US 2026/0202848 A1 · Fixed-Time Sliding Mode Control Method and System for Tiltrotor Unmanned Aerial Vehicles with Prescribed Performance

Abstract

The present invention relates to the technical field of unmanned aerial vehicle flight control, and proposes a fixed-time sliding mode control method and system for tiltrotor unmanned aerial vehicles with prescribed performance. The method includes: constructing the motion model of the tiltrotor unmanned aerial vehicle; constructing a transformed error based on a prescribed performance function; designing a fixed-time nonsingular terminal sliding mode surface combined with adaptive gain; combining the control model with the nonsingular terminal sliding mode surface based on the motion model to construct a control law, and controlling the tiltrotor unmanned aerial vehicle based on the control law. The present invention solves the singularity problem existing in the prior art and accelerates the convergence speed.

A fixed-time sliding mode control method for a tiltrotor unmanned aerial vehicle with prescribed performance, characterized by comprising the following steps:

constructing a motion model of the tiltrotor unmanned aerial vehicle;
constructing a transformed error based on the prescribed performance function;
designing a fixed-time nonsingular terminal sliding mode surface with adaptive gain;
based on the motion model, combining a control model with the nonsingular terminal sliding mode surface, constructing a control law, and controlling the tiltrotor unmanned aerial vehicle based on the control law;
wherein the step of constructing the transformed error based on the prescribed performance function includes:
designing tracking error and its boundary based on the prescribed performance function;
designing an error transformation function to convert the tracking error into an unconstrained error that is not restricted by the initial boundary of the prescribed performance function;
constructing the control model based on the unconstrained error;
wherein the error transformation function is expressed as follows:
Ψ
⁡
(
ε
)
=
γ
2
⁢
exp
⁡
(
ε
)
-
γ
1
⁢
exp
⁡
(
-
ε
)
exp
⁡
(
ε
)
+
exp
⁡
(
-
ε
)
=
γ
3
⁢
tanh
⁡
(
ϑ
⁢
e
⁡
(
t
)
ρ
⁡
(
t
)
)
γ
1
=
1
2
⁢
(
δ
-
1
)
⁢
sign
⁡
(
e
⁡
(
0
)
)
+
1
2
⁢
(
δ
+
1
)
γ
2
=
1
2
⁢
(
1
-
δ
)
⁢
sign
⁡
(
e
⁡
(
0
)
)
+
1
2
⁢
(
δ
+
1
)
γ
3
=
{
γ
2
,
e
⁡
(
t
)
≥
0
γ
1
,
e
⁡
(
t
)
<
0
where sign(⋅) is a signum function, 0<δ≤1, e(0) is an initial tracking error;
E is a transformed error, P is a constant greater than 1, e(t) is the tracking error, ρ(t) is the fixed-time prescribed performance function;
wherein the step of designing the fixed-time sliding mode surface combined with adaptive gain includes:
defining a fixed-time sliding mode surface containing control parameters and state variables;
introducing a nonsingular terminal sliding mode function, and introducing adaptive gain control into the derivative of the sliding mode surface to obtain a nonsingular terminal sliding mode surface;
the expression of the sliding mode surface s is as follows:
s
=
ε
+
k
1
⁢
s
⁢
i
⁢
g
α
1
(
ε
)
+
k
2
⁢
s
⁢
i
⁢
g
α
2
(
ε
˙
)
{
α
1
=
1
2
+
σ
1
2
+
sign
⁡
(
1
-
❘
"\[LeftBracketingBar]"
x
❘
"\[RightBracketingBar]"
)
⁢
(
1
2
-
σ
1
2
)
α
2
=
σ
2
s
⁢
i
⁢
g
⁢
n
⁡
(
1
-
❘
"\[LeftBracketingBar]"
x
❘
"\[RightBracketingBar]"
)
si
⁢
g
y
(
x
)
=
❘
"\[LeftBracketingBar]"
x
❘
"\[RightBracketingBar]"
y
⁢
sign
⁡
(
x
)
where k1>0, k2>0, α1 and α2 are control parameters to be designed;
wherein the expression for the derivative of the sliding mode surface is as follows:
s
.
=
-
l
ˆ
1
⁢
sign
⁡
(
s
)
-
l
2
⁢
sign
β
1
(
s
)
-
l
3
⁢
sign
β
2
(
s
)
l
^
.
1
=
ϑ
1
⁢
❘
"\[LeftBracketingBar]"
s
❘
"\[RightBracketingBar]"
-
ϑ
2
⁢
l
ˆ
1
where {circumflex over (l)}1 is an adaptive control gain, l2>0, l3>0,
β
1
=
n
1
si
⁢
gn
⁡
(
❘
"\[LeftBracketingBar]"
s
❘
"\[RightBracketingBar]"
-
1
)
,
β
2
=
n
2
s
⁢
i
⁢
g
⁢
n
⁡
(
1
-
❘
"\[LeftBracketingBar]"
s
❘
"\[RightBracketingBar]"
)
,
n1>1, 0<n2<1, ϑ1>0 and ϑ2>0.

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Fixed-Time Sliding Mode Control Method and System for Tiltrotor Unmanned Aerial Vehicles with Prescribed Performance

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Fixed-Time Sliding Mode Control Method and System for Tiltrotor Unmanned Aerial Vehicles with Prescribed Performance

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Abstract

Claims8