CN113961010A - Four-rotor plant protection unmanned aerial vehicle tracking control method based on anti-saturation finite time self-adaptive neural network fault-tolerant technology - Google Patents

Four-rotor plant protection unmanned aerial vehicle tracking control method based on anti-saturation finite time self-adaptive neural network fault-tolerant technology Download PDF

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CN113961010A
CN113961010A CN202110987581.2A CN202110987581A CN113961010A CN 113961010 A CN113961010 A CN 113961010A CN 202110987581 A CN202110987581 A CN 202110987581A CN 113961010 A CN113961010 A CN 113961010A
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neural network
aerial vehicle
unmanned aerial
plant protection
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CN113961010B (en
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王儒敬
刘康
张洁
董士风
李�瑞
刘海云
焦林
黄子良
滕越
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Hefei Institutes of Physical Science of CAS
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    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
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Abstract

The invention relates to a four-rotor plant protection unmanned aerial vehicle tracking control method based on an anti-saturation finite time self-adaptive neural network fault-tolerant technology, and compared with the prior art, the four-rotor plant protection unmanned aerial vehicle tracking control method overcomes the defect that the four-rotor plant protection unmanned aerial vehicle is difficult to realize high-precision tracking control. The invention comprises the following steps: setting and storing expected track data; acquiring and storing real-time track data; establishing a four-rotor-wing plant protection unmanned aerial vehicle composite mathematical model; establishing a flight error mathematical model of the four-rotor plant protection unmanned aerial vehicle; designing a saturation compensation system and storing data; designing and storing data of adaptive neural network parameters; designing a fault-tolerant tracking controller based on an anti-saturation finite time self-adaptive neural network and storing a control signal; updating real-time track data; and adjusting parameter values in the position system and the attitude system. The method can ensure that the track tracking error of the four-rotor plant protection unmanned aerial vehicle is converged in a limited time range.

Description

Four-rotor plant protection unmanned aerial vehicle tracking control method based on anti-saturation finite time self-adaptive neural network fault-tolerant technology
Technical Field
The invention relates to the technical field of control of a four-rotor plant protection unmanned aerial vehicle, in particular to a four-rotor plant protection unmanned aerial vehicle tracking control method based on an anti-saturation finite time self-adaptive neural network fault-tolerant technology.
Background
In recent years, the unmanned aerial vehicle has been widely applied to the field of modern agriculture due to the advantages of flexible movement, convenient operation, simple structure, strong terrain adaptability and the like. Compare in traditional manual fertilization, four rotor plant protection unmanned aerial vehicle have avoided influencing healthyly because of manual operation is improper through remote control's mode. Simultaneously, four rotor plant protection unmanned aerial vehicle are fit for the crops of large tracts of land and spout the medicine process, have improved work efficiency, have reduced intensity of labour, are favorable to realizing the accurate prevention and control of plant diseases and insect pests, promote agricultural economy's rapid growth.
In order to guarantee the efficient and accurate operation of the quad-rotor plant protection unmanned aerial vehicle, one of the main difficulties to be faced is how to realize the high-precision trajectory tracking of the unmanned aerial vehicle. However, there are many practical difficulties in designing a high performance trajectory tracking controller: firstly, the unmanned aerial vehicle platform has the characteristics of under-actuation, strong coupling, high nonlinearity and the like, and the designed controller is required to have good decoupling property and strong robustness; secondly, as the application scenes of the unmanned aerial vehicle are mostly outdoor environments, the unmanned aerial vehicle is very easily influenced by external time-varying wind disturbance, and a designed controller is required to have strong anti-interference performance; in addition, when the unmanned aerial vehicle flies for a long time, the actuator is easy to break down and input to be saturated, and the designed controller is required to have good fault tolerance performance and anti-saturation capacity. However, considering the above issues together increases the design difficulty and complexity of the controller.
At present, a lot of research works are carried out on the problem of trajectory tracking control of a four-rotor plant protection unmanned aerial vehicle by many scientific researchers, and the research works mainly comprise a linear control method and a nonlinear control method. Among them, the most common linear control methods are the Probabilistic Integral Derivative (PID), Linear Quadratic Regulator (LQR) and H-infinity control, which are basically thought of as firstly linearizing an unmanned aerial vehicle model at a balance point and then designing a linear controller based on the linear model. Therefore, the linear control method has low dependence degree on the model, simple design and strong practicability. However, when the unmanned aerial vehicle is performing a large operation flight mission, the control parameters of the linear control method are easy to change suddenly, resulting in a reduction in control accuracy.
In recent years, with the development of computer technology and control theory, some advanced nonlinear control methods are proposed to improve the tracking control performance of the unmanned aerial vehicle, mainly including a backstepping method, a synovial membrane control, a neural network control, an adaptive control and the like. The backstepping method can well inhibit disturbance or uncertainty in a nonlinear system and has strong robustness. However, in the reverse-estimation process, the virtual control input needs to be differentiated continuously, which easily causes the problem of "exponential explosion" and increases the calculation load. The sliding film control is a nonlinear control method with strong robustness, high response speed and simple design, but the actual output signal is easy to generate jitter, so that the track tracking quality is reduced.
To address this problem, some researchers have proposed using bounded layer techniques to replace discrete items in the controller. However, these methods reduce the tracking control accuracy of the system. The neural network control is particularly suitable for a complex nonlinear system which needs to consider a plurality of uncertain factors simultaneously by virtue of strong online approximation capability. The neural network weight is generally required to be adjusted on line by combining with a self-adaptive algorithm, so that the on-line calculation time and the calculation pressure of the control algorithm are greatly increased, and the requirement of the fast maneuvering flight task of the quad-rotor plant protection unmanned aerial vehicle is difficult to meet. In addition, it is very important to realize convergence of tracking errors in a limited time range in practical applications, and the convergence time is determined only by control parameters and is independent of the tracking initial state, so that it is very critical to design a limited time tracking controller.
Disclosure of Invention
The invention aims to solve the defect that the four-rotor plant protection unmanned aerial vehicle in the prior art is difficult to realize tracking control, and provides a four-rotor plant protection unmanned aerial vehicle tracking control method based on an anti-saturation finite time adaptive neural network fault-tolerant technology to solve the problems.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a four-rotor plant protection unmanned aerial vehicle tracking control method based on an anti-saturation finite time adaptive neural network fault-tolerant technology comprises the following steps:
setting and storing of the expected trajectory data: according to flight mission requirements executed by the quad-rotor plant protection unmanned aerial vehicle, inputting expected trajectory data through a ground terminal; receiving expected trajectory data input by a ground terminal through an airborne network module, and storing the expected trajectory data in a flight data memory I;
acquiring and storing real-time track data: real-time track data are collected through a position sensor and an attitude sensor carried by the quad-rotor plant protection unmanned aerial vehicle, and the collected real-time track data are stored in a flight data storage II;
four rotor plant protection unmanned aerial vehicle composite mathematical model's establishment: establishing a complete composite mathematical model of the four-rotor plant protection unmanned aerial vehicle according to the inherent mechanical characteristics of the four-rotor plant protection unmanned aerial vehicle and interference factors of actuator faults and input saturation during flying so as to timely change wind disturbance;
four rotor plant protection unmanned aerial vehicle flight error mathematical model's establishment: establishing a flight error mathematical model of the four-rotor-wing plant protection unmanned aerial vehicle based on the four-rotor-wing plant protection unmanned aerial vehicle composite mathematical model;
design and data storage of saturation compensation system: designing a saturation compensation system based on a flight error mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and updating and storing signal data of the saturation compensation system into a flight data memory III;
design and data storage of adaptive neural network parameters: designing adaptive neural network parameters based on a flight error mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and updating and storing data of the adaptive neural network parameters into a flight data memory IV;
designing a fault-tolerant tracking controller based on an anti-saturation finite time adaptive neural network and storing control signals: designing a fault-tolerant tracking controller based on an anti-saturation finite time adaptive neural network based on a flight error mathematical model and a saturation compensation system of the quad-rotor plant protection unmanned aerial vehicle, and updating and storing data of a fault-tolerant tracking control signal based on the anti-saturation finite time adaptive neural network into a flight data storage V;
updating real-time track data: inputting a fault-tolerant tracking control signal based on an anti-saturation finite time adaptive neural network into a complete composite mathematical model of the four-rotor plant protection unmanned aerial vehicle, outputting real-time trajectory data and storing the real-time trajectory data into a flight data storage II;
adjusting the numerical value of the position system parameter: design parameters and control parameters in a position system are adjusted by monitoring data change of a saturation compensation signal, data change of self-adaptive neural network parameters and difference value change of expected track data and actual track data, so that tracking control of the quad-rotor plant protection unmanned aerial vehicle is realized.
