Method for controlling a switched electronic circuit
To this end, the invention relates to a method for controlling a switched electronic circuit connecting an electrical voltage source u to a load R and forming a system having an output y and a plurality of operating modes i, at least some of which thus can be activated by following a switching rule o. According to the invention, the following steps are provided: —measuring state variables x of the system having equilibrium values x r ; —introducing at least one parameter p into the system, representing a measuring error of an electrical unknown of the operation of the circuit; —estimating the parameter from a state monitor and applying a Lyapunov function thereto; —deducing therefrom the equilibrium values of the system in order to obtain the control rule.
1. A method for controlling a switched electronic circuit connecting a voltage source u to a load R and forming a system having an output y and a plurality of operating modes i, at least some of which can therefore be activated by following a switching law σ, characterized in that the method comprises the steps of:
measuring state variables x of the system having equilibrium values x r ;
associating at least one error parameter p with at least one electrical operating unknown of the system so as to represent the system in the form
{
x
.
=
A
σ
x
+
B
σ
u
+
G
σ
p
p
.
=
0
A σ being the state matrix, B σ the input matrix and G σ the parameter matrix in at least one of the modes i controlled by the switching law σ;
estimating the values of the parameter p on the basis of a state observer of type
{
z
^
.
=
A
_
σ
z
^
+
B
_
σ
u
+
L
σ
(
y
-
y
^
)
y
^
=
C
_
z
^
where z is a state vector such that z T =[x T ,p T ], {tilde over (C)} is an observation matrix such that Ĉ=[I0], I is an identity matrix, and, and L σ is a gain matrix calculated by solving a linear matrix inequality (LMI) such that the error e with time between the state vector z and estimate ž thereof tends asymptotically toward zero;
deducing therefrom estimated equilibrium values {circumflex over (x)} r of the state variables x;
the switching law taking the following form
σ
*
(
x
^
,
x
^
r
,
p
^
)
=
arg
[
min
i
[
w
T
P
(
A
i
x
^
+
B
i
u
+
G
i
p
^
)
]
]
where w=({circumflex over (x)}−{circumflex over (x)} r ) and P is the solution to the Lyapunov equation.
2. The method as claimed in claim 1 , wherein the switched electronic circuit is a converter comprising a primary circuit and a secondary circuit, the primary circuit comprising the voltage source that is connected in series with a primary winding of a transformer and with a switch, an inductor L being connected in parallel with the primary winding and being under a voltage v L , the secondary circuit comprising a secondary winding of the transformer that is connected by a diode to a resistive load R, the method comprising the step of defining a current parameter p 1 to represent the error in the output load such that
i
=
p
1
+
v
R
i is a current in a conductor, v is a voltage in the conductor, p 2 to represent an error in the input voltage such that
x
.
1
=
ν
L
L
=
u
-
p
2
L
where x 1 represents the uncontrolled state variables.