CN114578696A - Self-adaptive neural network quantitative fault-tolerant control method for 2-DOF helicopter system - Google Patents

Self-adaptive neural network quantitative fault-tolerant control method for 2-DOF helicopter system Download PDF

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CN114578696A
CN114578696A CN202210209856.4A CN202210209856A CN114578696A CN 114578696 A CN114578696 A CN 114578696A CN 202210209856 A CN202210209856 A CN 202210209856A CN 114578696 A CN114578696 A CN 114578696A
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赵志甲
张健
邹涛
李致富
马鸽
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Guangzhou University
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Abstract

The invention relates to the technical field of helicopter system control, in particular to a 2-DOF helicopter system self-adaptive neural network quantitative fault-tolerant control method, which comprises the following steps: step 1: establishing a dynamic model of the 2-DOF helicopter system; step 2: reducing chatter in the quantized signal using a hysteresis quantizer; designing an auxiliary system to compensate for the effects of unknown dead zones and actuator faults; approximating the system by using a radial basis function neural network; and constructing a system equation; and step 3: constructing a Lyapunov equation; and 4, step 4: constructing a controller and an adaptive law of the system according to a Lyapunov equation; and 5: according to the Lyapunov equation, a system controller and an adaptive law, the stability of the 2-DOF helicopter system is proved; step 6: and (5) simulating and sorting results. The invention enables better helicopter system control.

Description

Self-adaptive neural network quantitative fault-tolerant control method for 2-DOF helicopter system
Technical Field
The invention relates to the technical field of helicopter system control, in particular to a 2-DOF helicopter system adaptive neural network quantitative fault-tolerant control method.
Background
Compared with a fixed wing unmanned plane, the unmanned helicopter can perform special operations such as transverse flight, vertical takeoff or hovering. The advantages of unmanned helicopters are of increasing interest to researchers and have been successfully used in many areas. However, the dynamic model of the unmanned helicopter is very complex and has the characteristics of nonlinearity, strong coupling, system instability and the like. In addition, input constraints from non-smooth actuators can also be imposed during flight, which adds difficulty to the analysis and design of their controllers.
In order to control helicopter systems with stability, researchers have proposed many control methods, including linearizing the nonlinear model of the helicopter before control, and designing the controller directly on the nonlinear model for which the system parameters are known. However, these methods only consider the design of helicopter flight controllers under the most ideal conditions, and in practical situations, the helicopter system is an unknown uncertain nonlinear system, and none of the above methods is applicable. In addition, in practical situations, the helicopter is inevitably affected by actuator faults and unknown dead zones, and meanwhile, the transmission of signals inside the helicopter is also affected by jitter of signals caused by overlarge communication pressure, and the influence of the factors can make the helicopter system unstable.
Disclosure of Invention
It is an object of the present invention to provide a method for adaptive neural network quantization fault-tolerant control of a 2-DOF helicopter system that overcomes some or all of the deficiencies of the prior art.
The invention discloses a 2-DOF helicopter system adaptive neural network quantitative fault-tolerant control method, which comprises the following steps of:
step 1: establishing a dynamic model of the 2-DOF helicopter system;
and 2, step: reducing chatter in the quantized signal using a hysteresis quantizer; designing an auxiliary system to compensate for the effects of unknown dead zones and actuator faults; approximating the system by using a radial basis function neural network; and constructing a system equation;
and step 3: constructing a Lyapunov equation;
and 4, step 4: constructing a controller and an adaptive law of the system according to a Lyapunov equation;
and 5: according to the Lyapunov equation, a system controller and an adaptive law, the stability of the 2-DOF helicopter system is proved;
step 6: and (5) simulating and sorting results.