The establishment of the four-rotor plant protection unmanned aerial vehicle composite mathematical model comprises the following steps:
based on a coordinate system conversion method, a position kinematics mathematical model and an attitude kinematics mathematical model of the four-rotor plant protection unmanned aerial vehicle are established, and specific expressions are respectively as follows:
Figure BDA0003231235130000031
wherein, P ═ x, y, z]TAnd
Figure BDA0003231235130000032
respectively represent Euclidean position vectors and Euler angle vectors of the quadrotor plant protection unmanned aerial vehicle in an earth coordinate system, wherein x, y and z respectively represent the Euclidean position vectors in xaAxis, yaAxis and zaPosition coordinates on the axis, phi, theta and
Figure BDA0003231235130000033
respectively represent a winding xaTransverse rocking angle degree of shaft, winding yaPitch angle of shaft and winding zaDegree of yaw angle of the shaft, V ═ u, V, w]TAnd Ω ═ p, q, r]TRespectively represent a linear velocity vector and an angular velocity vector of the four-rotor plant protection unmanned aerial vehicle in a body coordinate system, wherein u, v and w respectively represent xbAxis, ybAxis and zbLinear speed on axis, p, q and r representing respectively the winding xbYaw rate, wind y of shaftbPitch angular velocity of the shaft and wind zbThe yaw rate of the shaft is such that,
Figure BDA0003231235130000041
and
Figure BDA0003231235130000042
respectively represents the linear velocity vector and the angular velocity vector of the four-rotor plant protection unmanned aerial vehicle in the terrestrial coordinate system, wherein
Figure BDA0003231235130000043
And
Figure BDA0003231235130000044
are respectively represented at xaAxis, yaAxis and zaThe linear velocity on the shaft is,
Figure BDA0003231235130000045
and
Figure BDA0003231235130000046
respectively represent a winding xaYaw rate, wind y of shaftaPitch angular velocity of the shaft and wind zaYaw rate of the shaft, RtAnd RsIndividual watchAn orthogonal matrix and an Euler matrix are shown, and specific expressions are respectively shown as follows:
Figure BDA0003231235130000047
Figure BDA0003231235130000048
by utilizing an Euler Lagrange modeling method, considering the self mechanical structure characteristics of the four-rotor plant protection unmanned aerial vehicle and the influence of external time-varying wind disturbance received during flight, a position dynamics mathematical model and an attitude dynamics mathematical model of the four-rotor plant protection unmanned aerial vehicle are established, and the specific expressions are respectively as follows:
Figure BDA0003231235130000049
wherein, Ir＝diag(Ix,Iy,Iz) Representing a positive definite moment of inertia matrix, wherein Ix、IyAnd IzRespectively represents the rotational inertia coefficients around the x axis, the y axis and the z axis, m represents the self mass of the four-rotor plant protection unmanned aerial vehicle,
Figure BDA00032312351300000410
and
Figure BDA00032312351300000411
respectively representing the linear acceleration vector and the angular acceleration vector of the four-rotor plant protection unmanned aerial vehicle in a body coordinate system, wherein,
Figure BDA00032312351300000412
and
Figure BDA00032312351300000413
are respectively represented at xbAxis, ybAxis and zbThe linear acceleration on the axis of the shaft,
Figure BDA00032312351300000414
and
Figure BDA00032312351300000415
respectively represent a winding xbYaw angular acceleration, about y, of the shaftbPitch angular acceleration of the shaft and about zbYaw angular acceleration of the shaft;
Fs＝[0,0,uo,1]Tand Ts＝[uo,2,uo,3,uo,4]TThe lift force and the control moment are respectively represented,
wherein u iso,iSpecific calculation expressions of (i ═ 1,2,3,4) are as follows:
Figure BDA00032312351300000416
wherein, wiAnd (i ═ 1,2,3 and 4) represents the rotating speed of the ith motor rotor, d represents the distance between the motor and the mass center of the four-rotor plant protection unmanned aerial vehicle, and c represents1And c2Representing the thrust coefficient and the torque coefficient of the propeller, FaAnd TaRespectively representing air resistance in an attitude power system and a position power system, and respectively representing the following specific expressions:
Figure BDA0003231235130000051
wherein, Kf＝diag(Kf,1,Kf,2,Kf,3) And Kt＝diag(Kt,1,Kt,2,Kt,3) Respectively representing a resistance coefficient matrix of the attitude system and a resistance coefficient matrix of the position system;
Fgthe specific expression of the system gravity is as follows:
Figure BDA0003231235130000052
wherein E ═ 0,0,1]TM represents the self mass of the four-rotor plant protection unmanned aerial vehicle, g represents the gravity acceleration,
Figure BDA0003231235130000053
is an orthogonal matrix RtInverse matrix of, TgThe gyro moment is expressed, and the specific expression is as follows:
Figure BDA0003231235130000054
wherein J represents the coefficient of inertia of each rotor,
symbol (omega)×A diagonally symmetric matrix representing an omega vector, which satisfies the following form:
Figure BDA0003231235130000055
based on kinematics mathematical model, dynamics mathematical model, position dynamics mathematical model and attitude dynamics mathematical model of a four-rotor plant protection unmanned aerial vehicle, an incomplete composite mathematical model without considering actuator errors and input saturation is established, and specific expressions are respectively as follows:
Figure BDA0003231235130000056
wherein the content of the first and second substances,
Figure BDA0003231235130000057
representing a virtual input vector of a quad-rotor plant protection unmanned aerial vehicle;
Figure BDA0003231235130000058
and
Figure BDA0003231235130000059
and
Figure BDA00032312351300000510
representing non-linearities in the position system and the attitude system respectively,
Figure BDA00032312351300000511
da＝[dx,dy,dz]Tand
Figure BDA00032312351300000512
representing lumped disturbances in the position system and the attitude system, respectively;
considering the effect of actuator error, the specific mathematical expression is as follows:
uo,i＝ρiui+ri,i＝1,2,3,4，
wherein u iso,iAnd uiRespectively representing the actual control signal and the desired control signal, piAnd riRespectively representing the significant coefficient and the additional fault;
considering the effect of actuator input saturation, the specific mathematical expression is as follows:
sat(ui)＝sign(ui)min{|ui|,umax,i},i＝1,2,3,4，
wherein u ismax,iRepresenting the control signal uiUpper bound of (c), sign function sign (u)i) Is defined as
Figure BDA0003231235130000061
Establishing a complete composite mathematical model considering actuator errors and input saturation based on an incomplete composite mathematical model, a mathematical expression of actuator errors and a mathematical expression of input saturation
Figure BDA00032312351300000611
And
Figure BDA00032312351300000612
the specific expression is as follows:
Figure BDA0003231235130000062
where ρ isb＝[ρ1,ρ2,ρ3]T，rb＝[r1,r2,r3]T
And
Figure BDA0003231235130000063
the establishment of the flight error mathematical model of the four-rotor plant protection unmanned aerial vehicle comprises the following steps:
defining a position error e1Attitude error e2Linear velocity error
Figure BDA0003231235130000064
And error of angular velocity
Figure BDA0003231235130000065
Specific mathematical expressions are respectively as follows:
e1＝P-Pd，e2＝Θ-Θd，
Figure BDA0003231235130000066
wherein, Pd＝[xd,yd,zd]TAnd
Figure BDA0003231235130000067
respectively representing a desired position signal and a desired attitude signal in a terrestrial coordinate system;
based on the defined position error e1Attitude error e2Linear velocity error
Figure BDA0003231235130000068
And error of angular velocity
Figure BDA0003231235130000069
Design ofFiltered tracking error xi for position system1Filtered tracking error xi of sum attitude system2The specific mathematical expression is as follows:
Figure BDA00032312351300000610
wherein, γ1>0 and gamma2>0 denotes the filter coefficient by increasing gamma1And gamma2The convergence rate of the tracking error can be improved;
filtered tracking error xi based on position1And the filtering tracking error xi of the attitude2And complete composite mathematical model
Figure BDA0003231235130000071
And
Figure BDA0003231235130000072
flight error mathematical model for establishing four-rotor-wing plant protection unmanned aerial vehicle
Figure BDA0003231235130000073
And
Figure BDA0003231235130000074
the specific mathematical expression is as follows:
Figure BDA0003231235130000075
wherein the content of the first and second substances,
Figure BDA0003231235130000076
and
Figure BDA0003231235130000077
representing complex non-linear variables in the position system and the pose system, respectively.
The design and data storage of the saturation compensation system comprises the following steps:
filtering tracking error xi based on position system1Filtered tracking error xi of sum attitude system2Establishing a saturation compensation system
Figure BDA0003231235130000078
And
Figure BDA0003231235130000079
the specific mathematical expression is as follows:
Figure BDA00032312351300000710
Figure BDA00032312351300000711
wherein the content of the first and second substances,
Figure BDA00032312351300000712
△U2＝Tt-sat(Tt)，K1>0 and K2>0 denotes the control parameter, upsilon, of the input-compensated auxiliary system1And upsilon2Representing the compensating auxiliary variable, p, of the input in the position system and attitude system, respectively1And ρ2Represents a positive odd number and satisfies a condition ρ1<ρ2；
Compensated auxiliary variable data v1And upsilon2Updated and saved to flight data storage III.
The design and data storage of the adaptive neural network parameters comprise the following steps:
according to s1And s2Is defined by the following inequality:
Figure BDA00032312351300000713
Figure BDA00032312351300000714
then, based on the strong approximation capability of the radial basis function neural network to the nonlinear function, the radial basis function neural network is introduced, and the specific mathematical expression is as follows:
h(Z)＝W*TΞ(Z)+δ(Z)，
wherein the content of the first and second substances,
Figure BDA00032312351300000715
and W*TXi (Z) denotes the input and output of the radial basis function neural network, respectively, n denotes the number of inputs, h (Z) denotes a nonlinear function, δ (Z) denotes an approximation error, W*An optimal weight vector is represented, which is calculated according to the following formula:
Figure BDA00032312351300000716
wherein the content of the first and second substances,
Figure BDA0003231235130000081
a weight vector representing a radial basis function neural network,
Figure BDA0003231235130000082
a gaussian basis function is represented, the specific mathematical expression of which is as follows:
Figure BDA0003231235130000083
wherein m is 1,2, …, ksum，ksumRepresenting the total neurons in the hidden layer;
Figure BDA0003231235130000084
and μ represents the center and radius of the radial basis function neural network, respectively;
approximation of a nonlinear function η using a radial basis function neural network1(Z1) And η2(Z2) The specific mathematical expression is as follows:
Figure BDA0003231235130000085
further obtaining:
Figure BDA0003231235130000086
wherein the content of the first and second substances,
Figure BDA0003231235130000087
and Ψi(Zi)＝1+Ξi(Zi) (i ═ 1,2) denote an unknown imaginary parameter and a known calculable positive scalar parameter, respectively;
designed adaptive neural network parameters
Figure BDA0003231235130000088
And
Figure BDA0003231235130000089
as follows:
Figure BDA00032312351300000810
wherein, biAnd ci(i ═ 1,2) each represent a positive design parameter;
Figure BDA00032312351300000811
is represented by betaiAn upper bound estimate of (d);
adapting neural network parameter data
Figure BDA00032312351300000812
And
Figure BDA00032312351300000813
updated and saved to the flight data memory IV.
The design and control signal storage based on the anti-saturation finite time adaptive neural network fault-tolerant tracking controller comprises the following steps:
tracking error xi based on filtering1And xi2Saturation compensation system
Figure BDA00032312351300000814
And
Figure BDA00032312351300000815
adaptive neural network parameters
Figure BDA00032312351300000816
And
Figure BDA00032312351300000817
and complete composite mathematical model
Figure BDA00032312351300000818
And
Figure BDA00032312351300000819
the design is based on an anti-saturation finite time self-adaptive neural network fault-tolerant tracking controller, and the specific mathematical expression is as follows:
Figure BDA00032312351300000820
wherein k isiAnd ai(i-1, 2) represents a positive design parameter,
since quad-rotor plant protection unmanned aerial vehicle has four inputs (u)o,1,uo,2,uo,3,uo,4)6 outputs
Figure BDA00032312351300000821
Using three virtual control input signals (q)1,q2,q3) Calculating the actual control input signal uo,1Namely:
Figure BDA0003231235130000091
in addition, the desired pitch angle φdAnd a desired yaw angle thetadThe calculation formulas of (a) and (b) are respectively as follows:
Figure RE-GDA0003373534770000092
control signal data based on anti-saturation finite time adaptive neural network fault-tolerant tracking
Figure RE-GDA0003373534770000093
And TtUpdated and saved to the flight data memory V.
The updating of the real-time trajectory data comprises the following steps:
inputting a fault-tolerant tracking control signal based on an anti-saturation finite time self-adaptive neural network into a complete composite mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and outputting a second derivative of real-time trajectory data, namely: three linear accelerations
Figure BDA0003231235130000093
And three angular accelerations
Figure BDA0003231235130000094
And storing the data into a flight data memory II;
for three linear accelerations
Figure BDA0003231235130000095
And three angular accelerations
Figure BDA0003231235130000096
And performing secondary integration to obtain real-time track data.
