Control Systems MCQs 2026

Transfer function of a linear time-invariant system is defined as

1. A ratio of time-domain outputs without transformation ✓
2. B ratio of Laplace transform of output to input with zero initial conditions ✓
3. C Fourier series coefficients only ✓
4. D PID tuning constants only ✓

Poles of a transfer function are values of s where

1. A numerator equals zero only ✓
2. B output is maximum always ✓
3. C denominator equals zero ✓
4. D gain margin is infinite always ✓

Zeros of a transfer function are values of s where

1. A denominator equals zero ✓
2. B system is always unstable ✓
3. C phase margin is zero only ✓
4. D numerator equals zero ✓

Standard first-order system G(s) = K/(τs+1) has time constant

1. A τ ✓
2. B K only ✓
3. C τ/K only ✓
4. D 1/K only without τ ✓

DC gain of transfer function G(s) is found by

1. A s approaching infinity only always for DC gain definition—DC is s=0 ✓
2. B only imaginary axis without s=0 ✓
3. C only at resonant frequency always ✓
4. D evaluating G(s) at s = 0 ✓

Second-order underdamped system is characterized by

1. A real distinct poles only always ✓
2. B complex conjugate poles with damping ratio ζ < 1 ✓
3. C ζ greater than 1 always ✓
4. D no transient response ever ✓

Natural frequency ωn of second-order system appears in standard form

1. A s² + 2ζωn s + ωn² ✓
2. B s + ωn only without quadratic term ✓
3. C ωn² s + 1 only ✓
4. D PID derivative term only ✓

Block diagram reduction uses rules for

1. A series, parallel and feedback loop algebra ✓
2. B only Bode plotting without algebra ✓
3. C only symmetrical components only on AC faults ✓
4. D only fuse coordination curves only ✓

Closed-loop transfer function with unity feedback H=1 is

1. A G/(1-G) always ✓
2. B 1/G always ✓
3. C G only without feedback effect ✓
4. D G/(1+G) where G is open-loop transfer function ✓

Type of a system indicates number of

1. A zeros at origin only ✓
2. B delay elements counted twice always without definition ✓
3. C PID derivative paths only ✓
4. D integrators (poles at origin) in open-loop transfer function ✓

Steady-state error to step input for type 0 system with step input is

1. A finite and generally non-zero unless gain is infinite ✓
2. B always zero for any type 0 without integrator—generally non-zero ✓
3. C always infinite for step on type 0—actually finite non-zero typically ✓
4. D undefined without Laplace ✓

Lead compensator transfer function typically has

1. A pole closer to origin than zero always for lead definition—lead has zero closer ✓
2. B equal zero and pole at origin only always ✓
3. C zero closer to origin than pole ✓
4. D no effect on phase ✓

Lag compensator provides

1. A positive phase boost at all frequencies without attenuation ever ✓
2. B elimination of all poles ✓
3. C high-frequency gain reduction and improved steady-state accuracy ✓
4. D only derivative action without lag pole-zero pair ✓

Transport delay e^(-Ts) in transfer function causes

1. A constant gain at all frequencies without phase effect ever ✓
2. B phase lag increasing linearly with frequency ✓
3. C elimination of stability issues always ✓
4. D infinite bandwidth always ✓

Impulse response of LTI system is inverse Laplace transform of

1. A input only without system dynamics ✓
2. B PID output only without plant ✓
3. C distance relay impedance only ✓
4. D transfer function G(s) ✓

Convolution in time domain corresponds to

1. A subtraction of transfer functions only ✓
2. B division of zeros only ✓
3. C multiplication in Laplace domain ✓
4. D Fourier series only without Laplace ✓

State-space model ẋ=Ax+Bu, y=Cx+Du relates to transfer function by

1. A only Bode magnitude plot without matrices ✓
2. B G(s)=C(sI−A)⁻¹B+D ✓
3. C only per unit impedance conversion ✓
4. D only symmetrical sequence networks only ✓

Minimum phase system has all zeros in

1. A left half of s-plane (or on jω axis) ✓
2. B right half plane always ✓
3. C origin only always ✓
4. D infinity only always without left half plane constraint ✓

Bode plot displays

1. A only time response without frequency content ever ✓
2. B only pole-zero map on complex plane without frequency axis as Bode definition ✓
3. C only Nyquist real axis only without magnitude and phase plots ✓
4. D magnitude in dB and phase versus frequency on logarithmic scale ✓