Preferably, in step 1, according to the lagrangian mechanical model, the nonlinear dynamical equation of the system is as follows:
Figure BDA0003530527220000021
Figure BDA0003530527220000022
wherein, JpAnd JyExpressed as moments of inertia, V, about the pitch and yaw axes, respectivelypAnd VyRepresenting the input voltages of the two motors, M representing the mass of the helicopter, laRepresenting the centroid distance from the origin of the fixed frame of the fuselage, theta representing the pitch angle, phi representing the yaw angle, KppRepresenting the torque thrust gain acting on the pitch axis in the pitch propeller, KpyRepresenting the torque thrust gain on the pitch axis in the yaw-rotor, KyyRepresenting the torque thrust gain acting on the yaw axis in the yaw propeller, KypRepresenting the torque thrust gain acting on the yaw axis in the pitching propellers, DpAnd DyRepresents a viscous friction coefficient;
definition q ═ q1,q2]T，q1＝[θ,φ]TAnd
Figure BDA0003530527220000023
considering the uncertainty in the system, the nonlinear 2-DOF helicopter system model is:
Figure BDA0003530527220000024
Figure BDA0003530527220000025
y＝q1(5)
wherein q, q1,q2Respectively, system variable, output angle variable and angular speed variable, wherein delta A (q) and delta B (q) represent uncertain items obtained by the system,
Figure BDA0003530527220000026
respectively representing the derivative of the angular variable and the derivative of the angular velocity variable, u ═ Vp,Vy]TRepresents a control input to the system; a (q) and B (q) are gain matrices for the system, respectively:
Figure BDA0003530527220000031
Figure BDA0003530527220000032
g represents the gravitational acceleration.
Preferably, in step 2, the actuator faults include a gain fault and a bias fault, which are collectively described as follows:
Figure BDA0003530527220000036
wherein u isf(t) represents an actuator fault input,
Figure BDA0003530527220000033
represents a significant factor, ζ (t) represents an unknown bounded signal;
the dead zone expression is as follows:
Figure BDA0003530527220000034
where u (t) represents the output of the dead zone, D () represents the sign of the dead zone, v (t) represents the input of the dead zone, ψ > 0, bl＞0、br> 0 all represent unknown parameters of the dead zone;
the dead zone equation (9) is rewritten as:
D(v(t))＝ψv(t)+χ(v(t)) (10)
wherein the content of the first and second substances,
Figure BDA0003530527220000035
χ denotes the dead zone term, the dead zone parameter ψ is bounded, and therefore, call (9) has:
|χ(v(t))|≤χ* (11)
wherein χ ═ max { ψ bl,-ψbr}；
To reduce the communication burden, the signal needs to be quantized, and to avoid jitter during the quantization of the signal, a lag quantizer is introduced, so the input to the dead zone can be expressed as:
v(t)＝Q(τ)
where v (t) is the input of the dead zone, Q (τ) represents the hysteresis quantizer, τ represents the signal to be quantized;
then, quantization is defined as:
Figure BDA0003530527220000041
wherein, taui＝ρ1-iτmin,(i＝1,2,…),
Figure BDA0003530527220000042
τminQuantization density is more than 0, and rho is more than 0 and less than 1; q (tau) ∈ U { (0, ±. tau)i,±τi(1+δ),i＝1,2,…}，τminRepresenting a quantized dead zone size; q (t)-) Represents the state at the time before Q (τ);
furthermore, the hysteresis quantizer may also be expressed as:
Q(τ)＝G(τ)τ(t)+T(t) (12)
wherein G (tau) is more than 1-delta and less than 1+ delta, and | T (t) | is less than or equal to tauminAre gain functions, G (τ) represents an unknown gain, τ (t) represents the signal to be quantized, δ represents a quantization parameter;
considering (8), (10) and (12), rewrite as:
Figure BDA0003530527220000043
definition of
Figure BDA0003530527220000044
Figure BDA0003530527220000045
Is an unknown positive integer because
Figure BDA0003530527220000046
ψ is an unknown positive integer, which has:
Figure BDA0003530527220000047
wherein A (q), B (q) denote the gain matrix of the system, Δ A (q), Δ B (q) denote the uncertainty terms in the system,
Figure BDA0003530527220000051
is an unknown positive integer that is not known,
Figure BDA0003530527220000052
representing the significance factor, ζ (T) representing the unknown bounded signal, T gain function, ψ representing the dead zone parameter, χ representing the dead zone term;
since the inverse of the gain matrix B may not exist, τ ═ B is introducedT(q) v, wherein v is an expected control signal; then, a system equation is obtained
Figure BDA0003530527220000053
As follows:
Figure BDA0003530527220000054
wherein γ is a design parameter;
Figure BDA0003530527220000055
an unknown equation is represented as a function of,
Figure BDA0003530527220000056
also represents an unknown equation;
because ζ (t) represents the unknown bounded signal and | χ (v (t) | ≦ χ ≦ xi, we derive | xi ≦ xi |fWherein xi isfRepresents an unknown positive integer;
in addition, a radial basis function neural network is introduced to estimate Q (Q, v) in the system, and therefore, the following equation is derived:
Q(q,ν)＝Ψ*TD(X)+∈(X)
therein, Ψ*TRank of ideal weight of the neural network, D (X) represents neuron activation function, e (X) represents approximation error of the neural network, and an unknown normal number e exists*Making | < ∈ | < ∈ |)*。
Preferably, in step 3, according to the content given in step 1, a lyapunov function equation is constructed:
Figure BDA0003530527220000057
Figure BDA0003530527220000058
Figure BDA0003530527220000059
wherein the content of the first and second substances,
Figure BDA00035305272200000510
represents an unknown positive integer that is not a positive integer,
Figure BDA00035305272200000511
the weight error of the radial basis function neural network,
Figure BDA00035305272200000512
and
Figure BDA00035305272200000513
denotes the constant error, z1＝q1-qdRepresenting angular tracking error, q1Angle variable representing system output, qdRepresenting the desired trajectory, z2＝q2- α represents the derivative of the tracking error, q2Variable of angular velocity representing the output of the system, alpha representing a virtual controller, lambda1And λ2Representing a design parameter; v1、V2、V3Both represent lyapunov equations.
