Deadbeat control method and control unit for an asynchronous rotary electrical machine and a storage medium therefor
View Patent ↗This deadbeat control method of controlling an asynchronous rotary electrical machine consists of: a) a step of establishing a set point current that is adapted to achieve at the end of the interval T both the mechanical force set point and a set point magnetic flux and is established on the basis of a relationship between the set point current, the set point magnetic flux and initial current and magnetic flux values at the beginning of the interval T; and b) a step of calculating an average control vector to be applied continuously during the interval T to obtain at the end of the interval T a current equal to the set point current established during the step a).
1. A deadbeat control method of controlling an asynchronous rotary electrical machine whose magnetic flux depends on its energization current, the method applying an average control vector continuously or applying an average value thereof over a time interval T to obtain a mechanical force generated by the machine equal to a predetermined mechanical force set point at the end of the interval T, which method comprises:
a) a step of establishing a set point current that is adapted to achieve at the end of the interval T both the mechanical force set point and a set point magnetic flux and is established on the basis of a relationship between the set point current, the set point magnetic flux and initial current and magnetic flux values at the beginning of the interval T; and
b) a step of calculating the average control vector to be applied continuously during the interval T to obtain at the end of the interval T a current equal to the set point current established during the step a).
2. A method according to claim 1 , wherein the set point current is a solution of the following complex relationship:
( a 2 ·p 11 −a 1 ·p 21 )· {right arrow over (I)} c +( a 2 ·p 12 −a 1 ·p 22 )·{right arrow over (Φ)} c =( a 2 ·e 1 ·p 11 −a 1 ·e 2 ·p 21 )· {right arrow over (I)} 0 +( a 2 ·e 1 ·p 12 −a 1 ·e 2 ·p 22 )·{right arrow over (Φ)} 0
in which:
P ij are the coefficients of the inverse of a matrix P of eigenvalues defined by the following relationship A=P·D·P −1 , where D is the diagonal matrix of the eigenvalues μ i of the matrix A, P −1 is the inverse of the matrix P, and the matrix A is the matrix of free behavior of the machine in a linear system of state equations modeling the operation of the machine;
the coefficients a i are the coefficients of a matrix C defined by the following relationship C=D −1 ·(e D·T −I)·(P −1 ·B), in which the matrix I is the unit matrix and the matrix B is the control matrix of the machine in the linear system of state equations;
the vectors {right arrow over (Φ)} 0 and {right arrow over (I)} 0 respectively represent the initial state of the current and of the magnetic flux of the machine at the beginning of the interval T;
the vectors {right arrow over (I)} c and {right arrow over (Φ)} c are respectively the set point current vector and the set point magnetic flux vector; and
the coefficients e i are defined by the following relationship e i =e μ i ·T .
3. A method according to claim 2 for an asynchronous rotary electrical machine having a stator and a rotor, wherein the state vector of the linear system of state equations modeling the operation of the machine is formed of a stator current vector and a rotor magnetic flux vector.
4. A method according to claim 1 , wherein the average control vector is the exact solution of the following discrete system of state equations of the machine:
{right arrow over (X)} c =F ( T )· {right arrow over (X)} 0 +G ( T )· {right arrow over ( V
in which:
the vector {right arrow over (X)} 0 is a state vector defining the initial states of the current and the magnetic flux of the machine at the beginning of the interval T;
the vector {right arrow over (X)} c is a set point state vector defining the set point current and the set point magnetic flux of the machine;
the vector {right arrow over ( V is the average control vector of the machine;
the matrix F(T) is a transition matrix of the machine defined by the relationship F=e A·T , where A is the matrix of free behavior of the machine in a linear system of state equations modeling the operation of the machine; and
the matrix G(T) is a control matrix of the machine whose value is a function of the value of the interval T.
5. A method according to claim 1 , wherein the average control vector is the result of the following relationship:
V
→
_
=
ⅇ
ⅈ
·
θ
0
·
ⅇ
μ
1
·
T
[
p
11
(
I
0
d
0
+
i
·
I
0
q
0
)
+
p
12
·
Φ
0
d
0
]
·
[
p
21
·
(
I
cd
+
i
·
I
cq
)
+
p
22
·
Φ
cd
]
-
ⅇ
μ
2
·
T
·
[
p
21
·
(
I
0
d
0
+
i
·
I
0
q
0
)
+
p
22
·
Φ
0
d
0
]
·
[
p
11
·
(
I
cd
+
i
·
I
cq
)
+
p
12
·
Φ
cd
]
a
2
·
[
p
11
·
(
I
cd
+
i
·
I
cq
)
+
p
12
·
Φ
cd
]
-
a
1
·
[
p
21
·
(
I
cd
+
i
·
I
cq
)
+
p
22
·
Φ
cd
]
in which:
θ 0 is the angular position of an initial system of axes whose abscissa axis is aligned with an initial magnetic flux vector of the machine at the beginning of the interval T;
the coefficients p ij are the coefficients of the inverse of a matrix P of eigenvectors defined by the relation A=P·D·P −1 , where D is the diagonal matrix of the eigenvalues μ i of the matrix A, P −1 is the inverse of the matrix P, and the matrix A is the matrix of free behavior of the machine in a linear system of state equations modeling the operation of the machine;
I 0d 0 , I 0d 0 are the coordinates of the initial current vector at the beginning of the interval T in an initial system of axes whose abscissa axis is aligned with the direction of the initial magnetic flux vector;
Φ 0d 0 is the abscissa of the initial magnetic flux vector in the initial system of axes;
I cd , I cq are the coordinates of the set point current vector at the end of the interval T in a set point system of axes whose abscissa axis is aligned with the direction of the set point magnetic flux vector; and
Φ cd is the abscissa of the set point magnetic flux vector in the set point system of axes.
6. A method according to claim 1 , wherein the set point current has coordinates I cd and I cq at the end of interval T, in a set point system of axes whose abscissa axis is aligned with the direction of the set point magnetic flux vector, and wherein coordinate I cd is established from coordinate I cq and the set point magnetic flux.
7. An information storage medium containing instructions for executing a method according to claim 1 when said instructions are executed by an electronic computer.
8. A deadbeat control unit for controlling an asynchronous rotary electrical machine the magnetic flux whereof is controlled on the basis of its energization current, wherein said unit includes:
a module for establishing a set point current that is adapted to achieve at the end of the interval T both the mechanical force set point and a set point magnetic flux and is established on the basis of a relationship between the set point current, the set point magnetic flux and initial current and magnetic flux values at the beginning of the interval T; and
a module for calculating the average control vector to be applied continuously during the interval T to obtain at the end of the interval T a current equal to the set point current established by the module.