The adjustment of the parameter values in the position system and the attitude system comprises the following steps:
inputting the expected trajectory data, the real-time adaptive neural network parameters and the complex nonlinear variables stored in the flight data memories I, II and III into the saturation compensation system and the radial basis function neural network, and outputting new saturation compensation signals and new adaptive neural network parameters;
inputting the real-time trajectory data and the expected trajectory data stored in the flight data memories I and II, a new saturation compensation signal and a new adaptive neural network parameter into an anti-saturation finite time adaptive neural network-based fault-tolerant tracking controller, and outputting a control signal for adjusting the trajectory of the four-rotor plant protection unmanned aerial vehicle;
the control signal who will be used for adjusting four rotor plant protection unmanned aerial vehicle orbits is input into four rotor plant protection unmanned aerial vehicle's complete compound mathematical model, the second derivative of the real-time orbit data of output, promptly: three linear accelerations
Figure BDA0003231235130000097
And three angular accelerations
Figure BDA0003231235130000098
And then, carrying out second integration on the second derivative of the real-time track data to obtain new real-time track data, namely: at xaAxis, yaAxis and zaPosition coordinates on axis x, y and z, and around xaThe roll angle phi and the winding y of the shaftaPitch angle of the shaft theta and zaDegree of yaw angle of an axle
Figure BDA0003231235130000099
Updating new real-time track data, new saturation compensation signal data, new adaptive neural network parameter data and input control signals for adjusting the track of the quad-rotor plant protection unmanned aerial vehicle, and respectively storing the updated real-time track data, the new saturation compensation signal data, the new adaptive neural network parameter data and the input control signals in flight data memories II, III, IV and V;
observing changes in saturation compensation signal data in flight database III:
design parameter k in a position system1And a1The change adjustment of (2): the design parameter k is determined if the absolute value of the saturation compensation signal in the position system varies in a range of 0.2 or more1Increased by 0.5 size, and design parameter a1Until the absolute value of the saturation compensation signal in the position system changes in a range of 0.2 or less; the design parameter k is designed if the absolute value of the saturation compensation signal in the position system varies in a range of 0.2 or less1Increased by 0.3 size, and design parameter a1Until the absolute value of the saturation compensation signal in the position system changes in a range of 0.02 or less; if the absolute value of the saturation compensation signal in the position system varies in the range of 0.02 or less, the design parameter k1And a1The values are not changed, so that the performance requirement of the four-rotor plant protection unmanned aerial vehicle on input signal compensation in a position system is met;
design parameter k in attitude system2And a2The change adjustment of (2): if the absolute value of the saturation compensation signal in the attitude system varies in a range of 0.2 or more, the design parameter k2Increased by 0.5 size, and design parameter a2Until the absolute value of the saturation compensation signal in the attitude system changes in a range of less than or equal to 0.2; if the absolute value of the saturation compensation signal in the attitude system varies in a range of 0.2 or less, the design parameter k2Increased by 0.3 size, and design parameter a2Until the absolute value of the saturation compensation signal in the attitude system changes in a range of less than or equal to 0.02; if the absolute value of the saturation compensation signal in the attitude system changes in a range of 0.02 or less, the design parameter k2And a2The value of (2) is not changed, and the performance requirement of the four-rotor plant protection unmanned aerial vehicle on input signal compensation in the attitude system is met.
Observing the change of the adaptive neural network parameter data in the flight database IV:
design parameter b in location system1And c1The change adjustment of (2): design parameter b if adaptive neural network parameter values in the location system change incrementally over time1Is decreased by a value of 0.2 while designing the parameter c1Until the adaptive neural network in the location system increases by a magnitude of 0.25The value of the complex parameter monotonically decreases with time; if the adaptive neural network parameter value in the location system takes more than 25 seconds to converge to zero, the design parameter b1Is decreased by a value of 0.08 while designing the parameter c1The value of (a) is increased by 0.12 until the adaptive neural network parameter value in the position system needs less than 25 seconds to converge to near zero; design parameter b if the adaptive neural network parameter value in the location system requires less than 25 seconds to converge to near zero1Is decreased by a value of 0.04 while designing the parameter c1The value of (2) is increased according to the size of 0.06, and the adaptive neural network parameter value in the position system can not be converged to be near zero until the value is within the range of 10 seconds to 25 seconds; design parameter b if the adaptive neural network parameter values in the location system take 10 seconds to 25 seconds to converge to near zero1While the value of (c) is not changed, while the parameter c is designed1The value of (A) is increased by 0.04 until the adaptive neural network parameter value in the position system can be converged to be near zero within 10 seconds; design parameter b if the adaptive neural network parameter value in the location system converges to zero within 10 seconds1And c1The values are not changed, so that the performance requirement of the four-rotor plant protection unmanned aerial vehicle on adaptive neural network parameter convergence in a position system is met;
design parameter b in attitude system2And c2The change adjustment of (2): design parameter b if adaptive neural network parameter values in the attitude system change incrementally over time2Is decreased by a value of 0.2 while designing the parameter c2The value of (2) is increased according to the size of 0.25 until the self-adaptive neural network parameter value in the attitude system is monotonically decreased along with the time; if the adaptive neural network parameter value in the attitude system needs more than 25 seconds to converge to zero, the design parameter b2Is decreased by a value of 0.08 while designing the parameter c2The value of (2) is increased according to the size of 0.12 until the self-adaptive neural network parameter value in the attitude system needs less than 25 seconds to converge to the vicinity of zero; design parameter b if the adaptive neural network parameter value in the attitude system needs less than 25 seconds to converge to near zero2Is decreased by a value of 0.04 while designing the parameter c2The value of (2) is increased according to the size of 0.06 until the self-adaptive neural network parameter value in the attitude system can be converged to be near zero within the range of 10 seconds to 25 seconds; if the adaptive neural network parameter values in the attitude system need to converge to near zero in the range of 10 seconds to 25 seconds, the design parameter b2While the value of (c) is not changed, while the parameter c is designed2The value of (A) is increased by 0.04 until the adaptive neural network parameter value in the attitude system converges to zero within the range of 10 seconds; design parameter b if the adaptive neural network parameter values in the attitude system converge to zero within 10 seconds2And c2The values are not changed, and the performance requirement of self-adaptive neural network parameter convergence of the four-rotor plant protection unmanned aerial vehicle in the attitude system is met.
Comparing the difference value of the expected track data and the actual track data in the flight databases I and II:
control parameter gamma in position system1The change adjustment of (2): if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is greater than 1.5, the control parameter γ is then determined1Until the sum of the absolute values of the differences is less than or equal to 1.5; if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 1.5, and the control parameter gamma is1The value of (a) is increased by 0.1 until the sum of the absolute values of the differences is less than or equal to 0.1; if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 0.1, and the control parameter gamma is1The value of (a) is increased by 0.06 until the sum of the absolute values of the differences is less than or equal to 0.01; if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 0.01, and a control parameter gamma1The value of (2) is not changed, so that the performance requirement of the trajectory tracking precision of the four-rotor plant protection unmanned aerial vehicle in a position system is met;
if three desired attitude angles
Figure BDA0003231235130000121
Corresponding to the number of real-time attitude angles
Figure BDA0003231235130000122
If the sum of the absolute values of the differences is greater than 1, the control parameter gamma is set2The value of (a) is increased by 0.15 until the sum of the absolute values of the differences is less than or equal to 1; if three desired attitude angle numbers
Figure BDA0003231235130000123
Corresponding to the number of real-time attitude angles
Figure BDA0003231235130000124
The sum of the absolute values of the differences is less than or equal to 1, and the control parameter gamma is2The value of (a) is increased by 0.08 until the sum of the absolute values of the differences is less than or equal to 0.1; if three desired attitude angle numbers
Figure BDA0003231235130000125
Corresponding to the number of real-time attitude angles
Figure BDA0003231235130000126
The sum of the absolute values of the differences is less than or equal to 0.1, the control parameter gamma2The value of (A) is increased by 0.03 until the sum of the absolute values of the differences is less than or equal to 0.01; if three desired attitude angle numbers
Figure BDA0003231235130000127
Corresponding to the number of real-time attitude angles
Figure BDA0003231235130000128
The sum of the absolute values of the differences is less than or equal to 0.01, and then the control parameter gamma is2The value of (2) does not change, and this satisfies the performance requirement of four rotor plant protection unmanned aerial vehicle orbit tracking precision in attitude system.
Advantageous effects
Compared with the prior art, the four-rotor plant protection unmanned aerial vehicle tracking control method based on the anti-saturation finite time adaptive neural network fault-tolerant technology can ensure that the trajectory tracking error of the four-rotor plant protection unmanned aerial vehicle is converged in a finite time range; secondly, the method has strong robustness, good saturation resistance and actuator fault tolerance, and can realize high-performance track tracking control of the four-rotor plant protection unmanned aerial vehicle under the condition that external time-varying interference, input saturation and actuator errors simultaneously exist; meanwhile, the method can effectively reduce the online calculation quantity of the self-adaptive neural network parameters and reduce the online calculation burden.
The method can ensure that the trajectory tracking error can still be converged to a bounded range within a limited time under the influence of external disturbance, input saturation and actuator error, improves the robustness, the saturation resistance and the actuator fault-tolerant capability of a flight control system, reduces the number of self-adaptive parameters in a controller, and reduces the burden of parameter online calculation.
Drawings
FIG. 1 is a sequence diagram of the method of the present invention;
FIG. 2 is a schematic model of a quad-rotor plant protection drone according to the present invention;
FIG. 3 is a graph of the real-time three-dimensional trajectory tracking response of the present invention;
FIG. 4 is a graph of the trace-tracking response of the present invention in the x-direction;
FIG. 5 is a graph of the trajectory tracking response of the invention in the y-direction;
FIG. 6 is a graph of the z-axis trajectory tracking response of the present invention;
FIG. 7 is a roll angle trajectory tracking response graph of the present invention;
FIG. 8 is a graph of pitch trajectory tracking response of the present invention;
FIG. 9 is a yaw rate trajectory tracking response graph of the present invention;
FIG. 10 is a graph of the actual control input response of the present invention;
FIG. 11 is a graph of an adaptive neural network parameter response of the present invention.
Detailed Description
So that the manner in which the above recited features of the present invention can be understood and readily understood, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings, wherein:
as shown in fig. 1, the model of a quad-rotor plant protection unmanned aerial vehicle according to the present invention is schematically illustrated, wherein 4 identical motors (numbered as motor 1, motor 2, motor 3, and motor 4) are mounted at symmetrical positions of the unmanned aerial vehicle, and the positions and attitude motions of the unmanned aerial vehicle are controlled by adjusting the rotation speeds of the four motors. { Oa,xa,ya,zaIs the terrestrial coordinate system, { O }b,xb,yb,zbThe coordinate system of the unmanned plane is set, and d, m and g respectively represent the distance between the motor and the center of mass of the unmanned plane, and the self mass and the gravity coefficient of the four-rotor plant protection unmanned plane.
As shown in fig. 2, the method for tracking and controlling a quadrotor plant protection unmanned aerial vehicle based on an anti-saturation finite time adaptive neural network fault-tolerant technology, provided by the invention, comprises the following steps:
first, setting and storing of expected track data: according to flight mission requirements executed by the quad-rotor plant protection unmanned aerial vehicle, inputting expected trajectory data through a ground terminal; and receiving expected trajectory data input by the ground terminal through the airborne network module, and storing the expected trajectory data in the flight data memory I. Wherein the desired trajectory data comprises: desired attitude angle degrees (desired roll angle degrees, desired pitch angle degrees, and desired yaw angle degrees) and desired position coordinates (desired x-axis position coordinates, desired y-axis position coordinates, and desired z-axis position coordinates).