Preferably, in step 4, the virtual controller is:
Figure BDA0003530527220000061
wherein k is1Representing a gain diagonal matrix, z1The error in the angle is represented by an angular error,
Figure BDA0003530527220000062
a derivative representing the desired trajectory;
the controller is as follows:
Figure BDA0003530527220000063
Figure BDA0003530527220000064
where, v is the desired controller,
Figure BDA0003530527220000065
and
Figure BDA0003530527220000066
represents an estimated value of a constant, A (q), B (q) represents a gain matrix of the system,
Figure BDA0003530527220000067
a rank representing an estimated weight value of the radial basis function neural network, γ representing a design parameter, δ representing a quantization parameter,
Figure BDA0003530527220000068
representing a hyperbolic tangent function, d1Representing a small positive integer.
The adaptive law is:
Figure BDA0003530527220000069
Figure BDA00035305272200000610
Figure BDA00035305272200000611
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00035305272200000612
the adaptation law of a neural network is represented,
Figure BDA00035305272200000613
and
Figure BDA00035305272200000614
an adaptation law representing a constant; Γ denotes a diagonal matrix, λ1、λ2、σ1、σ2、σ3Representing design parameters in the system, all of which are positive numbers;
Figure BDA00035305272200000615
weights representing radial basis function neural network estimates, D (X) represents a function representing neuron activation,
Figure BDA00035305272200000617
indicating the rank of the rotation of the angular velocity error.
Preferably, in step 5, V is first aligned2And (3) carrying out derivation:
Figure BDA00035305272200000616
then to V3Taking the derivative, we can get:
Figure BDA0003530527220000071
and (17) is substituted into the formula to obtain:
Figure BDA0003530527220000072
the following inequality is derived:
Figure BDA0003530527220000073
and obtaining the following result according to the Young inequality:
Figure BDA0003530527220000074
wherein ξ1And xi2Are all constants, | | Ψ*| | represents the norm of the radial basis function neural network;
substituting (19) and (20) into (18) yields:
Figure BDA0003530527220000075
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003530527220000076
Figure BDA0003530527220000077
furthermore, the following inequality is derived:
Figure BDA0003530527220000081
Figure BDA0003530527220000082
when the above inequality satisfies the condition, it proves V3Is semi-globally stable.
The invention considers the comprehensive effect of actuator faults and an unknown dead zone 2-DOF helicopter system, and designs an auxiliary system to process the coupling effect in order to eliminate the nonlinearity caused by the actuator faults and the unknown dead zone coupling. Furthermore, a hysteresis quantizer is also introduced to reduce the jitter of the quantized signal. Meanwhile, coupling effects of quantized signals, actuator faults and unknown dead zones are comprehensively considered, and a reasonable controller is designed. The control method considers uncertainty, unknown dead zones and actuator faults in the actual 2-DOF helicopter system, can be applied to the actual helicopter system, and has certain practical value.
Drawings
FIG. 1 is a flow chart of a method for adaptive neural network quantization fault-tolerant control of a 2-DOF helicopter system in embodiment 1;
FIG. 2 is a model sketch of a 2-DOF helicopter in example 1.
FIG. 3: the angle of the pitch angle of the 2-DOF helicopter tracks the locus diagram of the expected angle;
FIG. 4: the 2-DOF helicopter yaw angle tracks a trajectory diagram of a desired angle;
FIG. 5: tracking the trajectory diagram of the expected angle by the angular velocity of the pitch angle of the 2-DOF helicopter;
FIG. 6: the angular velocity of the 2-DOF helicopter yaw angle tracks the trajectory diagram of the desired angle;
FIG. 7 is a schematic view of: 2-DOF helicopter angle error trajectory tracking response diagram;
FIG. 8: a control input to the 2-DOF helicopter system.
