Mikles J., Fikar M. Process Modelling, Identification, and Control
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References 473
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Index
adaptive control, 445
amplitude, 148
analysis
frequency, 145
ARMA model, 224
ARMAX model, 224
ARX model, 224
˚
Astr
¨
om-H
¨
agglund methods, 290
bandwidth, 261
BASIC, 130
Bezout identity, 111
block diagram, 8
Bode diagram, 152
Broida method of
identification, 232
bumpless transfer, 279
C language, 131
canonical decomposition, 83
canonical form
controllable, 104
observable, 107
characteristics
frequency, 145
statistical, 162
closed-loop system, 253
column
distillation, 28
packed absorption, 26
connection
feedback, 98
parallel, 97
serial, 97
control
dead-beat, 376
direct digital, 189, 205
error, 5
feedback, 6
feedforward, 9
integral action, 321
law, 5
optimal, 297
feedback, 305
predictive, 403
problem, 253
problem definition, 255
proportional, 5
standard configuration, 394
steady state error, 7
control device, 5
control error
steady-state, 212, 259
control performance, 257
frequency indices, 260
integral criteria, 259
time domain, 257
control quality, 212
controllability, 78
complete, 79
controllable canonical form, 210
controlled object, 3
controller
H
2
, 394
derivative, 272
integral, 270
integral action, 355
476 Index
LQ, 380
polynomial, 380
state-space, 380
LQG, 388
multivariable, 392
PID, 266
polynomial design, 350
proportional, 5, 266
gain, 5
stabilising, 368
state-space, 370
converter
analog-to-digital, 189
digital-to-analog, 189
correlation coefficient, 168
cost
IAE, 260
ISE, 260
covariance, 168
covariance matrix, 169
cross-power spectral density, 175
cutoff rate, 261
damping ratio, 258
dead-beat control, 376
derivation operator, 85
Diophantine equation, 351
solvability, 352
directional forgetting, 242
dominant poles, 263
dominant time constant, 258
dual parametrisation, 372
dynamic programming, 322
continuous-time systems, 322
discrete-time systems, 329
equation
algebraic, 34
differential, 34
set, 34
solution, 62
Diophantine, 351
Hamilton-Jacobi-Bellman, 326
Lyapunov, 77
output, 36
Riccati, 309
state, 34, 36
state balance, 14
state space, 66
balance, 66
solution, 67
Euler identity, 149
Euler method, 126
expected value, 171
exponential forgetting, 241
feedback
negative, 6
Fourier
transform, 102
Fourier expansion, 149
Fourier law, 25
fraction
partial, 61
polynomial
matrix, 107
fractional representation, 366
frequency
transfer function matrix, 102
frequency response
magnitude, 151, 152
phase, 151
phase angle, 152
frequency transfer function, 150
frequency transfer function
matrix, 151
function
auto-correlation, 171
auto-covariance, 171
correlation, 172
cross-correlation, 174
cumulative distribution, 164
dirac delta, 60
distribution, 164
exponential, 54
Lyapunov, 75
negative definite, 76
positive definite, 75
positive semidefinite, 76
probability density, 167
ramp, 54
step, 53
unit, 53
transfer, 85
trigonometric, 55
unit impulse, 60
weighting, 117
Index 477
gain, 120
gain crossover frequency, 261
gain margin, 260
Hamilton-Jacobi-Bellman
equation, 326
Hamiltonian
function, 301
heat exchanger
jacketed, 19
identifiability, 239
identification
continuous-time transfer
function, 245
discrete-time transfer
function, 233
parameter convergence, 239
step responses, 225
Broida method, 232
first order system, 226
higher order system, 230
second order system, 227
Strejc method, 230
identification methods, 222
impossible event, 162
integrator windup, 277
inverse Z transform, 197
partial fraction expansion, 199
polynomial division, 198
Kalman filter, 337
Laplace
transform, 51, 52
convolution, 58
derivatives, 57
integral, 57
inverse, 52, 61
properties, 57
time delay, 59
unit impulse, 60
least squares method, 233
recursive, 235
linearisation, 39
method, 39
LQ control, 380
LQG control, 388, 390
Luenberger observer, 335
magnitude frequency spectrum, 191
MATLAB, 130
matrix
auto-covariance, 172
eigenvalues, 70
exponential, 69
frequency transfer function, 102
fundamental, 69
impulse responses, 100
observability, 82
polynomial, 107
common divisor, 110
coprime, 110
degree, 108
determinant degree, 110
division algorithm, 111
greatest common divisor, 110
irreducibility, 110
left fraction, 110
rank, 109
relatively prime, 111
right fraction, 110
spectral factorisation, 112
stable, 109
unimodular, 109
rational
proper, 102
strictly proper, 102
state transition, 69
system, 70, 77
transfer function, 100, 101
matrix inversion lemma, 236
maximum overshoot, 257
method