And secondly, acquiring and storing real-time track data: the position sensor and the attitude sensor which are carried by the quad-rotor plant protection unmanned aerial vehicle are used for collecting real-time track data, and the collected real-time track data are stored in a flight data storage II. The real-time trajectory data includes: real-time attitude angle degrees (real-time roll angle degrees, real-time pitch angle degrees, and real-time yaw angle degrees) and real-time position coordinates (real-time x-axis position coordinates, real-time y-axis position coordinates, and real-time z-axis position coordinates).
And thirdly, establishing a four-rotor plant protection unmanned aerial vehicle composite mathematical model. According to the inherent mechanical characteristics of the quad-rotor plant protection unmanned aerial vehicle and the interference factors of actuator faults and input saturation in order to timely change wind disturbance during flight, a complete composite mathematical model of the quad-rotor plant protection unmanned aerial vehicle is established. It should be particularly noted that the invention considers three factors of external disturbance, input saturation and actuator error, and considers the coupling between the attitude power system and the position power system, which not only can better reflect the flight characteristics of the quadrotor plant protection unmanned aerial vehicle under the actual condition, but also can better cope with the emergency condition encountered in the actual flight process. However, these interference factors greatly increase the design difficulty and complexity of the controller. The method comprises the following specific steps:
(1) based on a coordinate system conversion method, a position kinematics mathematical model and an attitude kinematics mathematical model of the four-rotor plant protection unmanned aerial vehicle are established, and specific expressions are respectively as follows:
Figure BDA0003231235130000141
wherein, P ═ x, y, z]TAnd
Figure BDA0003231235130000142
respectively represent Euclidean position vectors and Euler angle vectors of the quadrotor plant protection unmanned aerial vehicle in an earth coordinate system, wherein x, y and z respectively represent the Euclidean position vectors in xaAxis, yaAxis and zaPosition coordinates on the axis, phi, theta and
Figure BDA0003231235130000143
respectively represent a winding xaTransverse rocking angle degree of shaft, winding yaPitch angle of shaft and winding zaDegree of yaw angle of the shaft, V ═ u, V, w]TAnd Ω ═ p, q, r]TRespectively represent a linear velocity vector and an angular velocity vector of the four-rotor plant protection unmanned aerial vehicle in a body coordinate system, wherein u, v and w respectively represent xbAxis, ybAxis and zbLinear speed on axis, p, q and r representing respectively the winding xbYaw rate, wind y of shaftbOf shaftsPitch angle rate and wind zbThe yaw rate of the shaft is such that,
Figure BDA0003231235130000144
and
Figure BDA0003231235130000145
respectively represents the linear velocity vector and the angular velocity vector of the four-rotor plant protection unmanned aerial vehicle in the terrestrial coordinate system, wherein
Figure BDA0003231235130000146
And
Figure BDA0003231235130000147
are respectively represented at xaAxis, yaAxis and zaThe linear velocity on the shaft is,
Figure BDA0003231235130000148
and
Figure BDA0003231235130000149
respectively represent a winding xaYaw rate, wind y of shaftaPitch angular velocity of the shaft and wind zaYaw rate of the shaft, RtAnd RsRespectively representing an orthogonal matrix and an Euler matrix, wherein specific expressions are respectively as follows:
Figure BDA00032312351300001410
Figure BDA00032312351300001411
(2) by utilizing an Euler Lagrange modeling method, considering the self mechanical structure characteristics of the four-rotor plant protection unmanned aerial vehicle and the influence of external time-varying wind disturbance received during flight, a position dynamics mathematical model and an attitude dynamics mathematical model of the four-rotor plant protection unmanned aerial vehicle are established, and the specific expressions are respectively as follows:
Figure BDA0003231235130000151
wherein, Ir＝diag(Ix,Iy,Iz) Representing a positive definite moment of inertia matrix, wherein Ix、IyAnd IzRespectively represents the rotational inertia coefficients around the x axis, the y axis and the z axis, m represents the self mass of the four-rotor plant protection unmanned aerial vehicle,
Figure BDA0003231235130000152
and
Figure BDA0003231235130000153
respectively representing the linear acceleration vector and the angular acceleration vector of the four-rotor plant protection unmanned aerial vehicle in a body coordinate system, wherein,
Figure BDA0003231235130000154
and
Figure BDA0003231235130000155
are respectively represented at xbAxis, ybAxis and zbThe linear acceleration on the axis of the shaft,
Figure BDA0003231235130000156
and
Figure BDA0003231235130000157
respectively represent a winding xbYaw angular acceleration, about y, of the shaftbPitch angular acceleration of the shaft and about zbYaw angular acceleration of the shaft;
Fs＝[0,0,uo,1]Tand Ts＝[uo,2,uo,3,uo,4]TThe lift force and the control moment are respectively represented,
wherein u iso,iSpecific calculation expressions of (i ═ 1,2,3,4) are as follows:
Figure BDA0003231235130000158
wherein, wiAnd (i ═ 1,2,3 and 4) represents the rotating speed of the ith motor rotor, d represents the distance between the motor and the mass center of the four-rotor plant protection unmanned aerial vehicle, and c represents1And c2Representing the thrust coefficient and the torque coefficient of the propeller, FaAnd TaRespectively representing air resistance in an attitude power system and a position power system, and respectively representing the following specific expressions:
Figure BDA0003231235130000159
wherein, Kf＝diag(Kf,1,Kf,2,Kf,3) And Kt＝diag(Kt,1,Kt,2,Kt,3) Respectively representing a resistance coefficient matrix of the attitude system and a resistance coefficient matrix of the position system;
Fgthe specific expression of the system gravity is as follows:
Figure BDA00032312351300001510
wherein E ═ 0,0,1]TM represents the self mass of the four-rotor plant protection unmanned aerial vehicle, g represents the gravity acceleration,
Figure BDA00032312351300001511
is an orthogonal matrix RtInverse matrix of, TgThe gyro moment is expressed, and the specific expression is as follows:
Figure BDA00032312351300001512
wherein J represents the coefficient of inertia of each rotor,
symbol (omega)×A diagonally symmetric matrix representing an omega vector, which satisfies the following form:
Figure BDA0003231235130000161
(3) based on kinematics mathematical model, dynamics mathematical model, position dynamics mathematical model and attitude dynamics mathematical model of a four-rotor plant protection unmanned aerial vehicle, an incomplete composite mathematical model without considering actuator errors and input saturation is established, and specific expressions are respectively as follows:
Figure BDA0003231235130000162
wherein the content of the first and second substances,
Figure BDA0003231235130000163
representing a virtual input vector of a quad-rotor plant protection unmanned aerial vehicle;
Figure BDA0003231235130000164
and
Figure BDA0003231235130000165
and
Figure BDA0003231235130000166
representing non-linearities in the position system and the attitude system respectively,
Figure BDA0003231235130000167
da＝[dx,dy,dz]Tand
Figure BDA0003231235130000168
representing the lumped disturbances in the position system and the attitude system, respectively.
(4) Considering the effect of actuator error, the specific mathematical expression is as follows:
uo,i＝ρiui+ri,i＝1,2,3,4，
wherein u iso,iAnd uiRespectively representing the actual control signal and the desired control signal，ρiAnd riThe significant factor and the additional fault are represented separately.
(5) Considering the effect of actuator input saturation, the specific mathematical expression is as follows:
sat(ui)＝sign(ui)min{|ui|,umax,i},i＝1,2,3,4，
wherein u ismax,iRepresenting the control signal uiUpper bound of (c), sign function sign (u)i) Is defined as
Figure BDA0003231235130000169
(6) Establishing a complete composite mathematical model considering actuator errors and input saturation based on an incomplete composite mathematical model, a mathematical expression of actuator errors and a mathematical expression of input saturation
Figure BDA00032312351300001610
And
Figure BDA0003231235130000171
the specific expression is as follows:
Figure BDA0003231235130000172
where ρ isb＝[ρ1,ρ2,ρ3]T，rb＝[r1,r2,r3]T
And
Figure BDA0003231235130000173
step four, establishing a flight error mathematical model of the four-rotor plant protection unmanned aerial vehicle: based on the four-rotor plant protection unmanned aerial vehicle composite mathematical model, the flight error mathematical model of the four-rotor plant protection unmanned aerial vehicle is established. It should be particularly noted that the flight error model of the quad-rotor plant protection unmanned aerial vehicle established by the invention is used for guidingFilter coefficient gamma1And gamma2So that the convergence speed of the position error and the convergence speed of the attitude error can be adjusted more directly.
The establishment of the flight error mathematical model of the four-rotor plant protection unmanned aerial vehicle comprises the following steps:
(1) defining a position error e1Attitude error e2Linear velocity error
Figure BDA0003231235130000174
And error of angular velocity
Figure BDA0003231235130000175
Specific mathematical expressions are respectively as follows:
e1＝P-Pd，e2＝Θ-Θd，
Figure BDA0003231235130000176
wherein, Pd＝[xd,yd,zd]TAnd
Figure BDA0003231235130000177
representing the desired position signal and the desired attitude signal, respectively, in the terrestrial coordinate system.
(2) Based on the defined position error e1Attitude error e2Linear velocity error
Figure BDA0003231235130000178
And error of angular velocity
Figure BDA0003231235130000179
Filtering tracking error xi of design position system1Filtered tracking error xi of sum attitude system2The specific mathematical expression is as follows:
Figure BDA00032312351300001710
wherein，γ1>0 and gamma2>0 denotes the filter coefficient by increasing gamma1And gamma2The convergence rate of the tracking error can be improved.
(3) Filtered tracking error xi based on position1And the filtering tracking error xi of the attitude2And complete composite mathematical model
Figure BDA00032312351300001711
And
Figure BDA00032312351300001712
flight error mathematical model for establishing four-rotor-wing plant protection unmanned aerial vehicle
Figure BDA00032312351300001713
And
Figure BDA00032312351300001714
the specific mathematical expression is as follows:
Figure BDA00032312351300001715
wherein the content of the first and second substances,
Figure BDA00032312351300001716
and
Figure BDA00032312351300001717
representing complex non-linear variables in the position system and the pose system, respectively.
And fifthly, designing a saturation compensation system and storing data: a saturation compensation system is designed based on a flight error mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and signal data of the saturation compensation system are updated and stored in a flight data storage III. The saturation compensation system designed by the invention does not need to assume that the magnitude of the expected control input is bounded, and can ensure that the saturation compensation system is converged in a limited time.
The design and data storage of the saturation compensation system comprises the following steps:
(1) filtering tracking error xi based on position system1Filtered tracking error xi of sum attitude system2Establishing a saturation compensation system
Figure BDA0003231235130000181
And
Figure BDA0003231235130000182
the specific mathematical expression is as follows:
Figure BDA0003231235130000183
Figure BDA0003231235130000184
wherein the content of the first and second substances,
Figure BDA0003231235130000185
△U2＝Tt-sat(Tt)，K1>0 and K2>0 denotes the control parameter, upsilon, of the input-compensated auxiliary system1And upsilon2Representing the compensating auxiliary variable, p, of the input in the position system and attitude system, respectively1And ρ2Represents a positive odd number and satisfies a condition ρ1<ρ2；
(2) Will compensate the auxiliary variable data upsilon1And upsilon2Updated and saved to flight data storage III.