Detailed Description
For a further understanding of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples. It is to be understood that the examples are illustrative of the invention and not limiting.
Example 1
As shown in fig. 1, the present embodiment provides a method for quantitatively controlling fault tolerance of an adaptive neural network of a 2-DOF helicopter system, which includes the following steps:
step 1: establishing a dynamic model of the 2-DOF helicopter system;
in step 1, according to a Lagrange mechanical model, a nonlinear dynamical equation of the system is as follows:
Figure BDA0003530527220000091
Figure BDA0003530527220000092
wherein, JpAnd JyExpressed as moments of inertia, V, about the pitch and yaw axes, respectivelypAnd VyRepresenting the input voltages of two motors, M representing the mass of the helicopter, laRepresenting the centroid distance from the origin of the fixed frame of the fuselage, theta representing the pitch angle, phi representing the yaw angle, KppIndicating effects in pitching propellersTorque thrust gain on pitch axis, KypRepresenting the torque thrust gain on the pitch axis in the yaw-rotor, KyyRepresenting the torque thrust gain acting on the yaw axis in the yaw propeller, KypRepresenting the torque thrust gain acting on the yaw axis in the pitching propellers, DpAnd DyRepresents a viscous friction coefficient;
definition q ═ q1,q2]T，q1＝[θ,φ]TAnd
Figure BDA0003530527220000093
considering the uncertainty in the system, the nonlinear 2-DOF helicopter system model is:
Figure BDA0003530527220000094
Figure BDA0003530527220000095
y＝q1 (5)
wherein q, q1,q2Respectively, system variable, output angle variable and angular speed variable, wherein delta A (q) and delta B (q) represent uncertain items obtained by the system,
Figure BDA0003530527220000096
respectively representing the derivative of the angular variable and the derivative of the angular velocity variable, u ═ Vp,Vy]TRepresents a control input to the system; a (q) and B (q) are gain matrices for the system, respectively:
Figure BDA0003530527220000097
Figure BDA0003530527220000101
g represents the gravitational acceleration.
Step 2: reducing chatter in the quantized signal using a hysteresis quantizer; designing an auxiliary system to compensate for the effects of unknown dead zones and actuator faults; approximating the system by using a radial basis function neural network; constructing a system equation;
in step 2, the actuator faults include gain faults and bias faults, which are described in a unified manner as follows:
Figure BDA0003530527220000105
wherein u isf(t) represents an actuator fault input,
Figure BDA0003530527220000102
represents a significant factor, ζ (t) represents an unknown bounded signal;
the dead zone expression is as follows:
Figure BDA0003530527220000103
where u (t) represents the output of the dead zone, D () represents the sign of the dead zone, v (t) represents the input of the dead zone, ψ > 0, bl＞0、br> 0 all represent unknown parameters of the dead zone;
the dead zone equation (9) is rewritten as:
D(v(t))＝ψv(t)+χ(v(t)) (10)
wherein the content of the first and second substances,
Figure BDA0003530527220000104
χ denotes the dead zone term, the dead zone parameter ψ is bounded, and therefore, call (9) has:
|χ(v(t))|≤χ* (11)
wherein χ ═ max { ψ bl,-ψbr}；
To reduce the communication burden, the signal needs to be quantized, and to avoid jitter during the quantization of the signal, a lag quantizer is introduced, so the input to the dead zone can be expressed as:
v(t)＝Q(τ)
where v (t) is the input of the dead zone, Q (τ) represents the hysteresis quantizer, τ represents the signal to be quantized;
then, quantization is defined as:
Figure BDA0003530527220000111
wherein, taui＝ρ1-iτmin,(i＝1,2,…),
Figure BDA0003530527220000112
τminQuantization density is more than 0, and rho is more than 0 and less than 1; q (tau) ∈ U { (0, ±. tau)i,±τi(1+δ),i＝1,2,…}，τminRepresenting a quantized dead zone size; q (t)-) Represents the state at the time before Q (τ);
furthermore, the hysteresis quantizer may also be expressed as:
Q(τ)＝G(τ)τ(t)+T(t) (12)
wherein G (tau) is more than 1-delta and less than 1+ delta, and | T (t) | is less than or equal to tauminAre gain functions, G (τ) represents an unknown gain, τ (t) represents the signal to be quantized, δ represents a quantization parameter;
