US 12,562,662 B2 · Nonlinear predictive position control method suitable for biaxial permanent magnet servo system

Abstract

The disclosure discloses a nonlinear predicative position control method suitable for a biaxial permanent magnet servo system. In consideration of uncertainty disturbance of the biaxial permanent magnet synchronous motor driving system, a value function for the biaxial permanent magnet synchronous motor driving system and a constraint condition of the value function are constructed, and the value function is solved to obtain a voltage control quantity of the permanent magnet synchronous motor, and the voltage control quantity of the permanent magnet synchronous motor is input into the stator voltage input end of the permanent magnet synchronous motor, thereby realizing the adjustment control of the nonlinear prediction position of the biaxial permanent magnet synchronous motor driving system.

A nonlinear predictive position control method suitable for a biaxial permanent magnet servo system, wherein the method comprises:

the biaxial permanent magnet servo system is a biaxial permanent magnet synchronous motor driving system, in consideration of an uncertainty disturbance of the biaxial permanent magnet synchronous motor driving system, a value function for the biaxial permanent magnet synchronous motor driving system and a constraint condition of the value function are constructed, and the value function is solved to obtain a voltage control quantity of a permanent magnet synchronous motor, the voltage control quantity of the permanent magnet synchronous motor is input into a stator voltage input end of the permanent magnet synchronous motor, thereby realizing an adjustment control of a nonlinear predicative position of the biaxial permanent magnet synchronous motor driving system,
wherein the value function for the biaxial permanent magnet synchronous motor driving system is constructed as follows:
J
=
1
2
⁢
∫
0
T
1
(
Y
1
ref
-
Y
1
)
T
⁢
H
1
T
⁢
H
1
(
Y
1
ref
-
Y
1
)
⁢
d
⁢
τ
+
1
2
⁢
∫
0
T
2
(
Y
2
ref
-
Y
2
)
T
⁢
H
2
T
⁢
H
2
(
Y
2
ref
-
Y
2
)
⁢
d
⁢
τ
H
1
=
[
1
τ
]
,
H
2
=
[
1
τ
τ
2
2
!
τ
3
3
!
]
,
Y
1
=
[
y
1
(
t
)
y
.
1
(
t
)
]
T
,
Y
2
=
[
y
2
(
t
)
y
.
2
(
t
)
y
¨
2
(
t
)
y
…
2
(
t
)
]
T
Y
1
ref
=
[
y
1
ref
⁢
(
t
)
y
.
1
ref
(
t
)
]
T
;
Y
2
ref
=
[
y
2
ref
⁢
(
t
)
y
.
2
ref
(
t
)
y
¨
2
ref
(
t
)
y
…
2
ref
(
t
)
]
T
{
y
1
ref
(
t
)
=
i
di
*
(
t
)
y
2
ref
(
t
)
=
θ
i
*
(
t
)
y
1
(
t
)
=
i
di
(
t
)
y
2
(
t
)
=
θ
i
(
t
)
wherein J is a value of the value function, T1 and T2 are predicative step sizes of a current loop and a position loop of the permanent magnet synchronous motor respectively;
Y1ref and Y2ref respectively represent a reference output vector of the value function, H1 and H2 respectively represent a weight coefficient matrix of the value function, Y1 and Y2 respectively represent an output evaluation vector of the value function, t represents a time, t represents a future control time domain;
y1 (t) and y2 (t) respectively represent a first component and a second component of an actual output vector of a control system at the time t;
{dot over (y)}1(t) and {dot over (y)}2(t) respectively represent first-order derivatives of the first component and the second component of the actual output vector of the control system at the time t;
ÿ2(t) represents a second-order derivative of the second component of the actual output vector of the control system at the time t;
y1ref(t) and y2ref(t) respectively represent a first component and a second component of a reference output vector of the control system at time the t;
{dot over (y)}1ref(t) and {dot over (y)}2ref(t) respectively represent first-order derivatives of the first component and the second component of the reference output vector of the control system at the time t;
ÿ2ref(t) and ÿ2ref(t) respectively represent a second-order derivative and a third-order derivative of the second component of the reference output vector of the control system at the time t;
idi(t) and idi*(t) respectively represent an actual value and a reference value of a d-axis current of the two permanent magnet synchronous motors at the time t, θi (t) and θi*(t) respectively represent an actual value and a reference value of a position angle of the two permanent magnet synchronous motors at the time t, i=1,2 represents a reference sign of the two permanent magnet synchronous motors;
under the value function, nonlinear constraint conditions of the permanent magnet synchronous motor are further established:
{
x
.
(
t
)
=
f
⁡
(
x
⁡
(
t
)
)
+
g
1
(
x
⁡
(
t
)
)
⁢
u
⁡
(
t
)
+
g
2
(
x
⁡
(
t
)
)
⁢
b
⁡
(
t
)
y
⁡
(
t
)
=
h
⁡
(
x
⁡
(
t
)
)
f
⁡
(
x
)
=
[
1
L
s
⁢
(
-
R
s
⁢
i
di
+
p
⁢
ω
i
⁢
L
s
⁢
i
qi
)
1
L
s
⁢
(
-
R
s
⁢
i
qi
+
p
⁢
ω
i
(
ψ
f
+
L
s
⁢
i
di
)
)
1
J
m
⁢
(
1.5
p
⁢
ψ
f
⁢
i
qi
-
B
⁢
ω
i
)
ω
i
]
g
1
(
x
)
=
[
1
L
s
0
0
1
L
s
0
0
0
0
]
,
g
2
(
x
)
=
[
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
]
x
⁡
(
t
)
=
[
i
di
i
q
⁢
i
ω
i
θ
i
]
T
u
⁡
(
t
)
=
[
u
di
u
qi
]
T
y
⁡
(
t
)
=
[
y
1
y
2
]
T
b
⁡
(
t
)
=
[
b
di
b
qi
b
ω
⁢
i
b
θ
⁢
i
]
T
wherein x(t) represents a state variable at the time t, {dot over (x)}(t) represents a first-order derivative of the state variable at the time t, iqi represents an actual value of a q-axis current of the two permanent magnet synchronous motors, ωi is a mechanical angular velocity of the two permanent magnet synchronous motors, u(t) represents an input vector of a motor control system at the time t, udi and uqi respectively represent voltage control quantities of the permanent magnet synchronous motor at d-axis and q-axis;
bdi, bqi, bωi, and bθi respectively represent a disturbance caused by d-axis parameter changes, q-axis parameter changes, external load changes and a mechanical interference in the permanent magnet synchronous motor system;
f(x) represents a nonlinear function of the motor control system, h(x(t)) represents an output function of the motor control system, b (t) represents an uncertainty disturbance vector at the time t, g1(x) and g2(x) respectively represent coefficient matrix functions of the input vector and the disturbance vector;
Rs, Ls, ψf, p, Jm, and B respectively represent a stator resistance, an inductance, a rotor permanent magnet flux, number of pole pairs, a moment of inertia, and a friction coefficient of the permanent magnet synchronous motor;
then, the voltage control quantity u(t) of the permanent magnet synchronous motor is obtained by minimizing an expression of the value function as a target for solving.

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Nonlinear predictive position control method suitable for biaxial permanent magnet servo system

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Nonlinear predictive position control method suitable for biaxial permanent magnet servo system

Life of this patent

Abstract

Claims5