Sixthly, designing adaptive neural network parameters and storing data: the self-adaptive neural network parameters are designed based on the flight error mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and the data of the self-adaptive neural network parameters are updated and stored in a flight data storage IV. The invention utilizes the designed self-adaptive algorithm to update two lumped parameters on line instead of updating two vectors or two matrixes. This therefore greatly reduces the number of adaptive parameters in the controller, effectively reducing the computational burden. In addition, the adaptive algorithm is designed based on the delta-modification technology, so that the problem of parameter drift is effectively avoided. The design and data storage of the adaptive neural network parameters comprise the following steps:
(1) according to s1And s2Is defined by the following inequality:
Figure BDA0003231235130000186
Figure BDA0003231235130000187
then, based on the strong approximation capability of the radial basis function neural network to the nonlinear function, the radial basis function neural network is introduced, and the specific mathematical expression is as follows:
h(Z)＝W*TΞ(Z)+δ(Z)，
wherein the content of the first and second substances,
Figure BDA0003231235130000188
and W*TXi (Z) denotes the input and output of the radial basis function neural network, respectively, n denotes the number of inputs, h (Z) denotes a nonlinear function, δ (Z) denotes an approximation error, W*An optimal weight vector is represented, which is calculated according to the following formula:
Figure BDA0003231235130000191
wherein the content of the first and second substances,
Figure BDA0003231235130000192
a weight vector representing a radial basis function neural network,
Figure BDA0003231235130000193
a gaussian basis function is represented, the specific mathematical expression of which is as follows:
Figure BDA0003231235130000194
wherein, m is 1,2sum，ksumRepresenting the total neurons in the hidden layer;
Figure BDA0003231235130000195
and μ denotes the center and radius of the radial basis function neural network, respectively.
(2) Approximation of a nonlinear function η using a radial basis function neural network1(Z1) And η2(Z2) The specific mathematical expression is as follows:
Figure BDA0003231235130000196
further obtaining:
Figure BDA0003231235130000197
wherein the content of the first and second substances,
Figure BDA0003231235130000198
and Ψi(Zi)＝1+Ξi(Zi) And (i ═ 1,2) denote an unknown imaginary parameter and a known calculable positive scalar parameter, respectively.
(3) Designed adaptive neural network parameters
Figure BDA0003231235130000199
And
Figure BDA00032312351300001910
as follows:
Figure BDA00032312351300001911
wherein, biAnd ci(i ═ 1,2) each represent a positive design parameter;
Figure BDA00032312351300001912
is represented by betaiAn upper bound estimate of (d);
(4) adapting neural network parameter data
Figure BDA00032312351300001913
And
Figure BDA00032312351300001914
updated and saved to the flight data memory IV.
Seventhly, designing the fault-tolerant tracking controller based on the anti-saturation finite time self-adaptive neural network and storing control signals: a flight error mathematical model and a saturation compensation system based on a four-rotor plant protection unmanned aerial vehicle are designed, a fault-tolerant tracking controller based on an anti-saturation finite time self-adaptive neural network is designed, and signal data based on the anti-saturation finite time self-adaptive neural network fault-tolerant tracking control are updated and stored in a flight data storage V. The fault-tolerant tracking controller based on the anti-saturation finite time self-adaptive neural network can simultaneously solve the problems of external disturbance, actuator error and input saturation, and the problems greatly increase the design difficulty of the controller. Besides, the number of adaptive parameters in the controller is greatly reduced, the design structure is simplified, and the burden of parameter online calculation is reduced. Therefore, the designed controller is more economical and reliable, can better deal with emergency situations encountered in the actual flying process and meets the requirement of safe flying. The design and control signal storage based on the anti-saturation finite time adaptive neural network fault-tolerant tracking controller comprises the following steps:
(1) tracking error xi based on filtering1And xi2Saturation compensation system
Figure BDA0003231235130000201
And
Figure BDA0003231235130000202
adaptive neural network parameters
Figure BDA0003231235130000203
And
Figure BDA0003231235130000204
and complete composite mathematical model
Figure BDA0003231235130000205
And
Figure BDA0003231235130000206
the design is based on an anti-saturation finite time self-adaptive neural network fault-tolerant tracking controller, and the specific mathematical expression is as follows:
Figure BDA0003231235130000207
wherein k isiAnd ai(i-1, 2) represents a positive design parameter,
since quad-rotor plant protection unmanned aerial vehicle has four inputs (u)o,1,uo,2,uo,3,uo,4)6 outputs
Figure BDA0003231235130000208
Using three virtual control input signals (q)1,q2,q3) Calculating the actual control input signal uo,1Namely:
Figure BDA0003231235130000209
in addition, the desired pitch angle φdAnd a desired yaw angle thetadThe calculation formulas of (a) and (b) are respectively as follows:
Figure BDA00032312351300002010
(2) control signal data based on anti-saturation finite time adaptive neural network fault-tolerant tracking
Figure BDA00032312351300002011
And TtUpdated and saved to the flight data memory V.
And eighth step, updating the real-time track data: inputting a fault-tolerant tracking control signal based on an anti-saturation finite time self-adaptive neural network into a complete composite mathematical model of the quad-rotor plant protection unmanned aerial vehicle, outputting real-time trajectory data and storing the real-time trajectory data into a flight data storage II.
(1) Inputting a fault-tolerant tracking control signal based on an anti-saturation finite time self-adaptive neural network into a complete composite mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and outputting a second derivative of real-time trajectory data, namely: three linear accelerations
Figure BDA00032312351300002012
And three angular accelerations
Figure BDA00032312351300002013
And saved to flight data storage II.
(2) For three linear accelerations
Figure BDA00032312351300002014
And three angular accelerations
Figure BDA00032312351300002015
And performing secondary integration to obtain real-time track data.
And ninthly, adjusting parameter values in a position system and an attitude system: design parameters and control parameters in a position system are adjusted by monitoring data change of saturation compensation signals, data change of adaptive neural network parameters and difference value change of expected track data and actual track data, so that tracking control of the quad-rotor plant protection unmanned aerial vehicle is realized.
The method comprises the following specific steps:
(1) the desired trajectory data, the real-time trajectory data, and the real-time adaptive neural network parameters stored in the flight data memories I, II and III, and the complex nonlinear variables are input to the saturation compensation system and the radial basis function neural network, and new saturation compensation signals and new adaptive neural network parameters are output.
(2) And inputting the real-time track data and the expected track data stored in the flight data memories I and II, a new saturation compensation signal and a new adaptive neural network parameter into an anti-saturation finite time adaptive neural network-based fault-tolerant tracking controller, and outputting a control signal for adjusting the track of the four-rotor plant protection unmanned aerial vehicle.
(3) The control signal who will be used for adjusting four rotor plant protection unmanned aerial vehicle orbits is input into four rotor plant protection unmanned aerial vehicle's complete compound mathematical model, the second derivative of the real-time orbit data of output, promptly: three linear accelerations
Figure BDA0003231235130000211
And three angular accelerations
Figure BDA0003231235130000212
And then, carrying out second integration on the second derivative of the real-time track data to obtain new real-time track data, namely: at xaAxis, yaAxis and zaPosition coordinates on axis x, y and z, and around xaThe roll angle phi and the winding y of the shaftaPitch angle of the shaft theta and zaDegree of yaw angle of an axle
Figure BDA0003231235130000213
(4) And updating the new real-time track data, the new saturation compensation signal data, the new adaptive neural network parameter data and the input control signal for adjusting the track of the quad-rotor plant protection unmanned aerial vehicle, and respectively storing the updated input control signal into flight data memories II, III, IV and V.
(5) Observing changes in saturation compensation signal data in flight database III:
A1) design parameter k in a position system1And a1The change adjustment of (2): if the absolute value of the saturation compensation signal in the position system varies in a range of 0.2 or more,then the design parameter k1Increased by 0.5 size, and design parameter a1Until the absolute value of the saturation compensation signal in the position system changes in a range of 0.2 or less; the design parameter k is designed if the absolute value of the saturation compensation signal in the position system varies in a range of 0.2 or less1Increased by 0.3 size, and design parameter a1Until the absolute value of the saturation compensation signal in the position system changes in a range of 0.02 or less; if the absolute value of the saturation compensation signal in the position system varies in the range of 0.02 or less, the design parameter k1And a1The values are not changed, so that the performance requirement of the four-rotor plant protection unmanned aerial vehicle on input signal compensation in a position system is met;
A2) design parameter k in attitude system2And a2The change adjustment of (2): if the absolute value of the saturation compensation signal in the attitude system varies in a range of 0.2 or more, the design parameter k2Increased by 0.5 size, and design parameter a2Until the absolute value of the saturation compensation signal in the attitude system changes in a range of less than or equal to 0.2; if the absolute value of the saturation compensation signal in the attitude system varies in a range of 0.2 or less, the design parameter k2Increased by 0.3 size, and design parameter a2Until the absolute value of the saturation compensation signal in the attitude system changes in a range of less than or equal to 0.02; if the absolute value of the saturation compensation signal in the attitude system changes in a range of 0.02 or less, the design parameter k2And a2The value of (2) is not changed, and the performance requirement of the four-rotor plant protection unmanned aerial vehicle on input signal compensation in the attitude system is met.
(6) Observing the change of the adaptive neural network parameter data in the flight database IV:
B1) design parameter b in location system1And c1The change adjustment of (2): design parameter b if adaptive neural network parameter values in the location system change incrementally over time1Is decreased by 0.2 while designingParameter c1Until the adaptive neural network parameter value in the position system monotonically decreases with time; if the adaptive neural network parameter value in the location system takes more than 25 seconds to converge to zero, the design parameter b1Is decreased by a value of 0.08 while designing the parameter c1The value of (a) is increased by 0.12 until the adaptive neural network parameter value in the position system needs less than 25 seconds to converge to near zero; design parameter b if the adaptive neural network parameter value in the location system requires less than 25 seconds to converge to near zero1Is decreased by a value of 0.04 while designing the parameter c1The value of (2) is increased according to the size of 0.06, and the adaptive neural network parameter value in the position system can not be converged to be near zero until the value is within the range of 10 seconds to 25 seconds; design parameter b if the adaptive neural network parameter values in the location system take 10 seconds to 25 seconds to converge to near zero1While the value of (c) is not changed, while the parameter c is designed1The value of (A) is increased by 0.04 until the adaptive neural network parameter value in the position system can be converged to be near zero within 10 seconds; design parameter b if the adaptive neural network parameter value in the location system converges to zero within 10 seconds1And c1The values are not changed, so that the performance requirement of the four-rotor plant protection unmanned aerial vehicle on adaptive neural network parameter convergence in a position system is met;
B2) design parameter b in attitude system2And c2The change adjustment of (2): design parameter b if adaptive neural network parameter values in the attitude system change incrementally over time2Is decreased by a value of 0.2 while designing the parameter c2The value of (2) is increased according to the size of 0.25 until the self-adaptive neural network parameter value in the attitude system is monotonically decreased along with the time; if the adaptive neural network parameter value in the attitude system needs more than 25 seconds to converge to zero, the design parameter b2Is decreased by a value of 0.08 while designing the parameter c2The value of (2) is increased according to the size of 0.12 until the self-adaptive neural network parameter value in the attitude system needs less than 25 seconds to converge to the vicinity of zero; if the adaptive neural network parameter value in the attitude system needs to be received in less than 25 secondsConverging to near zero, then design parameter b2Is decreased by a value of 0.04 while designing the parameter c2The value of (2) is increased according to the size of 0.06 until the self-adaptive neural network parameter value in the attitude system can be converged to be near zero within the range of 10 seconds to 25 seconds; if the adaptive neural network parameter values in the attitude system need to converge to near zero in the range of 10 seconds to 25 seconds, the design parameter b2While the value of (c) is not changed, while the parameter c is designed2The value of (A) is increased by 0.04 until the adaptive neural network parameter value in the attitude system converges to zero within the range of 10 seconds; design parameter b if the adaptive neural network parameter values in the attitude system converge to zero within 10 seconds2And c2The values are not changed, and the performance requirement of self-adaptive neural network parameter convergence of the four-rotor plant protection unmanned aerial vehicle in the attitude system is met.