considering (8), (10) and (12), rewrite as:
Figure BDA0003530527220000113
definition of
Figure BDA0003530527220000114
Figure BDA0003530527220000115
Is an unknown positive integer because
Figure BDA0003530527220000116
ψ is an unknown positive integer, which has:
Figure BDA0003530527220000117
wherein A (q), B (q) represent the gain matrix of the system, Δ A (q), Δ B (q) represent the uncertainty term in the system,
Figure BDA0003530527220000118
is an unknown positive integer that is not known,
Figure BDA0003530527220000119
representing the significance factor, ζ (T) representing the unknown bounded signal, T gain function, ψ representing the dead zone parameter, χ representing the dead zone term;
since the inverse of the gain matrix B may not exist, τ ═ B is introducedT(q) v, wherein v is an expected control signal; then, a system equation is obtained
Figure BDA0003530527220000121
As follows:
Figure BDA0003530527220000122
wherein γ is a design parameter;
Figure BDA0003530527220000123
an unknown equation is represented as a function of,
Figure BDA0003530527220000124
also represents an unknown equation;
because ζ (t) represents the unknown bounded signal and | χ (v (t) | ≦ χ ≦ xi, we derive | xi ≦ xi |fWherein xi isfRepresents an unknown positive integer;
in addition, a radial basis function neural network is introduced to estimate Q (Q, v) in the system, and therefore, the following equation is derived:
Q(q,ν)＝Ψ*TD(X)+∈(X)
therein, Ψ*TRank of ideal weight of the neural network, D (X) represents neuron activation function, e (X) represents approximation error of the neural network, and an unknown normal number e exists*Making | < ∈ | < ∈ |)*。
And 3, step 3: constructing a Lyapunov equation;
in step 3, according to the content given in step 1, a Lyapunov function equation is constructed:
Figure BDA0003530527220000125
Figure BDA0003530527220000126
Figure BDA0003530527220000127
wherein the content of the first and second substances,
Figure BDA0003530527220000128
represents an unknown positive integer that is not a positive integer,
Figure BDA0003530527220000129
the weight error of the radial basis function neural network,
Figure BDA00035305272200001210
and
Figure BDA00035305272200001211
denotes the constant error, z1＝q1-qdRepresenting angular tracking error, q1Angle variable representing system output, qdRepresenting the desired trajectory, z2＝q2- α represents the derivative of the tracking error, q2Variable of angular velocity representing the output of the system, alpha representing a virtual controller, lambda1And λ2Representing a design parameter; v1、V2、V3Both represent lyapunov equations.
And 4, step 4: constructing a controller and an adaptive law of the system according to a Lyapunov equation;
in step 4, the virtual controller is:
Figure BDA0003530527220000131
wherein k is1Representing a gain diagonal matrix, z1The error in the angle is represented by an angular error,
Figure BDA0003530527220000132
a derivative representing the desired trajectory;
the controller is as follows:
Figure BDA0003530527220000133
Figure BDA0003530527220000134
where, v is the desired controller,
Figure BDA0003530527220000135
and
Figure BDA0003530527220000136
represents an estimated value of a constant, A (q), B (q) represents a gain matrix of the system,
Figure BDA0003530527220000137
a rank representing an estimated weight value of the radial basis function neural network, γ representing a design parameter, δ representing a quantization parameter,
Figure BDA0003530527220000138
representing a hyperbolic tangent function, d1Representing a small positive integer.
The adaptive law is:
Figure BDA0003530527220000139
Figure BDA00035305272200001310
Figure BDA00035305272200001311
wherein the content of the first and second substances,
Figure BDA00035305272200001312
the adaptation law of a neural network is represented,
Figure BDA00035305272200001313
and
Figure BDA00035305272200001314
an adaptation law representing a constant; Γ denotes a diagonal matrix, λ1、λ2、σ1、σ2、σ3Representing design parameters in the system, all of which are positive numbers;
Figure BDA00035305272200001315
weights representing radial basis function neural network estimates, D (X) represents a function representing neuron activation,
Figure BDA00035305272200001316
indicating the rank of the rotation of the angular velocity error.
