US 2025/0052251 A1 · AVIATION COMPRESSOR ACTIVE STABILIZATION CONTROL METHOD BASED ON DISTURBANCE OBSERVATION AND COMPENSATION

Abstract

The present invention belongs to the field of aviation compressor control, and relates to an aviation compressor active stabilization control method based on disturbance observation and compensation. Modeling errors and external disturbances of models used in design of a controller are observed, and sub-controllers are individually designed for state variables of interest to compensate for the disturbances, thus to simultaneously solve the problems of rotating stall and surge of an aviation compressor in a variety of complex situations. Partial differential model of the compressor is converted to an ordinary differential equation by Galerkin projection method, partial differential characteristics of the compressor are reserved in the form of disturbances during conversion, and an active stabilization controller of the aviation compressor is designed in combination with disturbance observation and compensation technology, thus to ensure that the models used in the design of the controller have higher accuracy, high robustness and high reliability.

An aviation compressor active stabilization control method based on disturbance observation and compensation, comprising the following steps:

step 1:
establishing aviation compressor partial differential mathematical models containing external disturbances;
l
c
⁢
Φ
.
=
-
Ψ
+
1
2
⁢
π
⁢
∫
0
2
⁢
π
⁢
Ψ
c
(
Φ
+
∂
φ
^
∂
η
❘
"\[RightBracketingBar]"
η
=
0
)
⁢
d
⁢
θ
+
d
φ
(
1
)
Ψ
.
=
1
4
⁢
B
2
⁢
l
c
⁢
(
Φ
-
Φ
T
(
Ψ
,
u
)
)
+
d
ψ
(
2
)
Ψ
=
Ψ
c
(
Φ
+
∂
φ
^
∂
η
❘
"\[RightBracketingBar]"
η
=
0
)
-
l
c
⁢
Φ
.
-
m
⁢
∂
φ
^
∂
t
❘
"\[RightBracketingBar]"
η
=
0
-
1
2
⁢
a
⁢
(
2
⁢
∂
2
φ
^
∂
η
⁢
∂
t
❘
"\[RightBracketingBar]"
η
=
0
+
∂
2
φ
^
∂
η
⁢
∂
θ
❘
"\[RightBracketingBar]"
η
=
0
)
+
d
φ
^
(
3
)
wherein Φ represents an annulus averaged flow coefficient for flowing through a compressor, Ψ represents an annulus averaged pressure rise coefficient of the compressor, {circumflex over (φ)} represents a disturbance velocity potential in a flow channel of the compressor, which is a function of a compressor circumferential angle θ, a compressor axial distance η and time t, and the above are parameters describing an operating state of the compressor;
Φ represents a derivative of the annulus averaged flow coefficient Φ, and {dot over (Ψ)} represents a derivative of the annulus averaged pressure rise coefficient Ψ;
dφ, dψ, d{circumflex over (φ)} and d represent bounded external disturbances subjected by the compressor, wherein dφ represents an external disturbance affecting the annulus averaged flow coefficient Φ, dψ represents an external disturbance affecting the annulus averaged pressure rise coefficient Ψ, both of which are functions of the time t, and d{circumflex over (φ)} represents an external disturbance affecting the disturbance velocity potential {circumflex over (φ)}, is a function of the time t and the angle θ, and satisfies that dφ(t)=(½π)∫02πd{circumflex over (φ)}(t, θ)dθ;
ΦT(Ψ, u) represents a characteristic of a throttle, which is expressed by the following formula:
Φ
T
(
Ψ
,
u
)
=
(
u
+
1
)
⁢
γ
⁢
Ψ
(
4
)
wherein u represents an input of a compressor system, and γ represents a positive constant of an inherent parameter of the throttle;
Ψc(x) represents a mapping relationship function of compressor characteristics, which is written as a cubic polynomial of an independent variable x:
Ψ
c
(
x
)
=
Ψ
c
⁢
0
+
H
⁡
(
1
+
3
2
⁢
(
x
W
-
1
)
-
1
2
⁢
(
x
W
-
1
)
3
)
(
5
)