(7) Comparing the difference value of the expected track data and the actual track data in the flight databases I and II:
C1) control parameter gamma in position system1The change adjustment of (2): if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is greater than 1.5, the control parameter γ is then determined1Until the sum of the absolute values of the differences is less than or equal to 1.5; if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 1.5, and the control parameter gamma is1The value of (a) is increased by 0.1 until the sum of the absolute values of the differences is less than or equal to 0.1; if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 0.1, and the control parameter gamma is1The value of (a) is increased by 0.06 until the sum of the absolute values of the differences is less than or equal to 0.01; if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 0.01, and a control parameter gamma1The value of (2) is not changed, so that the performance requirement of the trajectory tracking precision of the four-rotor plant protection unmanned aerial vehicle in a position system is met;
C2) control parameter gamma in attitude system2The change adjustment of (2): if three desired attitude angles
Figure BDA0003231235130000231
Corresponding to the number of real-time attitude angles
Figure BDA0003231235130000232
If the sum of the absolute values of the differences is greater than 1, the control parameter gamma is set2The value of (a) is increased by 0.15 until the sum of the absolute values of the differences is less than or equal to 1; if three desired attitude angle numbers
Figure BDA0003231235130000233
Corresponding to the number of real-time attitude angles
Figure BDA0003231235130000234
The sum of the absolute values of the differences is less than or equal to 1, and the control parameter gamma is2The value of (a) is increased by 0.08 until the sum of the absolute values of the differences is less than or equal to 0.1; if three desired attitude angle numbers
Figure BDA0003231235130000241
Corresponding to the number of real-time attitude angles
Figure BDA0003231235130000242
The sum of the absolute values of the differences is less than or equal to 0.1, the control parameter gamma2The value of (A) is increased by 0.03 until the sum of the absolute values of the differences is less than or equal to 0.01; if three desired attitude angles are provided
Figure BDA0003231235130000243
Corresponding to the number of real-time attitude angles
Figure BDA0003231235130000244
The sum of the absolute values of the differences is less than or equal to 0.01, and then the control parameter gamma is2The value of (2) does not change, and this satisfies the performance requirement of four rotor plant protection unmanned aerial vehicle orbit tracking precision in attitude system.
To prove thatTracking error signal e of four-rotor plant protection unmanned aerial vehicle1And e2Converge to a bounded region in a limited time frame, consider the following complex lyapunov function V:
Figure BDA0003231235130000245
wherein the content of the first and second substances,
Figure BDA0003231235130000246
and
Figure BDA0003231235130000247
which is indicative of an estimation error that is,
Figure BDA0003231235130000248
and
Figure BDA0003231235130000249
respectively represents beta1And beta2An estimate of (d).
Substituting the flight error mathematical model, the saturation compensation system and the adaptive neural network parameters based on the anti-saturation finite time adaptive neural network fault-tolerant tracking controller and the four-rotor plant protection unmanned aerial vehicle into the first derivative of the Lyapunov function V to obtain:
Figure BDA00032312351300002410
wherein the content of the first and second substances,
Figure BDA00032312351300002411
Figure BDA00032312351300002412
and
Figure BDA00032312351300002413
according to the stability of limited timeBy qualitative theorem, it can be found that
Figure BDA0003231235130000251
And K2>0, tracking signal xi of closed loop system1,ξ2,
Figure BDA0003231235130000252
υ1,υ2At a finite time T1Converge to a bounded region omega near the origin1。
In particular, a finite time T1Is calculated by the formula
Figure BDA0003231235130000253
Figure BDA0003231235130000254
Wherein: 0<ε1<1，T0Indicating the initial time.
In particular, the bounded area Ω1Is calculated by the formula
Figure BDA0003231235130000255
Therefore, based on the designed position filtering tracking error and attitude filtering tracking error, it can be derived that the position tracking error and attitude tracking error will converge to the following bounded regions, respectively:
Figure BDA0003231235130000256
Figure BDA0003231235130000257
in conclusion, under the influence of external time-varying wind disturbance, input saturation and actuator errors, the designed fault-tolerant tracking controller based on the anti-saturation finite-time adaptive neural network can still ensure that all closed-loop system signals and tracking errors are converged to a bounded region within finite time, so that the robustness of the system, the anti-saturation performance of the actuator and the fault-tolerant capability of the actuator are enhanced, and the high-performance safe autonomous flight of the four-rotor plant protection unmanned aerial vehicle is ensured. Meanwhile, the online calculation quantity of the self-adaptive neural network parameters is reduced, and the calculation burden of an airborne control center is effectively reduced.
In order to verify the superiority of the controller provided by the invention, in a specific embodiment, a trajectory tracking control system of a four-rotor plant protection unmanned aerial vehicle is constructed on the basis of an MATLAB simulation platform. In the embodiment of the invention, the physical parameters of the four-rotor plant protection unmanned aerial vehicle are as follows: m is 2[ kg]，g＝9.8[m/s2]，d＝0.2[m]， Jr＝0.002[kg·m2]，Io,x＝Io,y＝1.2416[N·m·s2/rad]，Io,z＝2.4832[N·m·s2/rad]，Kf,1＝Kf,2＝Kf,3＝0.01[N·s/m]And Kt,1＝Kt,2＝Kt,3＝0.001[N·m·s/rad]。
The time-varying disturbance that four rotor plant protection unmanned aerial vehicle received is as follows:
Figure BDA0003231235130000261
and
Figure BDA0003231235130000262
the executor trouble that four rotor plant protection unmanned aerial vehicle received is as follows:
Figure BDA0003231235130000263
Figure BDA0003231235130000264
[r1,r2,r3,r4]T＝[0.1,0.02,0.1sin(0.2t),0]T. The input saturation limit that four rotor plant protection unmanned aerial vehicle received is as follows: u. ofmax,1＝35[N]And umax,2＝umax,3＝umax,4＝40[N·m]. Four rotor plant protection unmanned aerial vehicle follow initial orbit
Figure BDA0003231235130000265
Takeoff tracking desired trajectory
Figure BDA0003231235130000266
The selected control parameters are as follows:
γ1＝10，γ2＝6，k1＝10，k2＝2，a1＝a2＝1，b1＝0.003，b2＝0.002，c1＝c2＝0.6， β1(0)＝β2(0)＝0，σ＝0，μ＝5，ksum＝200，ρ1＝15，ρ2＝17，K12.5 and K2＝3.5。
As shown in fig. 3-10, it can be seen from fig. 3 that the actual trajectory of a quad-rotor plant protection drone tracks the upper desired trajectory well. From fig. 4, fig. 5, and fig. 6, it can be seen that under the influence of external wind disturbance, actuator error, and input saturation, the real-time trajectory signals of the quad-rotor plant protection unmanned aerial vehicle in the x, y, and z axes can accurately track the corresponding expected position signals, respectively. It can be seen from fig. 7, 8, and 9 that the real-time roll angle signal, the real-time pitch angle signal, and the real-time yaw angle signal of the quad-rotor plant protection unmanned aerial vehicle can accurately track the corresponding expected attitude signal respectively under the influence of external wind disturbance, actuator error, and input saturation. It can be seen from fig. 10 that the four output signals of the quad-rotor plant protection unmanned aerial vehicle all satisfy the constraint condition of input saturation, and the problem of input saturation is effectively solved. It can be seen from fig. 11 that the values of the two adaptive parameters are bounded and eventually converge to around 0, avoiding the problem of parameter drift.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (8)

1. A four-rotor plant protection unmanned aerial vehicle tracking control method based on an anti-saturation finite time adaptive neural network fault-tolerant technology is characterized by comprising the following steps:
11) setting and storing of the expected trajectory data: according to flight mission requirements executed by the quad-rotor plant protection unmanned aerial vehicle, inputting expected trajectory data through a ground terminal; receiving expected trajectory data input by a ground terminal through an airborne network module, and storing the expected trajectory data in a flight data memory I;
12) acquiring and storing real-time track data: real-time track data are collected through a position sensor and an attitude sensor carried by the quad-rotor plant protection unmanned aerial vehicle, and the collected real-time track data are stored in a flight data storage II;
13) four rotor plant protection unmanned aerial vehicle composite mathematical model's establishment: establishing a complete composite mathematical model of the four-rotor plant protection unmanned aerial vehicle according to the inherent mechanical characteristics of the four-rotor plant protection unmanned aerial vehicle and interference factors of actuator faults and input saturation during flying so as to timely change wind disturbance;
14) four rotor plant protection unmanned aerial vehicle flight error mathematical model's establishment: establishing a flight error mathematical model of the four-rotor-wing plant protection unmanned aerial vehicle based on the four-rotor-wing plant protection unmanned aerial vehicle composite mathematical model;
15) design and data storage of saturation compensation system: designing a saturation compensation system based on a flight error mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and updating and storing signal data of the saturation compensation system into a flight data memory III;
16) design and data storage of adaptive neural network parameters: designing adaptive neural network parameters based on a flight error mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and updating and storing data of the adaptive neural network parameters into a flight data memory IV;
17) designing a fault-tolerant tracking controller based on an anti-saturation finite time adaptive neural network and storing control signals: designing a fault-tolerant tracking controller based on an anti-saturation finite time adaptive neural network based on a flight error mathematical model and a saturation compensation system of the quad-rotor plant protection unmanned aerial vehicle, and updating and storing data of a fault-tolerant tracking control signal based on the anti-saturation finite time adaptive neural network into a flight data storage V;
18) updating real-time track data: inputting a fault-tolerant tracking control signal based on an anti-saturation finite time adaptive neural network into a complete composite mathematical model of the four-rotor plant protection unmanned aerial vehicle, outputting real-time trajectory data and storing the real-time trajectory data into a flight data storage II;
19) adjusting parameter values in a position system and an attitude system: design parameters and control parameters in a position system are adjusted by monitoring data change of a saturation compensation signal, data change of self-adaptive neural network parameters and difference value change of expected track data and actual track data, so that tracking control of the quad-rotor plant protection unmanned aerial vehicle is realized.
