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CTRL:010117With P=2/(s+1) and C=3 the step finals through T, PS, and -T are 6/7, 2/7, and -6/7

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Ctrl Sensitivity Complementary MapsCtrl Actuator Measurement Step Finals

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Dynamic models, linearization, and feedback structureControl Systems · Mixed review

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CTRL:010118The unity DC motor has Omega/V=1/(s^2+2s+2), poles -1±j, and step speed (1/2)[1-e^{-t}(cos t+sin t)]

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Ctrl Armature Motor TransfersCtrl Underdamped Speed Step

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Dynamic models, linearization, and feedback structureControl Systems · Mixed review

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CTRL:010219The map 2(1-s)/[(s+1)(s+2)] undershoots to -1/3 at ln(3/2) before finishing at 1

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Ctrl Rhp Zero Inverse ResponseCtrl Undershoot Time And Depth

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Time response and stability criteriaControl Systems · Mixed review

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CTRL:010220L=K(s+2)/[s^2(s+5)] is type 2, stable iff K>0, and the t^2/2 error is 5/(2K)

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Ctrl Type Two Routh GainCtrl Acceleration Constant Parabola

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Time response and stability criteriaControl Systems · Mixed review

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CTRL:010221P=I/2 solves the Lyapunov equation for A=[[-1,1],[-1,-1]] and the state norm decays as e^{-t}

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Ctrl Quadratic Lyapunov IdentityCtrl Rotation Semigroup Norm

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Time response and stability criteriaControl Systems · Mixed review

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CTRL:010322The K/[s(s+2)(s+4)] locus breaks away at -2+2sqrt(3)/3 and crosses at K=48

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Ctrl Evans Real Axis AsymptotesCtrl Breakaway JW Crossing

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Root-locus and frequency-response designControl Systems · Mixed review

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CTRL:010323The lead of z=1/sqrt(3), p=sqrt(3) makes |L(j)|=1 with phase -105 and PM 75

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Ctrl Lead Midband Phase MagnitudeCtrl Unity Crossover Phase Margin

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Root-locus and frequency-response designControl Systems · Mixed review

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CTRL:010324For L=K/[(s-1)(s+2)] the full Nyquist image encircles -1 once CCW when K>2

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Ctrl Quadratic Closed Loop StabilityCtrl Nyquist OL Rhp Encirclement

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Root-locus and frequency-response designControl Systems · Mixed review

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CTRL:010425The pair (A,B,C) is minimal with G=-s/[(s+1)(s+2)] and Rosenbrock kernel ((2,1),2)

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Ctrl Minimal Realization Pbh DetsCtrl Rosenbrock Invariant Zero

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State-space, controllability, and observabilityControl Systems · Mixed review

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CTRL:010526The ARE 2P-P^2+1=0 has stabilizing root 1+sqrt(2), pole -sqrt(2), and J*=(1+sqrt(2)) x0^2

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Ctrl Scalar Are CompletionCtrl Lqr Stabilizing Root Cost

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State feedback and observersControl Systems · Mixed review

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CTRL:010527Integral action holds x=r and rejects a constant d; the homogeneous poles are -2 and -3

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Ctrl Integral Augmented CharacteristicCtrl Constant Disturbance Equilibrium

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State feedback and observersControl Systems · Mixed review

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CTRL:010528The reduced-order observer with ell=3 runs on q=xhat2-3y and never differentiates y

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Ctrl Reduced Order Q CoordinateCtrl Observer Error Decay NO Ydot

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State feedback and observersControl Systems · Mixed review

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CTRL:010629Exact ZOH of the double integrator at T=1 is Ad=[[1,1],[0,1]], Bd=(1/2,1), Gd=(z+1)/(2(z-1)^2)

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Ctrl Exact Zoh Matrix ExponentialCtrl Pulse Transfer Discrete Zero

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Digital control and robustness foundationsControl Systems · Mixed review

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CTRL:010630Jury on K(z+1/2)/((z-1)(z-1/2)) forces 0<K<1; the endpoints hit z=1 and a unit-circle conjugate pair

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Ctrl Discrete Closed Loop PolynomialCtrl Jury Quadratic Gain Interval

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Digital control and robustness foundationsControl Systems · Mixed review

