... irrespective of
288 Analysis and Control of Linear Systems
Figure 10. 3. Corrector in a looped system
The control magnitude can be a function of bx,,
ε
or
e
. Based on the signals
considered and ...
)(
)(
)()(
31
p
pC
pp
β
µ
µ
304 Analysis and Control of Linear Systems
Figure 10. 21. Bode diagram of a lead-delay network
10. 3.1.1. Action me...
... K
1
N
10
1+
1
2
n
1
N
10
[7.21]
222 Analysis and Control of Linear Systems
iteration, unstable), interrupt the simulation and the calculation of sensitivity func-
tions, hence of the gradient, ... from the point of view
of calculation, in terms of linear regression (or linearized), i.e. it leads to a quadratic
196 Analysis and Control of Linear S...
... Congress Cataloging-in-Publication Data
[Analyse des systèmes linéaires/Commande des systèmes linéaires. eng] Analysis and control
of linear systems analysis and control of linear systems/ edited ... systems/ edited by Philippe de Larminat.
p. cm.
ISBN-13: 97 8-1 -9 0520 9-3 5-4
ISBN -1 0: 1-9 0520 9-3 5-5
1. Linear control systems. 2. Automat...
... values of
ξ
.
10
0
-1 0
-2 0
-3 0
0
-4 5
-9 0
-1 35
-1 80
1
T
1
1
T
2
Module (dB)Phase (degree)
Figure 1.23. Bode diagram of a second order system with
ξ
≥
1
20 Analysis and Control of Linear Systems ... phase difference of
Φ
0
()
f
.
10 Analysis and Control of Linear Systems
response, which considers the past in order to provid...
...
104 Analysis and Control of Linear Systems
Figure 3.5. Bode diagram of the continuous system and its discretization
3.4.5. The problem of sub-sampling
Let us consider the case of a “standardized” ... from the z-transform of
this impulse response.
102 Analysis and Control of Linear Systems
Due to this relation and Table 3.5, we will be able to easil...
... eigenvalues of A appear (certain powers l
ij
being
then equal to 0):
110 Analysis and Control of Linear Systems
The object of this chapter is to describe certain structural properties of linear
systems ... and
intersection of sub-spaces (the sum and intersection of two A-invariant sub-spaces
are A-invariant). Consequently, for any
L ⊂ X sub-space, ther...
... 144 Analysis and Control of Linear Systems
On the other hand, the Fourier transform preserves the energy (Parseval theorem).
Indeed, the energy of a continuous-time signal y(t) or of a discrete-time ... proximity of ν
0
.
142 Analysis and Control of Linear Systems
A discrete-time deterministic signal y[k],k ∈Zis, by definition, a sequence of
complex numbers:
y =...
... the condition of detectability by a careful choice of matrix Q.
162 Analysis and Control of Linear Systems
case of multi -control systems. As indicated in Chapter 2, the equations of state can ... at the expense of a stronger control.
176 Analysis and Control of Linear Systems
Figure 6.6. Stabilization by quadratic optimization
166 Analysis a...
... order, the
242 Analysis and Control of Linear Systems
Consequently, the field of absolute stability of multi-interval methods (implicit or
not depending on the value of β
0
) is the set of µ ∈ C so ... desired and to perform the corre-
sponding substitutions. Let us take the example of the classic PID regulator. Let e(t)
230 Analysis and Control of Linear Sys...
...
2 a
n-1
a
n-3
a
n-5
…
3 b
1
=a
n-2
-a
n
a
n-3
/a
n-1
b
2
=a
n-4
-a
n
a
n-5
/a
n-1
b
3
=a
n-6
-a
n
a
n-7
/a
n-1
…
4 c
1
=a
n-3
-b
2
a
n-1
/b
1
c
2
=a
n-5
-b
3
a
n-1
/b
1
...
study the case of open loop stable systems, that of integrator systems and finally the
case of open loop unstable systems.
270 Analysis and Control of Linear Systems
We...