Index
A
analog computer 207
analog computer implementation 163
augmented state-space equations 230
augmented system 186
B
block and beam 375
block matrix 470
Bode canonical form 256
Bode phase gain relationship 300
C
closed-loop Bode plot 297
closed-loop characteristic equation 162
closed-loop characteristic polynomial 88
closed-loop performance 273
closed-loop transfer function 88
co-factor 469
companion form 165
complex conjugate poles 455
complex numbers 251
complex numbers - polar coordinates 251
complex numbers - rectangular coordinates 251
computed torque 56
conjugate of a complex number 252
control canonical form 324
control implementation 324
controllable 186
controllable system 169
critically damped 100
crossover frequency 293
D
damping forces 33
derivative control 82
derivative gain 83
design model 3
design models 46
design process 1
desired characteristic polynomial 88
determinant of a matrix 469
diagonal matrix 473
digital differentiator 158
digital implementation 217
dirty derivative 145
discrete differentiator 145
discrete integrator 145
distinct eigenvalues 472
disturbance observer 229
E
eigen-decomposition 472
eigenvalue of a matrix 471
eigenvector 471
equilibrium point 48
estimated state 205
Euler's relationship 252
Euler-Lagrange equation 10
F
final value theorem 125
first-order response 95
forced response 450
free integrator 130
fundamental theorem of calculus 126
G
gain margin 296
generalized velocity 10
H
homogeneous response 450
I
innovation 206
integral feedback 212
integral gain 82
integrating factor 449
integrator anti-windup 145
interaction matrix 186
inverse of a matrix 470
J
K
L
Lagrangian 33
linear independence 473
linearized systems 214
loop shaping control 3
loop-shaping 313
loopshape 293
loopshaping 250
M
magnitude of a complex number 251
magnitude of a transfer function 253
matrix 467
matrix addition 467
matrix adjugate 469
matrix determinant 469
matrix eigenvalue 471
matrix inverse 470
matrix minor 469
matrix multiplication 467
matrix rank 473
matrix trace 469
matrix transpose 468
moments of inertia 16
N
noise 273
non-singular matrix 470
nonminimum phase zeros 104
O
observability matrix 211
observable 231
observable system 212
observation error 206
observer canonic form 208
observer error 206
observer-based control 3
observers 158
open-loop characteristic polynomial 87
ordinary differential equations 449
output equation 69
overdamped 100
P
parallel axis theorem 30
PD control 87
phase of a complex number 251
phase of a transfer function 253
pole locations 95
pole placement 185
potential energy of a spring 31
prefilter 325
proportional control 82
R
rank of a matrix 473
rational transfer function 102
realization of a transfer function 162
reference command 82
reference input 131
residue 453
S
s-function 427
sample period 145
sampled data system 143
second-order response 99
second-order systems 82
sensor noise 131
simulation Model 1
stability margins 313
state evolution equation 69
state feedback 158
T
Taylor series 47
trace of a matrix 469
transfer function model 162
transpose of a matrix 468
Tustin approximation 145
type 0 system 282
type 1 system 283
type 2 system 284
U
underdamped 100
upper companion form 474
upper triangular matrix 474
V
Vandermonde matrix 474
Z
z-transform 144