Euler, 126
Runge-Kutta, 127
mixing
ideal, 14
model
batch, 14
continuous, 14
discrete-time, 189
controllability, 212
examples, 214
input-output, 204, 208
observability, 212
stability, 211
state-space, 207
empirical, 14
478 Index
empirical-theoretical, 14
input output, 84
MIMO, 100
realisation, 101
linear, 39
mathematical, 13
theoretical, 14
moment
m-th, 167
central, 167
second, 167
Naslin method, 282
norm
vector, 73
normal distribution, 168
Nyquist diagram, 152
observability, 81
matrix, 82
observable canonical form, 210
observer, 335
optimal control, 297
optimal feedback, 331
optimal tracking, 317
Output Error model, 225
parametrisation
discrete-time systems, 375
persistent excitation, 239
phase margin, 261
physical realisability, 85
PID controller, 266
digital implementation, 279
integrator windup, 277
tuning, 281
˚
Astr
¨
om-H
¨
agglund methods, 290
experimental methods, 287
Naslin method, 282
pole placement, 284
standard forms, 281
Strejc method, 283
Ziegler-Nichols methods, 288
PID controller structures, 274
pole placement, 284, 317, 350
polynomial, 351
pole placement design, 345
poles, 101, 102
polynomial
characteristic, 77
polynomial design, 350
multivariable systems, 361
polynomial matrix
fraction, 107
power spectral density, 175
predictive control, 403
closed-loop, 411
constraints, 419
cost function, 406
derivation, 407
implementation, 416
model, 404
stability, 420
state-space, 412
tuning, 431
principle of optimality, 323
principle of minimum, 297
probability, 162
conditional, 162
density, 171
joint density, 168
law of distribution, 164
theory, 162
probability density, 167
process, 3
analysis, 51
automatic control, 4
control, 4
feedback, 5
distributed parameters, 14
dynamical model, 13
dynamical properties, 4
ergodic, 173
generalmodel,33
heat transfer, 19
liquid storage, 16
interacting tank, 17
single tank, 16
lumped parameters, 14
mass transfer, 26
mathematical model, 13
model
input-output, 51
non-stationary, 173
random, 170
response, 5, 6
space discretisation, 35
state space model, 101
Index 479
stationary, 173
stochastic, 170
expected value, 171
realisation, 170
variance, 171
vector mean value, 172
process identification, 221
process models, 223
stochastic, 223
random event, 162
reachability, 79
complete, 79
reactor
biochemical, 31, 33
chemical, 31
CSTR, 31
realisation
minimum, 101
recursive least squares method, 235
modifications, 241
resonance peak, 261
resonant frequency, 261
Riccati equation, 309
rise time, 258
Runge-Kutta method, 127
sampler, 189
sampling period, 189
self-tuning control, 445
continuous-time, 447
discrete-time, 446
separation principle, 341
servo problem, 318, 320
settling time, 258
Simulink, 130
stability, 72
asymptotic, 73, 77
linear system, 77
asymptotic in large, 73, 77
BIBO, 103
external, 103
Lyapunov, 73, 76
system
continuous, 72
state
concept, 45, 67
observability, 81, 82
complete, 81
reconstructibility, 81
complete, 81
steady, 3
deviation, 39
unsteady, 5
state estimation, 335
state plane, 75
state space, 75
representation, 66
state trajectory, 75
steady state, 3
steady-state behaviour, 256
step function, 119
step response, 119
step responses
identification, 225
stochastic process models, 223
Strejc method of controller tuning, 283
Strejc method of identification, 230
sure event, 162
system
abstract, 45
autonomous, 72
causal, 118
continuous, 45
stability, 72
deterministic
MIMO, 45
SISO, 45
dynamical, 46
equilibrium state, 72
forced, 72
free, 69, 72
linear, 45
nonautonomous, 72
order, 101
physical, 45
poles, 101, 207, 263
dominant, 263
representation
input-output, 51
state space, 51
response, 117, 119
stochastic, 46
unit impulse response, 117
zeros, 101, 207
Taylor series, 41
Taylor theorem, 39
480 Index
theorem
existence of optimal control, 327
LQ control with observer, 382
pole placement, 345
time constant, 6, 120
time delay, 59
tracking problem, 318
transfer function, 85
algebra, 96
discrete-time, 200, 202
frequency, 145
matrix, 100, 210
parametrisation, 371
transform
Fourier, 150
transformation
canonical, 70
value
expected, 164
random, 162
variable
disturbance, 4, 35
expected value, 164
input, 3
manipulated, 4, 35
deviation, 40
output, 3, 35
random, 162, 163
continuous, 166
discrete, 163
standard deviation, 168
setpoint, 4
state, 14, 35
deviation, 40
variance, 165
variance, 171
variational calculus, 299
white noise, 176
Youla-Kuˇcera parametrisation, 365
zeros, 101
Ziegler-Nichols methods, 288
Z transform, 195
exponential function, 197
inverse, 197
linearity, 197
table, 198
unit step function, 196