2. The method for tracking and controlling the quadrotor plant protection unmanned aerial vehicle based on the anti-saturation finite time adaptive neural network fault-tolerant technology according to claim 1, wherein the establishment of the compound mathematical model of the quadrotor plant protection unmanned aerial vehicle comprises the following steps:
21) based on a coordinate system conversion method, a position kinematics mathematical model and an attitude kinematics mathematical model of the four-rotor plant protection unmanned aerial vehicle are established, and specific expressions are respectively as follows:
Figure FDA0003231235120000021
wherein, P ═ x, y, z]TAnd
Figure FDA0003231235120000022
respectively representing Euclidean position vectors and Euler angle vectors of the quadrotor plant protection unmanned aerial vehicle in an earth coordinate system, wherein x, y and z are divided intoIs shown in xaAxis, yaAxis and zaPosition coordinates on the axis, phi, theta and
Figure FDA0003231235120000023
respectively represent a winding xaTransverse rocking angle degree of shaft, winding yaPitch angle of shaft and winding zaDegree of yaw angle of the shaft, V ═ u, V, w]TAnd Ω ═ p, q, r]TRespectively represent a linear velocity vector and an angular velocity vector of the four-rotor plant protection unmanned aerial vehicle in a body coordinate system, wherein u, v and w respectively represent xbAxis, ybAxis and zbLinear speed on axis, p, q and r representing respectively the winding xbYaw rate, wind y of shaftbPitch angular velocity of the shaft and wind zbThe yaw rate of the shaft is such that,
Figure FDA0003231235120000024
and
Figure FDA0003231235120000025
respectively represents the linear velocity vector and the angular velocity vector of the four-rotor plant protection unmanned aerial vehicle in the terrestrial coordinate system, wherein
Figure FDA0003231235120000026
And
Figure FDA0003231235120000027
are respectively represented at xaAxis, yaAxis and zaThe linear velocity on the shaft is,
Figure FDA0003231235120000028
and
Figure FDA0003231235120000029
respectively represent a winding xaYaw rate, wind y of shaftaPitch angular velocity of the shaft and wind zaYaw rate of the shaft, RtAnd RsRespectively representing orthogonal matrix and Euler matrix, concrete expressionRespectively as follows:
Figure FDA00032312351200000210
Figure FDA00032312351200000211
22) by utilizing an Euler Lagrange modeling method, considering the self mechanical structure characteristics of the four-rotor plant protection unmanned aerial vehicle and the influence of external time-varying wind disturbance received during flight, a position dynamics mathematical model and an attitude dynamics mathematical model of the four-rotor plant protection unmanned aerial vehicle are established, and the specific expressions are respectively as follows:
Figure FDA00032312351200000212
wherein, Ir＝diag(Ix,Iy,Iz) Representing a positive definite moment of inertia matrix, wherein Ix、IyAnd IzRespectively represents the rotational inertia coefficients around the x axis, the y axis and the z axis, m represents the self mass of the four-rotor plant protection unmanned aerial vehicle,
Figure FDA0003231235120000031
and
Figure FDA0003231235120000032
respectively representing the linear acceleration vector and the angular acceleration vector of the four-rotor plant protection unmanned aerial vehicle in a body coordinate system, wherein,
Figure FDA0003231235120000033
and
Figure FDA0003231235120000034
are respectively represented at xbAxis, ybAxis and zbThe linear acceleration on the axis of the shaft,
Figure FDA0003231235120000035
and
Figure FDA0003231235120000036
respectively represent a winding xbYaw angular acceleration, about y, of the shaftbPitch angular acceleration of the shaft and about zbYaw angular acceleration of the shaft;
Fs＝[0,0,uo,1]Tand Ts＝[uo,2,uo,3,uo,4]TThe lift force and the control moment are respectively represented,
wherein u iso,iSpecific calculation expressions of (i ═ 1,2,3,4) are as follows:
Figure FDA0003231235120000037
wherein, wiAnd (i ═ 1,2,3 and 4) represents the rotating speed of the ith motor rotor, d represents the distance between the motor and the mass center of the four-rotor plant protection unmanned aerial vehicle, and c represents1And c2Representing the thrust coefficient and the torque coefficient of the propeller, FaAnd TaRespectively representing air resistance in an attitude power system and a position power system, and respectively representing the following specific expressions:
Figure FDA0003231235120000038
wherein, Kf＝diag(Kf,1,Kf,2,Kf,3) And Kt＝diag(Kt,1,Kt,2,Kt,3) Respectively representing a resistance coefficient matrix of the attitude system and a resistance coefficient matrix of the position system;
Fgthe specific expression of the system gravity is as follows:
Figure FDA0003231235120000039
wherein E ═ 0,0,1]TM represents the self mass of the four-rotor plant protection unmanned aerial vehicle, g represents the gravity acceleration,
Figure FDA00032312351200000310
is an orthogonal matrix RtInverse matrix of, TgThe gyro moment is expressed, and the specific expression is as follows:
Figure FDA00032312351200000311
wherein J represents the coefficient of inertia of each rotor,
symbol (omega)×A diagonally symmetric matrix representing an omega vector, which satisfies the following form:
Figure FDA00032312351200000312
23) based on kinematics mathematical model, dynamics mathematical model, position dynamics mathematical model and attitude dynamics mathematical model of a four-rotor plant protection unmanned aerial vehicle, an incomplete composite mathematical model without considering actuator errors and input saturation is established, and specific expressions are respectively as follows:
Figure FDA0003231235120000041
wherein the content of the first and second substances,
Figure FDA0003231235120000042
representing a virtual input vector of a quad-rotor plant protection unmanned aerial vehicle;
Figure FDA0003231235120000043
and
Figure FDA0003231235120000044
and
Figure FDA0003231235120000045
representing non-linearities in the position system and the attitude system respectively,
Figure FDA0003231235120000046
da＝[dx,dy,dz]Tand
Figure FDA0003231235120000047
representing lumped disturbances in the position system and the attitude system, respectively;
24) considering the effect of actuator error, the specific mathematical expression is as follows:
uo,i＝ρiui+ri,i＝1,2,3,4，
wherein u iso,iAnd uiRespectively representing the actual control signal and the desired control signal, piAnd riRespectively representing the significant coefficient and the additional fault;
25) considering the effect of actuator input saturation, the specific mathematical expression is as follows:
sat(ui)＝sign(ui)min{|ui|,umax,i},i＝1,2,3,4，
wherein u ismax,iRepresenting the control signal uiUpper bound of (c), sign function sign (u)i) Is defined as
Figure FDA0003231235120000048
26) Establishing a complete composite mathematical model considering actuator errors and input saturation based on an incomplete composite mathematical model, a mathematical expression of actuator errors and a mathematical expression of input saturation
Figure FDA00032312351200000411
And
Figure FDA00032312351200000412
the specific expression is as follows:
Figure FDA0003231235120000049
where ρ isb＝[ρ1,ρ2,ρ3]T，rb＝[r1,r2,r3]T
And
Figure FDA00032312351200000410
3. the method for tracking and controlling the quadrotor plant protection unmanned aerial vehicle based on the anti-saturation finite time adaptive neural network fault-tolerant technology according to claim 1, wherein the establishment of the mathematical model of the flight errors of the quadrotor plant protection unmanned aerial vehicle comprises the following steps:
31) defining a position error e1Attitude error e2Linear velocity error
Figure FDA0003231235120000051
And error of angular velocity
Figure FDA0003231235120000052
Specific mathematical expressions are respectively as follows:
e1＝P-Pd，e2＝Θ-Θd，
Figure FDA0003231235120000053
wherein, Pd＝[xd,yd,zd]TAnd
Figure FDA0003231235120000054
respectively representing a desired position signal and a desired attitude signal in a terrestrial coordinate system;
32) based on the defined position error e1Attitude error e2Linear velocity error
Figure FDA0003231235120000055
And error of angular velocity
Figure FDA0003231235120000056
Filtering tracking error xi of design position system1Filtered tracking error xi of sum attitude system2The specific mathematical expression is as follows:
Figure FDA0003231235120000057
wherein, γ1>0 and gamma2>0 denotes the filter coefficient by increasing gamma1And gamma2The convergence rate of the tracking error can be improved;
33) filtered tracking error xi based on position1And the filtering tracking error xi of the attitude2And complete composite mathematical model
Figure FDA0003231235120000058
And
Figure FDA0003231235120000059
flight error mathematical model for establishing four-rotor-wing plant protection unmanned aerial vehicle
Figure FDA00032312351200000510
And
Figure FDA00032312351200000511
the specific mathematical expression is as follows:
Figure FDA00032312351200000512
wherein the content of the first and second substances,
Figure FDA00032312351200000513
and
Figure FDA00032312351200000514
representing complex non-linear variables in the position system and the pose system, respectively.
4. The method for tracking and controlling the quadrotor plant protection unmanned aerial vehicle based on the anti-saturation finite time adaptive neural network fault-tolerant technology according to claim 1, wherein the design and data storage of the saturation compensation system comprise the following steps:
41) filtering tracking error xi based on position system1Filtered tracking error xi of sum attitude system2Establishing a saturation compensation system
Figure FDA00032312351200000515
And
Figure FDA00032312351200000516
the specific mathematical expression is as follows:
Figure FDA00032312351200000517
Figure FDA00032312351200000518
wherein the content of the first and second substances,
Figure FDA00032312351200000519
△U2＝Tt-sat(Tt)，K1>0 and K2>0 represents inputControl parameter, upsilon, of an in-compensation auxiliary system1And upsilon2Representing the compensating auxiliary variable, p, of the input in the position system and attitude system, respectively1And ρ2Represents a positive odd number and satisfies a condition ρ1<ρ2；
42) Will compensate the auxiliary variable data upsilon1And upsilon2Updated and saved to flight data storage III.
5. The method for tracking and controlling the quadrotor plant protection unmanned aerial vehicle based on the anti-saturation finite time adaptive neural network fault-tolerant technology according to claim 1, wherein the design and data storage of the adaptive neural network parameters comprise the following steps:
51) according to s1And s2Is defined by the following inequality:
Figure FDA0003231235120000061
Figure FDA0003231235120000062
then, based on the strong approximation capability of the radial basis function neural network to the nonlinear function, the radial basis function neural network is introduced, and the specific mathematical expression is as follows:
h(Z)＝W*TΞ(Z)+δ(Z)，
wherein the content of the first and second substances,
Figure FDA0003231235120000063
and W*TXi (Z) denotes the input and output of the radial basis function neural network, respectively, n denotes the number of inputs, h (Z) denotes a nonlinear function, δ (Z) denotes an approximation error, W*An optimal weight vector is represented, which is calculated according to the following formula:
Figure FDA0003231235120000064
wherein the content of the first and second substances,
Figure FDA0003231235120000065
a weight vector representing a radial basis function neural network,
Figure FDA0003231235120000066
a gaussian basis function is represented, the specific mathematical expression of which is as follows:
Figure FDA0003231235120000067
wherein m is 1,2, …, ksum，ksumRepresenting the total neurons in the hidden layer;
Figure FDA0003231235120000068
and μ represents the center and radius of the radial basis function neural network, respectively;
52) approximation of a nonlinear function η using a radial basis function neural network1(Z1) And η2(Z2) The specific mathematical expression is as follows:
Figure FDA0003231235120000069
further obtaining:
Figure FDA00032312351200000610
wherein the content of the first and second substances,
Figure FDA00032312351200000611
and Ψi(Zi)＝1+Ξi(Zi) (i ═ 1,2) denote an unknown imaginary parameter and a known calculable positive scalar parameter, respectively;
53) designed adaptive neural network parameters
Figure FDA0003231235120000071
And
Figure FDA0003231235120000072
as follows:
Figure FDA0003231235120000073
wherein, biAnd ci(i ═ 1,2) each represent a positive design parameter;
Figure FDA0003231235120000074
is represented by betaiAn upper bound estimate of (d);
54) adapting neural network parameter data
Figure FDA0003231235120000075
And
Figure FDA0003231235120000076
updated and saved to the flight data memory IV.
