... y
2
)
=
y
1
y
2
[5. 9]
152 Analysis and Control of Linear Systems
Figure 5. 1. Typical power spectrum of an MA (left)
or AR (right) model
In the case of a single denominator (n
c
=0), we talk of an AR ... 144 Analysis and Control of Linear Systems
On the other hand, the Fourier transform preserves the energy (Parseval theorem).
Indeed, the energy of a...
... systems analysis and control of linear systems/ edited by Philippe de Larminat.
p. cm.
ISBN-13: 97 8-1 -9 052 0 9-3 5- 4
ISBN-10: 1-9 052 0 9-3 5- 5
1. Linear control systems. 2. Automatic control. I. Larminat, ...
5. 2. Signals and spectral analysis 141
5. 3. Generator processes and ARMA modeling 150
5. 4. Modeling of LTI systems and ARMAX mo...
... 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 ... of Linear Systems
Figure 1.19. Unit-step response of the second order system
ξ
≥
1
1=
ξ
: critical state. The roots of the d...
... Single-Variable Control through Pole Placement 355
Figure 11.11. Influence of the measurement noise according
to the dynamics chosen for A
o
and A
m
350 Analysis and Control of Linear Systems ... obtain:
5. 05. 0
3
5. 05. 0
2
2
2
++=
+=
++=
ssT
ssS
ssR
Hence, the control verifies:
YssCssUss )5. 05. 0( )5. 05. 0()3(
222
++−++=+
By leaving on the left the term...
...
Consequently, this type of control favors the selection of short sampling periods
and it proves to be well-adapted to the control of fast electro-mechanical systems
(machine-tool, high-speed machining, ... regulator of this restated problem in
terms of error signals:
)()()()(
11
tqRtqS
yoptu
εε
−−
−= [12.24]
392 Analysis and Control of Linear Systems
Hence,...
... internal model
[WON 85] associated with the mode
)(tm
and consequently the rejection of the
412 Analysis and Control of Linear Systems
the zeros of transmission of )(
12
sG and )(
21
sG . In ... p. 73 5- 7 41, 2000.
[MOO 81] MOORE B.C., “Principal Component analysis in linear systems: controllability,
observability and model reduction”, IEEE Trans. Auto....
...
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” ... polynomial of an order equal to 1−
i
n , where
i
n is the
multiplicity order of
i
λ
and i
th
the eigenvalue of A.
5 A canonical form called controllab...
... 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, there...
... 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...
... formulation of the identification algorithm is expressed, 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 ... [7.44]
Two parameters must be identified: the static gain of system K and the time con-
stant τ.
216 Analysis and Control of Linear Systems
so-called...