Image Processing Reference
In-Depth Information
D
x
·
(
t
)
x
(
t
)
+
+
y
(
t
)
B
u
(
t
)
+
C
+
A
FIGURE 4.1
Block diagram of a continuous LTI system in state space.
where A, B, C, and D are N
N, N
M, P
N, and P
M constant matrices,
respectively. The block diagram of a linear continuous time-invariant control system
in state-space form is shown in Figure 4.1.
In the next section, we show how the state equations can be derived for electrical
and mechanical systems.
4.3.3 S
TATE
-S
PACE
E
QUATIONS OF
E
LECTRICAL
S
YSTEMS
Example 4.1
Consider the series RLC circuit shown in Figure 4.2 with the input u(t) and
output y(t).
To determine the output of this system, one needs to know the input signal, the
initial charge on the capacitor, and the initial current
through the inductor;
therefore, the system has two states. The
ned as the voltage across
the capacitor and the second state the current through the inductor. Therefore, the
first state is de
first state is de
ned as
x
1
(t)
¼ v
C
(t)
(4
:
9)
and the second state is de
ned as
x
2
(t)
¼ i
L
(t)
(4
:
10)
L
R
+
+
i
L
(
t
)
+
y
(
t
)
v
C
(
t
)
C
u
(
t
)
-
-
-
FIGURE 4.2
Series RLC circuit.
Search WWH ::
Custom Search