wherein Ψc0 represents an ordinate intercept of the cubic function Ψc (x), H represents half of a height between two extremums of the cubic function, W represents half of a horizontal distance between the two extremums of the cubic function, and a shape of a specific compressor characteristic line can be determined through the parameters;
in formulas (1)-(3), lc is a parameter representing an equivalent total length of the compressor, α is a parameter representing an averaged lag of a compressor blade air flow, B is a Greitzer-B parameter used for representing a current rotating speed of the compressor, m is a parameter representing a length of a compressor outlet pipe, and the above parameters are all related to compressor size and design performance;
step 2:
establishing aviation compressor ordinary differential models containing disturbances by a Galerkin projection method;
first, the disturbance velocity potential {circumflex over (φ)} in the flow channel of the compressor is rewritten into a series form by Fourier transform, and the first N terms are reserved as follows:
φ
^
=
∑
k
=
1
N
⁢
1
k
⁢
e
k
⁢
η
⁢
A
k
⁢
sin
⁡
(
k
⁢
θ
+
r
k
)
wherein Ak represents an amplitude of Fourier series of the kth term, and rk represents a phase angle of Fourier series of the kth term;
the kth order disturbance mode Jk and a total disturbance mode J defining the disturbance velocity potential of the compressor are as follows:
J
k
=
A
k
2
W
2
,
J
=
∑
k
=
1
N
⁢
J
k
corresponding compressor models are obtained as follows:
J
.
k
=
3
⁢
aHk
(
k
+
ma
)
⁢
W
⁢
J
k
(
1
-
(
Φ
W
-
1
)
2
-
1
4
⁢
J
k
)
+
d
1
⁢
k
,
k
=
1
,
2
,
…
,
N
(
6
)
Φ
.
=
H
l
c
⁢
(
(
-
Ψ
+
Ψ
c
⁢
0
)
H
+
1
+
3
2
⁢
(
Φ
W
-
1
)
⁢
(
1
-
1
2
⁢
J
)
-
1
2
⁢
(
Φ
W
-
1
)
3
)
+
d
2
(
7
)
Ψ
.
=
1
4
⁢
B
2
⁢
l
c
⁢
(
Φ
-
Φ
T
)
+
d
3
(
8
)
wherein {dot over (J)}k represents a derivative of the kth order disturbance mode Jk, and {dot over (Φ)} and {dot over (Ψ)} have the same meaning as defined in formulas (1)-(3);
d1k(k=1,2, . . . , N), d2 and d3 represent total disturbances of the models, which are defined respectively as:
d
1
⁢
k
=
d
jk
+
d
φ
^
⁢
k
d
2
=
d
Φ
+
d
φ
l
c
d
3
=
d
ψ
wherein dJk represents a modeling error affecting the kth order disturbance mode, and dΦ represents a modeling error affecting the annulus averaged flow coefficient Φ;
d{circumflex over (φ)}k, dφ, and dψ are parameters representing the external disturbances subjected by the compressor system, which are described by formulas (1)-(3);
d{circumflex over (φ)}k represents the kth order component of the disturbance d{circumflex over (φ)}, which is calculated by the following formula:
d
φ
^
⁢
k
=
2
⁢
ak
k
+
ma
⁢
1
2
⁢
π
⁢
∫
0
2
⁢
π
d
φ
^
⁢
sin
⁢
ζ
k
⁢
d
⁢
ζ
k
wherein ξk=kθ+rk;
step 3:
establishing aviation compressor models after coordinate transform;
the following coordinate transform is selected:
Φ
s
=
Φ
-
2
⁢
W
,
Ψ
s
=
Ψ
-
Ψ
c
⁢
0
-
2
⁢
H
,
u
^
=
2
⁢
W
-
Φ
T
wherein Φs is an annulus averaged flow coefficient after coordinate transform, Ψs is a pressure rise coefficient after coordinate transform, and û is a compressor input after coordinate transform;
H, W and Ψc0 are compressor characteristics related parameters;
transformed aviation compressor models are obtained by the above coordinate transform:
J
.
k
=
3
⁢
aHk
(
k
+
ma
)
⁢
W
⁢
J
k
(
1
-
(
Φ
s
W
+
1
)
2
-
1
4
⁢
J
k
)
+
d
1
⁢
k
,
k
=
1
,
2
,
…
,
N
(
9
)
Φ
.
s
=
H
l
c
⁢
(
-
Ψ
s
H
-
1
+
3
2
⁢
(
Φ
s
W
+
1
)
⁢
(
1
-
1
2
⁢
J
)
-
1
2
⁢
(
Φ
s
W
+
1
)
3
)
+
d
2
(
10
)
Ψ
.
s
=
1
4
⁢
B
2
⁢
l
c
⁢
(
Φ
s
+
u
^
)
+
d
3
(
11
)
step 4:
establishing disturbance observers for d2 and d3;
Φ
~
.
s
=
-
1
l
c
⁢
Ψ
s
+
d
s
+
d
~
2
+
k
o
⁢
11
(
Φ
~
s
-
Φ
s
)
(
12
)
d
~
.
2
=
k
o
⁢
12
(
Φ
~
s
-
Φ
s
)
Ψ
~
.
s
=
1
4
⁢
B
2
⁢
l
c
⁢
(
Φ
s
+
u