6. The tracking control method of the four-rotor plant protection unmanned aerial vehicle based on the anti-saturation finite time adaptive neural network fault-tolerant technology according to claim 1, wherein the designing of the anti-saturation finite time adaptive neural network fault-tolerant tracking controller and the storing of the control signals comprise the following steps:
61) tracking error xi based on filtering1And xi2Saturation compensation system
Figure FDA0003231235120000077
And
Figure FDA0003231235120000078
adaptive neural network parameters
Figure FDA0003231235120000079
And
Figure FDA00032312351200000710
and complete composite mathematical model
Figure FDA00032312351200000711
And
Figure FDA00032312351200000712
the design is based on an anti-saturation finite time self-adaptive neural network fault-tolerant tracking controller, and the specific mathematical expression is as follows:
Figure FDA00032312351200000713
wherein k isiAnd ai(i-1, 2) represents a positive design parameter,
since quad-rotor plant protection unmanned aerial vehicle has four inputs (u)o,1,uo,2,uo,3,uo,4)6 outputs
Figure FDA00032312351200000714
Using three virtual control input signals (q)1,q2,q3) Calculating the actual control input signal uo,1Namely:
Figure FDA00032312351200000715
in addition, the desired pitch angle φdAnd a desired yaw angle thetadThe calculation formulas of (a) and (b) are respectively as follows:
Figure FDA00032312351200000716
62) control signal data based on anti-saturation finite time adaptive neural network fault-tolerant tracking
Figure FDA00032312351200000717
And TtUpdated and saved to the flight data memory V.
7. The method for tracking and controlling the quadrotor plant protection unmanned aerial vehicle based on the anti-saturation finite time adaptive neural network fault-tolerant technology according to claim 1, wherein the updating of the real-time trajectory data comprises the following steps:
71) inputting a fault-tolerant tracking control signal based on an anti-saturation finite time self-adaptive neural network into a complete composite mathematical model of the quad-rotor plant protection unmanned aerial vehicle, and outputting a second derivative of real-time trajectory data, namely: three linear accelerations
Figure FDA0003231235120000081
And three angular accelerations
Figure FDA0003231235120000082
And storing the data into a flight data memory II;
72) for three linear accelerations
Figure FDA0003231235120000083
And three angular accelerations
Figure FDA0003231235120000084
And performing secondary integration to obtain real-time track data.
8. The tracking control method for the quadrotor plant protection unmanned aerial vehicle based on the anti-saturation finite time adaptive neural network fault-tolerant technology according to claim 1, wherein the parameter values in the position system and the attitude system are adjusted by the following steps:
81) inputting the expected trajectory data, the real-time adaptive neural network parameters and the complex nonlinear variables stored in the flight data memories I, II and III into the saturation compensation system and the radial basis function neural network, and outputting new saturation compensation signals and new adaptive neural network parameters;
82) inputting the real-time trajectory data and the expected trajectory data stored in the flight data memories I and II, a new saturation compensation signal and a new adaptive neural network parameter into an anti-saturation finite time adaptive neural network-based fault-tolerant tracking controller, and outputting a control signal for adjusting the trajectory of the four-rotor plant protection unmanned aerial vehicle;
83) the control signal who will be used for adjusting four rotor plant protection unmanned aerial vehicle orbits is input into four rotor plant protection unmanned aerial vehicle's complete compound mathematical model, the second derivative of the real-time orbit data of output, promptly: three linear accelerations
Figure FDA0003231235120000085
And three angular accelerations
Figure FDA0003231235120000086
And then, carrying out second integration on the second derivative of the real-time track data to obtain new real-time track data, namely: at xaAxis, yaAxis and zaPosition coordinates on axis x, y and z, and around xaThe roll angle phi and the winding y of the shaftaPitch angle of the shaft theta and zaDegree of yaw angle of an axle
Figure FDA0003231235120000087
84) Updating new real-time track data, new saturation compensation signal data, new adaptive neural network parameter data and input control signals for adjusting the track of the quad-rotor plant protection unmanned aerial vehicle, and respectively storing the updated real-time track data, the new saturation compensation signal data, the new adaptive neural network parameter data and the input control signals in flight data memories II, III, IV and V;
85) observing changes in saturation compensation signal data in flight database III:
851) design parameter k in a position system1And a1The change adjustment of (2):
the design parameter k is determined if the absolute value of the saturation compensation signal in the position system varies in a range of 0.2 or more1Increased by 0.5 size, and design parameter a1Until the absolute value of the saturation compensation signal in the position system changes in a range of 0.2 or less;
the design parameter k is designed if the absolute value of the saturation compensation signal in the position system varies in a range of 0.2 or less1Increased by 0.3 size, and design parameter a1Until the absolute value of the saturation compensation signal in the position system changes in a range of 0.02 or less;
if the absolute value of the saturation compensation signal in the position system varies in the range of 0.02 or less, the design parameter k1And a1The values are not changed, so that the performance requirement of the four-rotor plant protection unmanned aerial vehicle on input signal compensation in a position system is met;
852) design parameter k in attitude system2And a2The change adjustment of (2):
if the absolute value of the saturation compensation signal in the attitude system varies in a range of 0.2 or more, the design parameter k2Increased by 0.5 size, and design parameter a2Until the absolute value of the saturation compensation signal in the attitude system changes in a range of less than or equal to 0.2;
if the absolute value of the saturation compensation signal in the attitude system varies in a range of 0.2 or less, the design parameter k2Increased by 0.3 size, and design parameter a2Until the absolute value of the saturation compensation signal in the attitude system changes in a range of less than or equal to 0.02;
if the absolute value of the saturation compensation signal in the attitude system changes in a range of 0.02 or less, the design parameter k2And a2The values are all not changed, so that the performance of the four-rotor plant protection unmanned aerial vehicle for input signal compensation in the attitude system is metRequiring;
86) observing the change of the adaptive neural network parameter data in the flight database IV:
861) design parameter b in location system1And c1The change adjustment of (2):
design parameter b if adaptive neural network parameter values in the location system change incrementally over time1Is decreased by a value of 0.2 while designing the parameter c1Until the adaptive neural network parameter value in the position system monotonically decreases with time;
if the adaptive neural network parameter value in the location system takes more than 25 seconds to converge to zero, the design parameter b1Is decreased by a value of 0.08 while designing the parameter c1The value of (a) is increased by 0.12 until the adaptive neural network parameter value in the position system needs less than 25 seconds to converge to near zero;
design parameter b if the adaptive neural network parameter value in the location system requires less than 25 seconds to converge to near zero1Is decreased by a value of 0.04 while designing the parameter c1Until the adaptive neural network parameter value in the position system can be converged to the vicinity of zero within 10 seconds to 25 seconds, the design parameter b1While the value of (c) is not changed, while the parameter c is designed1The value of (A) is increased by 0.04 until the adaptive neural network parameter value in the position system can be converged to be near zero within 10 seconds;
design parameter b if the adaptive neural network parameter value in the location system can converge to zero within 10 seconds1And c1The values are not changed, so that the performance requirement of the four-rotor plant protection unmanned aerial vehicle on adaptive neural network parameter convergence in a position system is met;
862) design parameter b in attitude system2And c2The change adjustment of (2):
design parameter b if adaptive neural network parameter values in the attitude system change incrementally over time2Is decreased by a value of 0.2 while designing the parameter c2Until the value of (2) is increased by 0.25The parameter value of the self-adaptive neural network in the attitude system is monotonically decreased along with time;
if the adaptive neural network parameter value in the attitude system needs more than 25 seconds to converge to zero, the design parameter b2Is decreased by a value of 0.08 while designing the parameter c2The value of (2) is increased according to the size of 0.12 until the self-adaptive neural network parameter value in the attitude system needs less than 25 seconds to converge to the vicinity of zero;
design parameter b if the adaptive neural network parameter value in the attitude system needs less than 25 seconds to converge to near zero2Is decreased by a value of 0.04 while designing the parameter c2The value of (2) is increased according to the size of 0.06 until the self-adaptive neural network parameter value in the attitude system is required to be converged to be near zero within the range of 10 seconds to 25 seconds;
if the adaptive neural network parameter values in the attitude system need to converge to near zero in the range of 10 seconds to 25 seconds, the design parameter b2While the value of (c) is not changed, while the parameter c is designed2The value of (A) is increased by 0.04 until the adaptive neural network parameter value in the attitude system converges to zero within the range of 10 seconds;
design parameter b if the adaptive neural network parameter values in the attitude system converge to zero within 10 seconds2And c2The values are not changed, so that the performance requirement of the four-rotor plant protection unmanned aerial vehicle on adaptive neural network parameter convergence in an attitude system is met;
87) comparing the difference value of the expected track data and the actual track data in the flight databases I and II:
871) control parameter gamma in position system1The change adjustment of (2):
if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is greater than 1.5, the control parameter γ is then determined1Until the sum of the absolute values of the differences is less than or equal to 1.5;
if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 1.5, and the control parameter is setNumber gamma1The value of (a) is increased by 0.1 until the sum of the absolute values of the differences is less than or equal to 0.1;
if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 0.1, and the control parameter gamma is1The value of (a) is increased by 0.06 until the sum of the absolute values of the differences is less than or equal to 0.01;
if three desired positions (x)d,yd,zd) The sum of the absolute values of the differences from the corresponding real-time position (x, y, z) is less than or equal to 0.01, and a control parameter gamma1The value of (2) is not changed, so that the performance requirement of the trajectory tracking precision of the four-rotor plant protection unmanned aerial vehicle in a position system is met;
872) control parameter gamma in attitude system2The change adjustment of (2):
if three desired attitude angle numbers
Figure FDA0003231235120000111
Corresponding to the number of real-time attitude angles
Figure FDA0003231235120000112
If the sum of the absolute values of the differences is greater than 1, the control parameter gamma is set2The value of (a) is increased by 0.15 until the sum of the absolute values of the differences is less than or equal to 1;
if three desired attitude angle numbers
Figure FDA0003231235120000113
Corresponding to the number of real-time attitude angles
Figure FDA0003231235120000114
The sum of the absolute values of the differences is less than or equal to 1, and the control parameter gamma is2The value of (a) is increased by 0.08 until the sum of the absolute values of the differences is less than or equal to 0.1;
if three desired attitude angle numbers
Figure FDA0003231235120000115
Corresponding to the number of real-time attitude angles
Figure FDA0003231235120000116
The sum of the absolute values of the differences is less than or equal to 0.1, the control parameter gamma2The value of (A) is increased by 0.03 until the sum of the absolute values of the differences is less than or equal to 0.01;
if three desired attitude angle numbers
Figure FDA0003231235120000117
Corresponding to the number of real-time attitude angles
Figure FDA0003231235120000118
The sum of the absolute values of the differences is less than or equal to 0.01, and then the control parameter gamma is2The value of (2) does not change, and this satisfies the performance requirement of four rotor plant protection unmanned aerial vehicle orbit tracking precision in attitude system.
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