Magnitude in Bode plot for gain K is

1. A K dB without log scaling incorrectly stated ✓
2. B 20 log10(K) dB horizontal line ✓
3. C log10 K without factor 20 only as incorrect variant ✓
4. D 20 log10(s) always without K ✓

Pole at origin (integrator) contributes to Bode magnitude slope of

1. A −20 dB/decade ✓
2. B +20 dB/decade ✓
3. C −40 dB/decade always for single pole at origin without other poles ✓
4. D 0 dB/decade always ✓

Zero at origin (differentiator) contributes magnitude slope of

1. A +20 dB/decade ✓
2. B −20 dB/decade for zero at origin—positive slope for differentiator ✓
3. C 0 dB/decade always ✓
4. D −6 dB/octave only without sign clarity—still +20 dB/decade ✓

Corner frequency of first-order pole at 1/τ rad/s is

1. A ω = τ only incorrectly ✓
2. B ω = 1/τ ✓
3. C ω = τ² only ✓
4. D ω = 0 always ✓

Phase of first-order lag at corner frequency is approximately

1. A 0° always ✓
2. B −90° at corner exactly for asymptotic mid—approx −45° at ω=1/τ ✓
3. C −45° ✓
4. D +45° always ✓

Gain crossover frequency is where

1. A phase equals −180° only without magnitude condition for gain crossover definition ✓
2. B output equals input in time domain step only without frequency definition ✓
3. C open-loop magnitude equals 0 dB (unity gain) ✓
4. D PID integral time constant only ✓

Phase crossover frequency is where

1. A magnitude equals 0 dB only without phase −180° condition for phase crossover ✓
2. B system becomes type 2 always ✓
3. C open-loop phase equals −180° ✓
4. D derivative action is maximum always ✓

Gain margin is

1. A phase increase in degrees at gain crossover only without gain definition ✓
2. B time delay only without dB definition ✓
3. C distance relay reach in ohms only ✓
4. D amount gain can increase before instability at phase crossover ✓

Phase margin is

1. A gain increase in dB at phase crossover only ✓
2. B steady-state error to ramp only without phase definition ✓
3. C motor slip at full load only ✓
4. D additional phase lag before −180° at gain crossover frequency ✓

Resonant peak in closed-loop frequency response relates to

1. A only DC gain without dynamics ✓
2. B damping ratio of dominant second-order poles ✓
3. C only transport delay only without resonance ✓
4. D only fuse cut-off current only ✓

Asymptotic Bode magnitude of second-order underdamped pair near ωn shows

1. A flat 0 dB always without roll-off ✓
2. B −40 dB/decade slope far above ωn with possible peak near ωn ✓
3. C +40 dB/decade always above ωn without resonance possibility ✓
4. D undefined without zeros always ✓

Decade on Bode frequency axis means

1. A twofold change only ✓
2. B tenfold change in frequency ✓
3. C phase change of 45° only without frequency meaning ✓
4. D one period of oscillation only without factor ten ✓

Octave corresponds to

1. A doubling of frequency ✓
2. B tenfold frequency change which is decade not octave ✓
3. C tripling frequency always ✓
4. D zero frequency span only ✓

Minimum phase system Bode plot is uniquely determined by

1. A phase curve alone without magnitude for minimum phase systems—magnitude alone suffices ✓
2. B time delay only without magnitude ✓
3. C magnitude curve alone ✓
4. D PID settings only without plant dynamics ✓

Transport delay adds phase

1. A constant −90° at all frequencies always ✓
2. B −ωT radians linearly with frequency ✓
3. C +ωT always positive linear phase which is wrong sign for delay ✓
4. D zero phase always regardless of delay ✓

Bode plot is useful for designing

1. A only DC machine commutation timing only without frequency design ✓
2. B lead-lag compensators and assessing closed-loop bandwidth ✓
3. C only cable joint stress cones only without control design ✓
4. D only insulator fog profile only without controls ✓

Slope of −20 dB/decade on Bode magnitude often indicates

1. A one pole or combination equivalent to first-order roll-off ✓
2. B two integrators always without checking net order ✓
3. C zero at origin always without sign ✓
4. D pure time delay only without magnitude slope contribution like integrator ✓

Linear system is BIBO stable if

1. A bounded input produces bounded output ✓
2. B any input produces zero output always ✓
3. C output always unbounded for step input always ✓
4. D poles need not be considered ever ✓

For continuous-time LTI system, internal stability (asymptotic) requires poles to lie