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CTRL:010631Additive small-gain on P0=1/(s+1), C=2 guarantees every stable Delta only for rho<1/2

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Ctrl Sensitivity Complementary CS MapsCtrl Additive Small Gain Radius

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Digital control and robustness foundationsControl Systems · Mixed review

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Models FeedbackControl Systems Problem Solving

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CTRL:9927011A signal-flow graph is constructed from a unity-feedback block diagram that also has a minor-loop rate return.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927012An armature-controlled DC motor is modelled, for t\ge 0, by with numerical values The armature voltage v_a is in vo…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927013The DC motor of this problem is the first-order mechanical reduction obtained by neglecting armature inductance.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927014A process plant is mapping a control effort U (in volts) to a temperature Y (in kelvin).

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927015A plant P(s)=3/(s+2) (dimensionless) is placed in the two-input architecture where D_u is an input disturbance of t…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927016A single-loop architecture with a non-unity sensor is where N is additive measurement noise referred to the compara…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927017A two-degree-of-freedom (2DOF) control law is with The plant equation is Y(s)=P(s)U(s)+D(s), where D is an output d…

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Models FeedbackControl Systems Problem Solving

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CTRL:9927018A measured output disturbance is available for feedforward.

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Models FeedbackControl Systems Problem Solving

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CTRL:9927019A cascade (inner–outer) architecture is defined by with and with inner-loop proportional gain equal to 1 already en…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927020A linearised liquid-level plant occupies a tank of constant horizontal area A=1.25\,\mathrm{m^2}.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927021A lumped thermal plant obeys with Here T(t) is the absolute temperature of the lumped body in kelvin, T_a(t) is the…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927022The classical Bode sensitivity of a closed-loop map to the plant is to be computed from first principles.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927023A return-ratio experiment is defined on a single-loop system.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927024A unity-feedback system with an additional load summing junction is specified by where The disturbance-to-output pa…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927025A cruise-control plant for longitudinal speed v(t) (in m/s) of a vehicle of mass m=1400\,\mathrm{kg} with linear dr…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927026A plant P(s)=(s-2)/(s+4) is nonminimum-phase.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927027A position-control architecture uses inner rate feedback and outer proportional position feedback.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927028A block diagram with a crossed feedback path is defined by the algebraic signal equations with Time is in seconds,…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927029An equivalent-architecture question compares three realisations of the same closed-loop map from R to Y.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927030A laboratory servo is modelled by the multi-input block diagram with the following exact summing-junction equations.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927031Time t is measured in seconds.

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Models FeedbackControl Systems Problem Solving

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CTRL:9927032Time t is in seconds and voltages are in volts.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927033Time t is in seconds; the output y is a shaft angle in radians and the reference r is in radians.

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Models FeedbackControl Systems Problem Solving

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CTRL:9927034Time t is in seconds.

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Models FeedbackControl Systems Problem Solving

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CTRL:9927035Time t is in seconds and the output y is in millimetres.

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Models FeedbackControl Systems Problem Solving

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Problem library

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Topic choices for Control Systems are shortened. Search still covers every problem.

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Problem results

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CTRL:010117With P=2/(s+1) and C=3 the step finals through T, PS, and -T are 6/7, 2/7, and -6/7

View access options

Ctrl Sensitivity Complementary MapsCtrl Actuator Measurement Step Finals

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Private saving unavailable

Dynamic models, linearization, and feedback structureControl Systems · Mixed review

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CTRL:010118The unity DC motor has Omega/V=1/(s^2+2s+2), poles -1±j, and step speed (1/2)[1-e^{-t}(cos t+sin t)]

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Ctrl Armature Motor TransfersCtrl Underdamped Speed Step

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Dynamic models, linearization, and feedback structureControl Systems · Mixed review

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CTRL:010219The map 2(1-s)/[(s+1)(s+2)] undershoots to -1/3 at ln(3/2) before finishing at 1

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Ctrl Rhp Zero Inverse ResponseCtrl Undershoot Time And Depth

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Time response and stability criteriaControl Systems · Mixed review

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CTRL:010220L=K(s+2)/[s^2(s+5)] is type 2, stable iff K>0, and the t^2/2 error is 5/(2K)

