US 12,088,224 B2 · Finite time speed control method for permanent magnet synchronous motor based on fast integral terminal sliding mode and disturbance estimation

Abstract

A finite time speed control method for a permanent magnet synchronous motor (PMSM) based on a fast integral terminal sliding mode and disturbance estimation comprises: firstly, determining a mathematical model of a speed loop of the PMSM under the influence of system parameters uncertainty and unknown load torque; secondly, designing an improved fast integral terminal sliding surface on the basis of the idea of terminal sliding mode control; then, proposing a disturbance estimation method based on an adaptive fuzzy system with respect to the disturbance in a PMSM system; designing a PMSM speed controller on this basis; and finally, completing the concrete implementation of the whole technical solution. The present invention designs the fast integral terminal sliding surface and a sliding mode control law to ensure that a motor speed tracking error converges to zero within finite time and enhances the rapidity of a PMSM speed regulating system.

A finite time speed control method for a permanent magnet synchronous motor (PMSM) based on a fast integral terminal sliding mode and disturbance estimation, comprising the following steps:

S1:
determining a mathematical model of a speed loop of the PMSM under a influence of system parameters uncertainty and unknown load torque;
in a d−q coordinate system, a mathematical model of a speed loop of a non-salient pole permanent magnet synchronous motor is:
ω
.
=
K
t
J
⁢
i
q
-
B
J
⁢
ω
-
T
L
J
where ω is motor speed;
iq represents stator current of q axis;
Kt is a torque constant;
J represents a moment of inertia;
B is a viscous friction coefficient;
and TL represents a load torque;
considering the influence of system parameters uncertainty, unknown load torque and current loop tracking error, the mathematical model of the speed loop of the PMSM is:
ω
.
=
K
t
J
n
⁢
i
q
*
-
B
o
+
Δ
⁢
B
J
n
+
Δ
⁢
J
⁢
ω
+
(
K
t
J
-
K
t
J
n
)
⁢
i
q
-
T
L
J
+
K
t
J
n
⁢
(
i
q
-
i
q
*
)
in a formula, Bo and Jn represent nominal values of a viscous friction coefficient and the moment of inertia respectively;
ΔB=B−Bo and ΔJ=J−Jn represent deviations between true values and the nominal values of the viscous friction coefficient and the moment of inertia;
iq* represents a reference value of the stator current of the q axis, a PMSM speed controller to be designed;
after processing the mathematical model of the speed loop of the PMSM which considers the system disturbance, obtaining:
{dot over (ω)}=aiq*+d
in the formula, d(t) represents a lumped disturbance term;
α is a known constant coefficient;
S2:
constructing a fast integral terminal sliding surface:
firstly, defining a speed tracking error:
e=ω−ωd, where ωd represents motor target speed;
then, designing the fast integral terminal sliding surface as:
s=e+α∫0tedσ+β∫0teq/pdσ;
where α, β>0 which are constant coefficients;
0<q/p<1;
and q and p are positive odd numbers;
when the tracking error of the motor speed converges to a sliding surface, s=0,
e=−α∫0tedσ−β∫0teq/pdσ;
solving a above equation to obtain time for a tracking error of the motor speed to converge to zero from reaching the sliding surface:
t
s
=
p
α
⁡
(
p
-
q
)
⁢
(
ln
[
α
⁢
e
⁡
(
0
)
(
p
-
q
)
/
p
+
β
]
-
ln
⁢
β
)
S3:
conducting disturbance estimation on the lumped disturbance term based on an adaptive fuzzy system:
estimating a lumped disturbance term d(t) defined in step S1 by the fuzzy system, and according to a universal approximation theorem of the fuzzy system, an optimal fuzzy system ΦT H(x) exists, so that:
d=ΦTH(x)+ε
in the formula, Φ=[ϕ1,ϕ2, . . . ,ϕr]T is a weight vector at optimal approximation, and r is the number of fuzzy rules;
ε represents an estimation error which satisfies |ε|<ρ;
ρ>0 is a positive constant;
the value of ε can be infinitely reduced by increasing the number of the fuzzy rules;