1. A strictly in left half of s-plane ✓
2. B on imaginary axis always without left half plane requirement for asymptotic stability ✓
3. C right half plane for stability incorrectly ✓
4. D at origin only always for all stable systems ✓

Marginally stable system has

1. A all poles in RHP always as marginal definition incorrectly ✓
2. B only zeros on jω axis without pole condition ✓
3. C non-repeated poles on jω axis and none in RHP ✓
4. D always exponentially decaying modes only ✓

Routh-Hurwitz criterion determines stability using

1. A only Bode phase at DC only without polynomial test ✓
2. B only Nyquist plot drawing without polynomial ✓
3. C characteristic equation coefficients without finding roots explicitly ✓
4. D only motor nameplate data only ✓

Nyquist criterion uses

1. A only step response overshoot percent only without Nyquist ✓
2. B only PID integral windup only without frequency encirclement ✓
3. C only symmetrical components only without Nyquist ✓
4. D open-loop frequency response encirclements of −1 point ✓

Negative feedback reduces sensitivity of closed-loop gain to

1. A increases sensitivity always at all frequencies without exception incorrectly as blanket statement ✓
2. B has no effect ever on sensitivity incorrectly ✓
3. C plant parameter variations at low frequencies often ✓
4. D only changes fuse rating without loop effect ✓

Root locus shows

1. A open-loop zeros only without pole motion ✓
2. B only Bode magnitude without pole paths ✓
3. C only steady-state error constants only without locus ✓
4. D closed-loop pole trajectories as gain varies from 0 to ∞ ✓

Adding a pole in forward path generally

1. A always improves phase margin without exception incorrectly ✓
2. B has no effect on phase ever incorrectly ✓
3. C eliminates need for feedback incorrectly ✓
4. D degrades stability by adding phase lag ✓

Adding a zero in forward path near crossover can

1. A always destabilize without exception incorrectly ✓
2. B eliminate all dynamics incorrectly ✓
3. C improve phase margin ✓
4. D replace sensor entirely incorrectly ✓

Stable closed-loop system with adequate gain and phase margins typically has

1. A guaranteed zero steady-state error to all inputs without type consideration incorrectly as blanket ✓
2. B infinite bandwidth always incorrectly ✓
3. C poles in RHP always incorrectly ✓
4. D well-damped transient response without excessive oscillation ✓

Limit cycle in nonlinear system refers to

1. A exponential decay always in nonlinear system incorrectly for limit cycle definition ✓
2. B only linear system resonance at natural frequency only without nonlinearity requirement for limit cycle term usage ✓
3. C only fuse arcing only without control context though arcing is nonlinear oscillation colloquially ✓
4. D sustained oscillation amplitude determined by nonlinearity ✓

Lyapunov stability analysis uses

1. A only Bode plot asymptotes only without Lyapunov function ✓
2. B energy-like Lyapunov function with negative semi-definite derivative ✓
3. C only per unit conversion only without state function ✓
4. D only distance relay mho circle only without Lyapunov ✓

Phase margin of 45° roughly corresponds to

1. A unstable response always incorrectly ✓
2. B overdamped without oscillation always incorrectly for 45° PM typical correlation ✓
3. C moderately damped closed-loop step response ✓
4. D zero overshoot always incorrectly as blanket ✓

Gain margin less than 0 dB indicates

1. A closed-loop instability for unity feedback minimum-phase assumptions typically ✓
2. B guaranteed stability always incorrectly ✓
3. C infinite phase margin always incorrectly ✓
4. D zero steady-state error always incorrectly ✓

Hurwitz polynomial has

1. A roots on RHP always incorrectly ✓
2. B only real roots always as Hurwitz requirement incorrectly stated—complex allowed with negative real parts ✓
3. C all roots with negative real parts ✓
4. D roots at infinity only incorrectly ✓

Delay in control loop tends to

1. A reduce phase margin and can destabilize system ✓
2. B always improve damping without exception incorrectly ✓
3. C eliminate steady-state error without integrator incorrectly as delay effect ✓
4. D increase gain margin always incorrectly ✓

Conditional stability may occur when

1. A system is stable only for limited gain range ✓
2. B system is stable for all gains always incorrectly ✓
3. C poles always in RHP incorrectly for conditional stability definition ✓
4. D only nonlinear systems without gain dependence incorrectly—linear can be conditionally stable with gain ✓