And 5: according to the Lyapunov equation, a system controller and an adaptive law, the stability of the 2-DOF helicopter system is proved;
in step 5, V is first aligned2And (3) carrying out derivation:
Figure BDA00035305272200001317
then to V3Derivation, we can obtain:
Figure BDA0003530527220000141
and (17) is substituted into the formula to obtain:
Figure BDA0003530527220000142
the following inequality is derived:
Figure BDA0003530527220000143
and obtaining the following result according to the Young inequality:
Figure BDA0003530527220000144
wherein ξ1And xi2Are all constants, | | Ψ*| | represents the norm of the radial basis function neural network;
substituting (19) and (20) into (18) yields:
Figure BDA0003530527220000145
wherein the content of the first and second substances,
Figure BDA0003530527220000146
Figure BDA0003530527220000147
furthermore, the following inequality is derived:
Figure BDA0003530527220000151
Figure BDA0003530527220000152
when the above inequality satisfies the condition, it proves V3Is semi-globally stable.
Step 6: and (5) simulating and sorting results.
The embodiment discloses an adaptive neural quantitative fault-tolerant control method for a 2-DOF helicopter system with unknown dead zones and actuator faults. The method achieves asymptotic attitude adjustment and tracking of the desired set point and trajectory. First, a hysteresis quantizer is used to reduce chattering in the quantized signal. To resolve the uncertainty in a nonlinear helicopter system, it is approximated using a radial basis function neural network. In addition, an auxiliary system is designed to compensate for the effects of unknown dead band and actuator faults. On the basis of a neural network and an auxiliary system, a self-adaptive neural network quantitative fault-tolerant control strategy is designed for a nonlinear 2-DOF helicopter system. The signal of the closed loop system was then demonstrated to be semi-globally uniform and bounded by rigorous Lyapunov stability analysis. Finally, the effectiveness and the reasonability of the control strategy are proved on MATLAB simulation software.
FIG. 2 is a schematic representation of a model of a 2-DOF helicopter in which Yaw is the Pitch angle, Pitch is the Yaw angle, X, Y, Z are the X, Y and Z axes, respectively, FpIs the thrust generated by the front motor, FyIs the thrust generated by the rear motor. FRONT and BACK denote FRONT and rear motors, respectively. Fig. 3 and 4 are schematic views of pitch and yaw angles, respectively, tracking a desired trajectory during control of helicopter motion. Fig. 5 and 6 are schematic diagrams of the angular velocities of the pitch and yaw angles, respectively, and the desired trajectory during control of the helicopter, from which it can also be seen that the angular velocities also track completely to the desired trajectory. FIG. 7Indicating the tracking error in pitch and yaw angle that occurs during the tracking of the desired trajectory. Fig. 8 shows the inputs to the control system. From the simulation results, the control method provided by the invention has certain superiority in controlling a 2-DOF helicopter system.
The present invention and its embodiments have been described above schematically, without limitation, and what is shown in the drawings is only one of the embodiments of the present invention, and the actual structure is not limited thereto. Therefore, if the person skilled in the art receives the teaching, without departing from the spirit of the invention, the person skilled in the art shall not inventively design the similar structural modes and embodiments to the technical solution, but shall fall within the scope of the invention.

Claims (6)

  1. The self-adaptive neural network quantitative fault-tolerant control method of the 2-DOF helicopter system is characterized by comprising the following steps of: the method comprises the following steps:
    step 1: establishing a dynamic model of the 2-DOF helicopter system;
    step 2: reducing chatter in the quantized signal using a hysteresis quantizer; designing an auxiliary system to compensate for the effects of unknown dead zones and actuator faults; approximating the system by using a radial basis function neural network; and constructing a system equation;
    and step 3: constructing a Lyapunov equation;
    and 4, step 4: constructing a controller and an adaptive law of the system according to a Lyapunov equation;
    and 5: according to the Lyapunov equation, a system controller and an adaptive law, the stability of the 2-DOF helicopter system is proved;
    step 6: and (5) simulating and sorting results.
  2. 2. The 2-DOF helicopter system adaptive neural network quantitative fault-tolerant control method of claim 1, characterized in that: in step 1, according to a Lagrange mechanical model, a nonlinear dynamical equation of the system is as follows:
    Figure FDA0003530527210000011
    Figure FDA0003530527210000012
    wherein, JpAnd JyExpressed as moments of inertia, V, about the pitch and yaw axes, respectivelypAnd VyRepresenting the input voltages of two motors, M representing the mass of the helicopter, laRepresenting the centroid distance from the origin of the fixed frame of the fuselage, theta representing the pitch angle, phi representing the yaw angle, KppRepresenting the torque thrust gain on the pitch axis in the pitch propeller, KpyRepresenting the torque thrust gain on the pitch axis in the yaw-rotor, KyyRepresenting the torque thrust gain acting on the yaw axis in the yaw propeller, KypRepresenting the torque thrust gain acting on the yaw axis in the pitching propellers, DpAnd DyRepresents a viscous friction coefficient;
    definition q ═ q1,q2]T，q1＝[θ,φ]TAnd
    Figure FDA0003530527210000013
    considering the uncertainty in the system, the nonlinear 2-DOF helicopter system model is:
    Figure FDA0003530527210000014
    Figure FDA0003530527210000021
    y＝q1 (5)
    wherein, q1,q2Respectively a system variable, an output angle variable and an angular velocity variable, wherein delta A (q) and delta B (q) represent uncertain items obtained by the system,
    Figure FDA0003530527210000022
    respectively representing the derivative of the angular variable and the derivative of the angular velocity variable, u ═ Vp,Vy]TRepresents a control input to the system; a (q) and B (q) are gain matrices for the system, respectively:
    Figure FDA0003530527210000023
    Figure FDA0003530527210000024
    g represents the gravitational acceleration.