x=[x1,x2, . . . ,xn]T is an input vector of the fuzzy system, and n is the number of fuzzy inputs;
selecting a fast integral terminal sliding surface and a speed tracking error as the inputs of the fuzzy system, x=[s,e]T, with H(x)=[h1(x),h2(x), . . . ,hr((x))]T representing a fuzzy basis function vector, and:
h
i
(
x
)
=
∏
k
=
1
n
μ
A
k
i
(
x
k
)
∏
i
=
1
r
[
∏
k
=
1
n
μ
A
k
i
(
x
k
)
]
,
i
=
1
,
…
,
r
where μAkl(xk) represents a membership function value of a fuzzy variable;
since a weight vector Φ in optimal approximation cannot be obtained directly, estimating Φ;
making {circumflex over (Φ)} represent the estimated value of Φ;
and based on an adaptive theory, designing a online adaptive weight adjustment rate of the fuzzy system as:
{circumflex over (Φ)}=ΓH(x)s
where Γ∈Rr×r is a positive definite symmetric matrix;
s represents a fast integral terminal sliding surface constructed in step S2;
after obtaining the estimated value {circumflex over (Φ)} of Φ according to the above adaptive weight adjustment rate, using {circumflex over (Φ)}T H(x) to estimate the lumped disturbance term d(t) online;
S4:
designing the PMSM speed controller:
designing a following form of PMSM speed controller based on steps S2 and S3:
i
q
*
=
1
a
[
ω
.
d
-
Φ
^
T
⁢
H
⁡
(
x
)
-
α
⁢
e
-
β
⁢
e
q
/
p
-
k
1
⁢
s
-
k
2
⁢
sign
⁡
(
s
)
]
in the formula, k1 and k2 are positive adjustable control gains;
k2>l+ρ;
l>0 is a upper bound of {tilde over (Φ)}T H(x), |{tilde over (Φ)}T H(x)|<l;
{tilde over (Φ)}=Φ−{circumflex over (Φ)} represents a weight estimation error vector;
and sign(s) represents a signum function;
based on the above PMSM speed controller, making the speed tracking error converge to the sliding surface in time to, with to satisfying a following relational expression:
t
o
≤
1
λ
⁢
❘
"\[LeftBracketingBar]"
s
⁡
(
0
)
❘
"\[RightBracketingBar]"
in a formula, λ=k2−ρ−l, which represents a constant coefficient;
and s(0) represents the value of the fast integral terminal sliding surface s constructed in step S2 at time of 0;
S5:
specifically realizing a technical solution:
5.1) firstly, measuring the motor speed ω in real time through a sensor installed in the PMSM, and after obtaining a motor speed signal ω, making a difference between the signal and the motor target speed ωd to obtain a speed tracking error e;
after obtaining e, further obtaining the value of the fast integral terminal sliding surface s;
and meanwhile, based on step S3, obtaining a disturbance estimation value {circumflex over (Φ)}T H(x) outputted by the adaptive fuzzy system;
5.2) secondly, substituting a speed tracking error e, the fast integral terminal sliding surface s and the disturbance estimation value {circumflex over (Φ)}T H(x) into the PMSM speed controller given in step S4, and using the controller as a speed loop controller under a PMSM vector control frame to generate a reference value iq* of stator current of the q axis;
5.3) in a current loop, obtaining a voltage in the d−q coordinate system according to the input stator current reference value using a classical PI controller, obtaining a voltage signal in a static coordinate system through inverse Park transformation, generating a corresponding duty cycle, and obtaining a switch signal of a three-phase inverter;
outputting PMSM three-phase stator voltage by the three-phase inverter, and then controlling the motor speed to track the target speed to realize the whole permanent magnet synchronous motor speed regulation process.

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Finite time speed control method for permanent magnet synchronous motor based on fast integral terminal sliding mode and disturbance estimation

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Finite time speed control method for permanent magnet synchronous motor based on fast integral terminal sliding mode and disturbance estimation

Life of this patent

Abstract

Claims2