PID controller transfer function is

1. A Gc(s) = Kp + Ki/s + Kd s ✓
2. B Kp only without integral or derivative paths ✓
3. C Ki s only incorrectly ✓
4. D Kd/s only incorrectly ✓

Proportional (P) action primarily

1. A eliminates all steady-state error always without integrator incorrectly as blanket ✓
2. B reduces rise time and steady-state error partially but not entirely for type 0 plants typically ✓
3. C eliminates overshoot always incorrectly ✓
4. D provides infinite gain at DC always incorrectly—that is integral ✓

Integral (I) action eliminates

1. A all measurement noise always without amplification concern incorrectly ✓
2. B need for sensor ever incorrectly ✓
3. C stability margins always improves without limit incorrectly ✓
4. D steady-state error to step input for stable closed-loop systems when properly applied ✓

Derivative (D) action responds to

1. A only steady-state error magnitude without rate sensitivity incorrectly ✓
2. B only DC offset always incorrectly ✓
3. C rate of change of error and adds damping ✓
4. D integral of error only incorrectly ✓

Integral windup occurs when

1. A derivative term exceeds proportional always incorrectly as windup definition ✓
2. B actuator saturates while integrator continues accumulating error ✓
3. C system is always stable during saturation incorrectly ✓
4. D gain margin is infinite incorrectly ✓

Anti-windup methods include

1. A stopping integration when output saturates or back-calculation ✓
2. B increasing integral gain during saturation incorrectly ✓
3. C removing proportional term always incorrectly ✓
4. D opening feedback loop permanently incorrectly ✓

Tuning PID by Ziegler-Nichols ultimate gain method uses

1. A only step response rise time without ultimate gain experiment incorrectly ✓
2. B only Bode zero placement without experiment incorrectly ✓
3. C only motor slip measurement incorrectly ✓
4. D critical gain Ku and oscillation period Pu at stability limit ✓

Increasing Kp too much can cause

1. A guaranteed stability always incorrectly ✓
2. B zero overshoot always incorrectly ✓
3. C instability and excessive oscillations ✓
4. D elimination of noise always incorrectly ✓

Too much derivative gain amplifies

1. A DC error only without high-frequency noise concern incorrectly ✓
2. B measurement noise ✓
3. C integral windup primarily incorrectly though D does not integrate noise same way ✓
4. D steady-state reference only incorrectly ✓

PID in parallel form differs from ideal series form in

1. A being unable to implement derivative ever incorrectly ✓
2. B requiring no tuning ever incorrectly ✓
3. C eliminating steady-state error without I incorrectly ✓
4. D algebraic arrangement but can be made equivalent with conversion ✓

Set-point weighting on PID separates

1. A response to reference changes versus load disturbances ✓
2. B only fuse blowing from overload incorrectly ✓
3. C only distance zones incorrectly ✓
4. D only symmetrical sequences incorrectly ✓

Sampled-data PID implementation must consider

1. A only analog Bode plot of continuous plant without sampling effects incorrectly ✓
2. B discretization, aliasing and integral approximation ✓
3. C infinite sampling rate without implementation constraints incorrectly ✓
4. D elimination of derivative always incorrectly as requirement ✓

Derivative filter in practical PID limits

1. A low-frequency gain to zero always incorrectly as filter purpose ✓
2. B high-frequency noise amplification by filtering D path ✓
3. C integral action entirely incorrectly ✓
4. D proportional gain to zero incorrectly ✓

Feedforward control added to PID can

1. A improve disturbance rejection for measurable disturbances ✓
2. B replace stability analysis always incorrectly ✓
3. C guarantee RHP poles always incorrectly ✓
4. D eliminate need for feedback entirely incorrectly ✓

Cascade control uses

1. A only single P controller always incorrectly ✓
2. B only open-loop control without feedback incorrectly ✓
3. C inner fast loop and outer slow loop for improved disturbance rejection ✓
4. D only fuse in series without controllers incorrectly ✓

PI controller is commonly used when

1. A derivative noise is desired to increase incorrectly ✓
2. B zero proportional gain is required incorrectly ✓
3. C system must be type 0 open-loop without closed-loop integrator effect incorrectly stated ✓
4. D steady-state accuracy needed without excessive noise sensitivity from D ✓

Closed-loop bandwidth with PID tuning is often traded against

1. A only cable charging current magnitude incorrectly ✓
2. B robustness margins and noise rejection ✓
3. C only tower sag at minimum temperature incorrectly ✓
4. D only SCR latching current only incorrectly ✓