  3. 3. The 2-DOF helicopter system adaptive neural network quantitative fault-tolerant control method of claim 2, characterized by: in step 2, the actuator faults include gain faults and bias faults, which are described in a unified manner as follows:
    Figure FDA0003530527210000026
    wherein u isf(t) represents an actuator fault input,
    Figure FDA0003530527210000027
    represents a significant factor, ζ (t) represents an unknown bounded signal;
    the dead zone expression is as follows:
    Figure FDA0003530527210000025
    where u (t) represents the output of the dead zone, D () represents the dead zone symbol, v (t) represents the input of the dead zone, ψ>0、bl>0、br>0 represents the unknown parameter of the dead zone;
    the dead zone equation (9) is rewritten as:
    D(v(t))＝ψv(t)+χ(v(t)) (10)
    wherein the content of the first and second substances,
    Figure FDA0003530527210000031
    χ denotes the dead zone term, the dead zone parameter ψ is bounded, and therefore, call (9) has:
    |χ(v(t))|≤χ* (11)
    wherein χ ═ max { ψ bl,-ψbr}；
    To reduce the communication burden, the signal needs to be quantized, and to avoid jitter during the quantization of the signal, a lag quantizer is introduced, so the input to the dead zone can be expressed as:
    v(t)＝Q(τ)
    where v (t) is the input of the dead zone, Q (τ) represents the hysteresis quantizer, τ represents the signal to be quantized;
    then, quantization is defined as:
    Figure FDA0003530527210000032
    wherein, taui＝ρ1-iτmin,(i＝1,2,…),
    Figure FDA0003530527210000033
    τmin>0，0<ρ<1 represents the quantization density; q (tau) ∈ U { (0, ±. tau)i,±τi(1+δ),i＝1,2,…}，τminRepresenting a quantized dead zone size; q (t)-) Represents the state at the time before Q (τ);
    furthermore, the hysteresis quantizer can also be expressed as:
    Q(τ)＝G(τ)τ(t)+T(t) (12)
    wherein, 1-delta<G(τ)<Tau is less than or equal to 1+ delta and | T (t) |minAre all gain functions, G (tau) representing an unknown increaseT (t) represents the signal to be quantized, δ represents a quantization parameter;
    considering (8), (10) and (12), rewrite as:
    Figure FDA0003530527210000041
    definition of
    Figure FDA0003530527210000042
    Figure FDA0003530527210000043
    Is an unknown positive integer because
    Figure FDA0003530527210000044
    ψ is an unknown positive integer, which has:
    Figure FDA0003530527210000045
    wherein A (q), B (q) denote the gain matrix of the system, Δ A (q), Δ B (q) denote the uncertainty terms in the system,
    Figure FDA0003530527210000046
    is an unknown positive integer that is not known,
    Figure FDA0003530527210000047
    representing the significance factor, ζ (T) representing the unknown bounded signal, T gain function, ψ representing the dead zone parameter, χ representing the dead zone term;
    since the inverse of the gain matrix B may not exist, τ ═ B is introducedT(q) v, wherein v is a desired control signal; then, a system equation is obtained
    Figure FDA0003530527210000048
    As follows:
    Figure FDA0003530527210000049
    wherein γ is a design parameter;
    Figure FDA00035305272100000410
    an unknown equation is represented as a function of,
    Figure FDA00035305272100000411
    also represents an unknown equation;
    because ζ (t) represents the unknown bounded signal and | χ (v (t) | ≦ χ ≦ xi, we derive | xi ≦ xi |fWherein xi isfRepresents an unknown positive integer;
    in addition, a radial basis function neural network is introduced to estimate Q (Q, v) in the system, and therefore, the following equation is derived:
    Q(q,ν)＝Ψ*TD(X)+∈(X)
    therein, Ψ*TRank of ideal weight of the neural network, D (X) represents neuron activation function, e (X) represents approximation error of the neural network, and an unknown normal number e exists*Making | < ∈ | < ∈ |)*。
  4. 4. The 2-DOF helicopter system adaptive neural network quantitative fault-tolerant control method of claim 3, characterized in that: in step 3, according to the content given in step 1, a Lyapunov function equation is constructed:
    Figure FDA00035305272100000412
    Figure FDA00035305272100000413
    Figure FDA0003530527210000051
