Index 889
J
Jet-pipe controller, 146–47
Jordan blocks, 679
Jordan canonical form, 651, 695, 706–07
K
Kalman, R. E., 12, 675
Kirchhoff’s current law, 72
Kirchhoff’s loop law, 72
Kirchhoff’s node law, 72
Kirchhoff’s voltage law, 72
L
Lag compensation, 321
Lag compensator, 311, 321, 502
Bode diagram of, 503
design by frequency-response method,
502–11
design by root-locus method, 321, 323
polar plot of, 503
Lag network, 82, 542
Lag–lead compensation, 330, 335, 338,
377, 511–18
Lag–lead compensator:
Bode diagram of, 558
design by frequency-response method,
513–17
design by root-locus method, 331–32,
380–82
electronic, 330–32
polar plot of, 512
Lag–lead network:
electronic, 330–32
mechanical, 366
Lagrange polynomial, 708
Lagrange’s interpolation formula, 708
Laminar-flow resistance, 102
Laplace transform, 862
properties of, 865
table of, 863–64
Lead compensator, 311, 493
Bode diagram of, 494
design by frequency-response method,
493–502
design by root-locus method, 311–18
polar plot of, 494
Lead, lag, and lag–lead compensators:
comparison of, 517–18
Lead network, 542
electronic, 82
mechanical, 365
Lead time, 5
Linear approximation:
of nonlinear mathematical models, 43
Linear system, 14
constant coefficient, 14
Linear time-invariant system, 14, 164
Linear time-varying system, 14
Linearization:
of nonlinear systems, 43
Liquid-level control system, 157
Liquid-level systems, 101, 103–04, 140–41
Log-magnitude curves of quadratic
transfer function, 411
Logarithmic decrement, 237
Logarithmic plot, 403
Log-magnitude versus phase plot, 403,
443–44
LRC circuit, 72–73M
M circles, 478–79
a family of constant, 479
Magnitude condition, 271
Manipulated variable, 3
Mapping theorem, 448–49
Mathematical model, 13
MATLAB commands:
MATLAB:
obtaining maximum overshoot with,
194
obtaining peak time with, 194
obtaining response to initial condition
with, 266
partial-fraction expansion with,
871–73
plotting Bode diagram with, 422–23
plotting root loci with, 290–91
writing text in diagrams with, 188–89
[A,B,C,D] = tf2ss(num,den), 40, 656,
698
bode(A,B,C,D), 422, 426
bode(A,B,C,D,iu), 426–27
bode(A,B,C,D,iu,w), 422
bode(A,B,C,D,w), 422
bode(num,den), 422
bode(num,den,w), 422, 425, 551
bode(sys), 422
bode(sys,w), 552
c = step(num,den,t), 190
for loop, 243, 249, 584
[Gm,pm,wcp,wcg,] = margin(sys),
468–69
gtext ('text'), 189
impulse(A,B,C,D), 195
impulse(num, den), 195
initial(A,B,C,D,[initial condition],t), 209
inv(A), 879
K = acker(A,B,J), 736
K = lqr(A,B,Q,R), 798
K = place(A,B,J), 736