^
)
+
d
~
3
+
k
o
⁢
21
(
Ψ
~
s
-
Ψ
s
)
d
~
.
3
=
k
o
⁢
22
(
Ψ
~
s
-
Ψ
s
)
wherein {tilde over (Φ)}S is an estimated value of the annulus averaged flow coefficient Φ s, and {tilde over ({dot over (Φ)})}s represents a derivative thereof;
{tilde over (Ψ)}s is an estimated value of the annulus averaged pressure rise coefficient Ψs, and {tilde over ({dot over (Ψ)})}s represents a derivative thereof, {tilde over (d)}2 is an estimated value of the total disturbance d2 of the system, and {tilde over ({dot over (d)})}2 represents a derivative thereof, {tilde over (d)}3 is an estimated value of the total disturbance d3 of the system, and {tilde over ({dot over (d)})}3 represents a derivative thereof;
ko11, ko12, ko21 and ko22 are observer parameters, which need to be selected artificially, and the selection of the parameters needs to ensure that an observer matrix:
A
o
=
[
k
o
⁢
11
1
0
0
k
o
⁢
12
0
0
0
0
0
k
o
⁢
21
1
0
0
k
o
⁢
22
0
]
is a Hurwitz matrix;
ds is a nonlinear term, which is defined as:
d
s
=
H
l
c
⁢
(
-
1
+
3
2
⁢
(
Φ
s
W
+
1
)
⁢
(
1
-
1
2
⁢
J
)
-
1
2
⁢
(
Φ
s
W
+
1
)
3
)
step 5:
establishing a sub-controller of the disturbance mode J;
Φ
^
s
=
Φ
set
-
2
⁢
W
+
k
1
⁢
J
(
13
)
wherein Φset is a set expected annulus averaged flow coefficient of the compressor;
{circumflex over (Φ)}s is a virtual control signal, which is also an expected tracking signal of the annulus averaged flow coefficient;
k1 is a controller parameter;
step 6:
establishing a sub-controller of the annulus averaged flow coefficient;
first, a virtual tracking error between the annulus averaged flow coefficient and the expected signal is calculated according to the sub-controller (13) of the disturbance mode designed in step 5:
e
1
=
Φ
s
-
Φ
^
s
(
14
)
then the sub-controller of the annulus averaged flow coefficient is written as:
Ψ
^
s
=
l
c
(
k
2
⁢
e
1
+
d
s
+
d
~
2
)
(
15
)
wherein {circumflex over (Ψ)}s is a virtual control signal, which is also an expected tracking signal of the annulus averaged pressure rise coefficient;
k2 is a controller parameter;
step 7:
establishing a sub-controller of the annulus averaged pressure rise coefficient;
first, a virtual tracking error between the annulus averaged pressure rise coefficient and the expected signal is calculated according to the sub-controller (15) of the disturbance mode designed in step 6:
e
2
=
Ψ
s
-
Ψ
^
s
(
16
)
then the sub-controller of the annulus averaged pressure rise coefficient is written as:
u
^
=
4
⁢
B
2
⁢
l
c
(
k
2
⁢
e
1
+
k
3
⁢
e
2
+
l
c
⁢
d
.
s
)
-
Φ
s
-
4
⁢
B
2
⁢
l
c
⁢
d
~
3
(
17
)
wherein û is a virtual control input of the compressor system, which is defined in step 3;
k3 is a controller parameter;
{dot over (d)}s represents a derivative of a nonlinear term ds, which is calculated by a numerical differentiator;
step 8:
calculating an actual control input;
the virtual control input u is calculated according to the sub-controllers (13), (15) and (17) as well as the virtual tracking errors (14) and (16);
an expression of the actual control input u is obtained according to the definition of the virtual control input û in step 3:
u
=
(
(
2
⁢
W
-
u
^
)
)
/
(
γ
⁢
Ψ
)
-
1
(
18
)
step 9:
selecting the controller parameters;
the controller parameters k1, k2 and k3 are required to satisfy that:
(1) k1>0;
(2) a control matrix
A
c
=
[
-
k
2
-
1
/
l
c
k
2
k
3
]
is a Hurwitz matrix.

1,025 more elements

Aviation compressor active stabilization control method based on disturbance observation and compensation

Life of this patent

Aviation compressor active stabilization control method based on disturbance observation and compensation

Life of this patent

Abstract

Claims1