Index 893
Root loci:
general rules for constructing, 283–87
for positive-feedback system, 303–07
Root locus, 271
method, 269–70
Routh’s stability criterion, 212–18
S
Schwarz matrix, 268
Second-order system, 164
impulse response of, 178–79
standard form of, 166
step response of, 165–75
transient-response specification of, 171
unit-step response curves of, 169
Sensor, 21
Series compensation, 308–09, 342
Servo system, 95, 164–65
design of, 739–51
with tachometer feedback, 268
with velocity feedback, 175–77
Servomechanism, 2
Set point, 21
Set-point kick, 590
Settling time, 170, 172–73
obtaining with MATLAB, 194
versuszcurve, 174
Sign inverter, 79
Simple pole, 861
Singular points, 861
Sinusoidal signal generator, 486
Sinusoidal transfer function, 401
Small gain theorem, 809
Space vehicle control system, 367, 538–39
Speed control system, 4, 148
Spool valve:
linealized mathematical model of, 127
Spring-loaded pendulum system, 98
Spring-mass-dashpot system, 66
Square-law nonlinearity, 43
S-shaped curve, 569
Stability analysis, 454–62
in the complex plane, 182
Stabilizability, 688
Stack controller, 115
Standard second-order system, 189
State, 29
State controllability:
complete, 676, 678, 680
State equation, 31
solution of homogeneous, 660
solution of nonhomogeneous, 666–67
Laplace transform solution of, 663
State-feedback gain matrix, 724
MATLAB approach to determine,
735–36
State matrix, 31
State observation:
necessary and sufficient conditions for,
754–55
State observer, 751–77
design with MATLAB, 773
type 1 servo system with, 746
State observer gain matrix: 755
Ackermann’s formula to obtain, 756–57
direct substitution approach to obtain,
756
transformation approach to obtain, 755
State space, 30
State-space equation, 30
correlation between transfer function
and, 649, 656
solution of, 660
State-space representation:
in canonical forms, 649
ofnth order system, 36–39
State-transition matrix, 664
properties of, 665
State variable, 29
State vector, 30
Static acceleration error constant,
228, 421
determination of, 421–22
Static position error constant,
226, 419
Static velocity error constant,
227, 420
Steady-state error, 160, 226
for unit parabolic input, 229
for unit ramp input, 228
in terms of gain K, 230
Steady-state response, 160
Step response, 699–700
of second-order system, 165–69
Summing point, 18
Suspension system:
automobile, 86–87
motorcycle, 87
Sylvester’s interpolation formula, 673,
709–713
System, 3
Sytem types, 419
type 0, 225, 230, 419, 433, 487–88
type 1, 225, 230, 420, 433, 487–88
type 2, 225, 230, 421, 433, 487–88
System response to initial condition:
MATLAB approach to obtain, 203–11T
Tachometer, 176
feedback, 343
Taylor series expansion, 43–45