    wherein, the first and the second end of the pipe are connected with each other,
    Figure FDA0003530527210000052
    represents an unknown positive integer that is not a positive integer,
    Figure FDA0003530527210000053
    the weight error of the radial basis function neural network,
    Figure FDA0003530527210000054
    and
    Figure FDA0003530527210000055
    denotes the constant error, z1＝q1-qdRepresenting angular tracking error, q1Angle variable representing system output, qdRepresenting the desired trajectory, z2＝q2- α represents the derivative of the tracking error, q2The angular velocity variable representing the output of the system, alpha representing the virtual controller, lambda1And λ2Representing a design parameter; v1、V2、V3Both represent lyapunov equations.
  5. 5. The 2-DOF helicopter system adaptive neural network quantitative fault-tolerant control method of claim 4, characterized in that: in step 4, the virtual controller is:
    Figure FDA0003530527210000056
    wherein k is1Representing a gain diagonal matrix, z1The error in the angle is represented by an angular error,
    Figure FDA0003530527210000057
    a derivative representing the desired trajectory;
    the controller is as follows:
    Figure FDA0003530527210000058
    Figure FDA0003530527210000059
    where, v is the desired controller,
    Figure FDA00035305272100000510
    and
    Figure FDA00035305272100000511
    represents an estimated value of a constant, A (q), B (q) represents a gain matrix of the system,
    Figure FDA00035305272100000512
    a rank representing an estimated weight value of the radial basis function neural network, γ representing a design parameter, δ representing a quantization parameter,
    Figure FDA00035305272100000513
    representing a hyperbolic tangent function, d1Represents a small positive integer;
    the adaptive law is:
    Figure FDA00035305272100000514
    Figure FDA00035305272100000515
    Figure FDA00035305272100000516
    wherein，
    Figure FDA00035305272100000517
    Represents the adaptation law of a neural network,
    Figure FDA00035305272100000518
    and
    Figure FDA00035305272100000519
    an adaptation law representing a constant; Γ denotes a diagonal matrix, λ1、λ2、σ1、σ2、σ3Representing design parameters in the system, all of which are positive numbers;
    Figure FDA00035305272100000520
    weights representing radial basis function neural network estimates, D (X) represents a function representing neuron activation,
    Figure FDA0003530527210000061
    indicating the rank of the rotation of the angular velocity error.
  6. 6. The 2-DOF helicopter system adaptive neural network quantitative fault-tolerant control method of claim 5, characterized in that: in step 5, V is first aligned2And (3) carrying out derivation:
    Figure FDA0003530527210000062
    then to V3Taking the derivative, we can get:
    Figure FDA0003530527210000063
    and (17) is substituted into the formula to obtain:
    Figure FDA0003530527210000064
    the following inequality is derived:
    Figure FDA0003530527210000065
    and obtaining the following result according to the Young inequality:
    Figure FDA0003530527210000066
    wherein ξ1And xi2Are all constants, | | Ψ*| | represents the norm of the radial basis function neural network;
    substituting (19) and (20) into (18) yields:
    Figure FDA0003530527210000071
    wherein the content of the first and second substances,
    Figure FDA0003530527210000072
    Figure FDA0003530527210000073
    furthermore, the following inequality is derived:
    Figure FDA0003530527210000074
    Figure FDA0003530527210000075
    when the above inequality satisfies the condition, it proves V3Is semi-globally stable.
CN202210209856.4A 2022-03-03 2022-03-03 Self-adaptive neural network quantitative fault-tolerant control method for 2-DOF helicopter system Pending CN114578696A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116909136A (en) * 2023-06-21 2023-10-20 山东大学 2-DOF helicopter sliding mode control method and system based on determined learning
CN116909136B (en) * 2023-06-21 2023-12-26 山东大学 2-DOF helicopter sliding mode control method and system based on determined learning

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