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Ctrl Type Two Routh GainCtrl Acceleration Constant Parabola

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Time response and stability criteriaControl Systems · Mixed review

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CTRL:010221P=I/2 solves the Lyapunov equation for A=[[-1,1],[-1,-1]] and the state norm decays as e^{-t}

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Ctrl Quadratic Lyapunov IdentityCtrl Rotation Semigroup Norm

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Time response and stability criteriaControl Systems · Mixed review

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CTRL:010322The K/[s(s+2)(s+4)] locus breaks away at -2+2sqrt(3)/3 and crosses at K=48

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Ctrl Evans Real Axis AsymptotesCtrl Breakaway JW Crossing

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Root-locus and frequency-response designControl Systems · Mixed review

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CTRL:010323The lead of z=1/sqrt(3), p=sqrt(3) makes |L(j)|=1 with phase -105 and PM 75

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Ctrl Lead Midband Phase MagnitudeCtrl Unity Crossover Phase Margin

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Root-locus and frequency-response designControl Systems · Mixed review

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CTRL:010324For L=K/[(s-1)(s+2)] the full Nyquist image encircles -1 once CCW when K>2

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Ctrl Quadratic Closed Loop StabilityCtrl Nyquist OL Rhp Encirclement

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Root-locus and frequency-response designControl Systems · Mixed review

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CTRL:010425The pair (A,B,C) is minimal with G=-s/[(s+1)(s+2)] and Rosenbrock kernel ((2,1),2)

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Ctrl Minimal Realization Pbh DetsCtrl Rosenbrock Invariant Zero

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State-space, controllability, and observabilityControl Systems · Mixed review

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CTRL:010526The ARE 2P-P^2+1=0 has stabilizing root 1+sqrt(2), pole -sqrt(2), and J*=(1+sqrt(2)) x0^2

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Ctrl Scalar Are CompletionCtrl Lqr Stabilizing Root Cost

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State feedback and observersControl Systems · Mixed review

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CTRL:010527Integral action holds x=r and rejects a constant d; the homogeneous poles are -2 and -3

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Ctrl Integral Augmented CharacteristicCtrl Constant Disturbance Equilibrium

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State feedback and observersControl Systems · Mixed review

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CTRL:010528The reduced-order observer with ell=3 runs on q=xhat2-3y and never differentiates y

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Ctrl Reduced Order Q CoordinateCtrl Observer Error Decay NO Ydot

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State feedback and observersControl Systems · Mixed review

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CTRL:010629Exact ZOH of the double integrator at T=1 is Ad=[[1,1],[0,1]], Bd=(1/2,1), Gd=(z+1)/(2(z-1)^2)

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Ctrl Exact Zoh Matrix ExponentialCtrl Pulse Transfer Discrete Zero

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Digital control and robustness foundationsControl Systems · Mixed review

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CTRL:010630Jury on K(z+1/2)/((z-1)(z-1/2)) forces 0<K<1; the endpoints hit z=1 and a unit-circle conjugate pair

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Ctrl Discrete Closed Loop PolynomialCtrl Jury Quadratic Gain Interval

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Digital control and robustness foundationsControl Systems · Mixed review

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CTRL:010631Additive small-gain on P0=1/(s+1), C=2 guarantees every stable Delta only for rho<1/2

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Ctrl Sensitivity Complementary CS MapsCtrl Additive Small Gain Radius

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Digital control and robustness foundationsControl Systems · Mixed review

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Models FeedbackControl Systems Problem Solving

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Models FeedbackControl Systems Problem Solving

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927011A signal-flow graph is constructed from a unity-feedback block diagram that also has a minor-loop rate return.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927012An armature-controlled DC motor is modelled, for t\ge 0, by with numerical values The armature voltage v_a is in vo…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927013The DC motor of this problem is the first-order mechanical reduction obtained by neglecting armature inductance.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927014A process plant is mapping a control effort U (in volts) to a temperature Y (in kelvin).

