
Answer: A. Left half-plane. A continuous-time linear system is asymptotically stable when its poles have negative real parts.
Right-half-plane poles in continuous time signal what behavior?
ACritical damping
BZero steady-state error
CInstability
DUnity feedback
Answer: C. Instability. A right-half-plane pole produces a growing natural response and indicates instability.
At one time constant, what fraction of a first-order step response is reached?
AAbout 63 percent
BAbout 10 percent
CAbout 90 percent
DExactly 100 percent
Answer: A. About 63 percent. A first-order step response reaches about 63.2 percent of its final change after one time constant.
Which expression represents a standard first-order transfer function?
AK over s squared
BK/(τs + 1)
CTau-s over K
DOne over K plus s
Answer: B. K/(τs + 1). A standard first-order model is G(s)=K/(τs+1), where K is gain and τ is time constant.
Which denominator applies to a standard second-order model?
As² + 2ζωₙs + ωₙ²
BOnly an integrator
COnly a delay term
DA constant gain only
Answer: A. s² + 2ζωₙs + ωₙ². The standard second-order denominator is s²+2ζωₙs+ωₙ².
Which transient features are mainly influenced by damping?
AOscillation and overshoot
BSteady-state input units
CSensor scale factor only
DReference signal polarity
Answer: A. Oscillation and overshoot. Damping affects how strongly the response oscillates and how much overshoot occurs.
After transients settle, how is steady-state error defined?
AFinal reference-output difference
BInitial output derivative
CPeak transient voltage
DController gain margin
Answer: A. Final reference-output difference. Steady-state error is the remaining difference between desired and actual output after transients settle.
System type counts open-loop poles at which location?
AIn the left half-plane
BAt the zeros
COn the unit circle
DAt the origin
Answer: D. At the origin. For standard unity-feedback systems, type equals the number of open-loop integrators or poles at the origin.
Position-error performance is assessed with what test input?
AImpulse input
BSinusoidal input
CStep input
DExponential input only
Answer: C. Step input. The position error constant describes steady-state tracking of a step in a unity-feedback system.
To assess the velocity error constant, which input is applied?
AStep input
BRamp input
CImpulse input
DConstant disturbance only
Answer: B. Ramp input. The velocity error constant characterizes steady-state tracking of a ramp input.
Acceleration error is assessed using which reference input?
AParabolic input
BStep input
CRamp input
DImpulse input
Answer: A. Parabolic input. The acceleration error constant describes steady-state tracking of a parabolic input.
Closed-loop poles are roots of which equation?
ASensor gain only
BReference amplitude
CPlant input units
DClosed-loop poles
Answer: D. Closed-loop poles. The roots of the closed-loop characteristic equation are the closed-loop poles.
As loop gain varies, what does a root-locus plot trace?
AOutput versus time only
BClosed-loop poles versus gain
CInput versus frequency only
DSensor error versus load
Answer: B. Closed-loop poles versus gain. A root locus shows how closed-loop poles move as a selected loop gain varies.
Each open-loop pole creates how many root-locus branches?
AOne per open-loop zero
BOne per open-loop pole
CAlways two
DOne per input signal
Answer: B. One per open-loop pole. Each open-loop pole starts a root-locus branch as gain increases from zero.
For two cascaded blocks, their equivalent transfer function is found by which operation?
AAddition
BSubtraction
CDivision
DMultiplication
Answer: D. Multiplication. For an ideal cascade, the equivalent transfer function is the product of the individual block transfer functions.