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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

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

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

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

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

Time response and stability criteriaControl Systems · Mixed review

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

Time response and stability criteriaControl Systems · Mixed review

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

Time response and stability criteriaControl Systems · Mixed review

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

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

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

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

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

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

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

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

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

State feedback and observersControl Systems · Mixed review

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

State feedback and observersControl Systems · Mixed review

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

State feedback and observersControl Systems · Mixed review

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

Digital control and robustness foundationsControl Systems · Mixed review

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

Digital control and robustness foundationsControl Systems · Mixed review

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

Digital control and robustness foundationsControl Systems · Mixed review