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927015A plant P(s)=3/(s+2) (dimensionless) is placed in the two-input architecture where D_u is an input disturbance of t…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927016A single-loop architecture with a non-unity sensor is where N is additive measurement noise referred to the compara…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927017A two-degree-of-freedom (2DOF) control law is with The plant equation is Y(s)=P(s)U(s)+D(s), where D is an output d…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927018A measured output disturbance is available for feedforward.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927019A cascade (inner–outer) architecture is defined by with and with inner-loop proportional gain equal to 1 already en…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927020A linearised liquid-level plant occupies a tank of constant horizontal area A=1.25\,\mathrm{m^2}.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927021A lumped thermal plant obeys with Here T(t) is the absolute temperature of the lumped body in kelvin, T_a(t) is the…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927022The classical Bode sensitivity of a closed-loop map to the plant is to be computed from first principles.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927023A return-ratio experiment is defined on a single-loop system.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927024A unity-feedback system with an additional load summing junction is specified by where The disturbance-to-output pa…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927025A cruise-control plant for longitudinal speed v(t) (in m/s) of a vehicle of mass m=1400\,\mathrm{kg} with linear dr…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927026A plant P(s)=(s-2)/(s+4) is nonminimum-phase.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927027A position-control architecture uses inner rate feedback and outer proportional position feedback.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927028A block diagram with a crossed feedback path is defined by the algebraic signal equations with Time is in seconds,…

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927029An equivalent-architecture question compares three realisations of the same closed-loop map from R to Y.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927030A laboratory servo is modelled by the multi-input block diagram with the following exact summing-junction equations.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927031Time t is measured in seconds.

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Models FeedbackControl Systems Problem Solving

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CTRL:9927032Time t is in seconds and voltages are in volts.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927033Time t is in seconds; the output y is a shaft angle in radians and the reference r is in radians.

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Models FeedbackControl Systems Problem Solving

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Dynamic models, linearization, and feedback structureControl Systems · Calculation

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CTRL:9927034Time t is in seconds.

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Models FeedbackControl Systems Problem Solving

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CTRL:9927035Time t is in seconds and the output y is in millimetres.

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Models FeedbackControl Systems Problem Solving

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Problem results

CTRL:9927001A single-loop unity-feedback architecture is defined as follows.

CTRL:9927002A non-unity feedback loop is assembled from the strictly proper plant the proper compensator C(s)=2.5, and the sens…

CTRL:9927003A translational plant consists of a mass m=2.00\,\mathrm{kg}, a viscous damper b=6.00\,\mathrm{N\cdot s/m}, and a s…

CTRL:9927004A block diagram contains exactly three dynamic blocks and two summing junctions, with all initial conditions zero a…

CTRL:9927005A nested block diagram is specified by the following equations, which already include every summing-junction sign.

CTRL:9927006A forward path consists of three blocks in cascade, with input U entering G_1 and output Y leaving G_3.

CTRL:9927007Block-diagram algebra is to be used to move a summing junction and a pickoff without changing the map from R to Y.

CTRL:9927008A unity-feedback loop contains a plant with a parallel inner structure.

CTRL:9927009A signal-flow graph has five nodes x_1,x_2,x_3,x_4,x_5.

CTRL:9927010A signal-flow graph has nodes x_1=R(s), x_2, x_3, x_4=Y(s).

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Problem results

CTRL:9927001A single-loop unity-feedback architecture is defined as follows.

CTRL:9927002A non-unity feedback loop is assembled from the strictly proper plant the proper compensator C(s)=2.5, and the sens…

CTRL:9927003A translational plant consists of a mass m=2.00\,\mathrm{kg}, a viscous damper b=6.00\,\mathrm{N\cdot s/m}, and a s…

CTRL:9927004A block diagram contains exactly three dynamic blocks and two summing junctions, with all initial conditions zero a…

CTRL:9927005A nested block diagram is specified by the following equations, which already include every summing-junction sign.

CTRL:9927006A forward path consists of three blocks in cascade, with input U entering G_1 and output Y leaving G_3.

CTRL:9927007Block-diagram algebra is to be used to move a summing junction and a pickoff without changing the map from R to Y.

CTRL:9927008A unity-feedback loop contains a plant with a parallel inner structure.

CTRL:9927009A signal-flow graph has five nodes x_1,x_2,x_3,x_4,x_5.

CTRL:9927010A signal-flow graph has nodes x_1=R(s), x_2, x_3, x_4=Y(s).