CN113220031A - Anti-saturation finite time-based attitude tracking control method for rotary wing type plant protection unmanned aerial vehicle - Google Patents
Anti-saturation finite time-based attitude tracking control method for rotary wing type plant protection unmanned aerial vehicle Download PDFInfo
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Abstract
The invention relates to a method for tracking and controlling the attitude of a rotor type plant protection unmanned aerial vehicle based on anti-saturation limited time, which overcomes the defect that the attitude tracking and controlling of the rotor type plant protection unmanned aerial vehicle are difficult to carry out compared with the prior art. The invention comprises the following steps: acquiring expected attitude angle data; acquiring real-time attitude angle data; establishing a complete attitude mathematical model; establishing a complete posture mathematical expansion model; the design of the finite time expansion observer; designing an auxiliary power system; designing a finite time attitude tracking controller; and controlling and adjusting the posture of the rotary wing type plant protection unmanned aerial vehicle. The invention can realize that the rotor type plant protection unmanned aerial vehicle tracks the expected attitude angle signal in a limited time, improves the anti-interference and actuator saturation suppression capability of the flight control system, accelerates the tracking error convergence speed and effectively suppresses the jitter phenomenon output by the system.
Description
Technical Field
The invention relates to the field of unmanned aerial vehicle control, in particular to a method for tracking and controlling the attitude of a rotary wing type plant protection unmanned aerial vehicle based on anti-saturation limited time.
Background
Along with the continuous improvement of our country to accurate agricultural development requirement, rotor formula plant protection unmanned aerial vehicle relies on its low in manufacturing cost, sprays evenly, easy operation has stronger environmental suitability, is difficult to destroy crops growth environment during the operation etc. a plurality of advantages and receives the extensive attention of industry and academic. Simultaneously, rotor formula plant protection unmanned aerial vehicle accessible remote control carries out remote operation, avoids the direct contact of operating personnel and medicine to the negative effects that the pesticide caused to operating personnel health have been reduced. Compared with the traditional backpack manual operation mode, the rotary-wing type plant protection unmanned aerial vehicle can improve the operation efficiency and reduce the labor intensity of workers.
At present, the research on how to realize high-precision operation of the rotor-type plant protection unmanned aerial vehicle in China is still in the early development stage, and a lot of challenges and obstacles are still faced in the research. Firstly, the rotary wing type plant protection unmanned aerial vehicle has the structural characteristics of under-actuation, strong coupling, high nonlinearity and the like, which requires that a flight control algorithm has strong decoupling property and strong robustness; secondly, due to the complexity and the changeability of the flight environment, the rotor type plant protection unmanned aerial vehicle is easily affected by external disturbance (such as time-varying strong wind disturbance and air resistance), so that the stability of a flight control system is reduced. In addition, in the operation process, structural parameters of the rotor type plant protection unmanned aerial vehicle (such as mass and inertia parameters) are changed continuously, and the flight stability and the operation accuracy are easy to damage. When the unmanned aerial vehicle flies autonomously, the flight track is generally required to be set in advance, and then the unmanned aerial vehicle tracks the position through the flight controller. However, position tracking needs to be achieved by attitude tracking control of the drone. Therefore, designing a high-performance attitude tracking control method is crucial to ensuring stable flight of the unmanned aerial vehicle.
In recent years, many related works are developed aiming at the attitude tracking control problem of the rotor type plant protection unmanned aerial vehicle, and the related works mainly comprise PID control, neural network, sliding mode control and the like. The PID control is used as a linear control strategy with wide application, and has the characteristics of simple design, strong practicability and the like. However, the design process of PID control requires linearization processing of the model of the rotor type plant protection unmanned aerial vehicle at a balanced state, which is not suitable for the operation of the rotor type plant protection unmanned aerial vehicle in a large operation range. The neural network serving as an intelligent control algorithm can accurately approximate a complex nonlinear system, and the modeling difficulty of the nonlinear system is effectively solved. However, the application of the neural network algorithm increases the computational burden and requires a higher-configured computer, making it difficult to widely spread in practical applications. The sliding mode control is a typical robust control method and has the advantages of high response speed, easiness in implementation, strong robustness and the like. Therefore, the control method is very suitable for a high-nonlinearity system such as a rotor-type plant protection unmanned aerial vehicle. However, it is difficult to avoid the chattering phenomenon in the actual output signal. To solve this problem, bounded layer techniques or hyperbolic tangent functions are often used to replace the discontinuous terms in sliding mode control, but these methods reduce the control accuracy of the system. Compared with the gradual stabilization of the system, the finite time stabilization can ensure that the system state reaches the equilibrium state in a finite time range, thereby greatly improving the quality of the control system. In recent years, although finite time stabilization of a dynamic system can be achieved by using a terminal sliding mode surface, there are problems such as singularity and low convergence speed.
Besides, when the rotor type plant protection unmanned aerial vehicle takes off and loads heavy pesticides or water, the actuator is easy to input and saturate, the stability of a flight control system is extremely easy to damage, and a crash accident can be caused seriously or even. Therefore, designing the anti-saturation controller has very important research significance in ensuring the stability and safety of the system. In practical application, the rotor type plant protection unmanned aerial vehicle usually needs to carry an additional speed sensor so as to acquire attitude angular speed information, which greatly increases the equipment cost. Therefore, in order to further reduce the manufacturing cost of the plant protection unmanned aerial vehicle, it is very important to design an effective detection method to acquire attitude angular velocity information.
Disclosure of Invention
The invention aims to solve the defect that the attitude tracking control of a rotor type plant protection unmanned aerial vehicle is difficult in the prior art, and provides a method for controlling the attitude tracking of the rotor type plant protection unmanned aerial vehicle based on anti-saturation limited time to solve the problems.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the attitude tracking control method of the rotor type plant protection unmanned aerial vehicle based on the anti-saturation finite time comprises the following steps:
11) acquisition of desired attitude angle data: acquiring expected attitude angle data input into a flight data memory of the rotor type plant protection unmanned aerial vehicle, wherein the expected attitude angle data is set according to flight attitude requirements of the rotor type plant protection unmanned aerial vehicle;
12) acquiring real-time attitude angle data: gather the real-time data of attitude angle through the attitude sensor that rotor formula plant protection unmanned aerial vehicle carried on to with the real-time attitude angle data storage of gathering in flight data memory, attitude angle real-time data includes: roll angle degree, pitch angle degree and yaw angle degree;
13) establishing a complete posture mathematical model: establishing a complete attitude mathematical model of the rotor type plant protection unmanned aerial vehicle according to the inherent characteristics of the rotor type plant protection unmanned aerial vehicle and the influence of actuator saturation and wind disturbance factors during flying;
14) establishing a complete posture mathematical expansion model: establishing a complete attitude mathematical expansion model of the rotor type plant protection unmanned aerial vehicle based on the complete attitude mathematical model of the rotor type plant protection unmanned aerial vehicle;
15) designing a limited time extended observer: designing a finite time expansion observer based on a complete attitude mathematical expansion model of the rotor type plant protection unmanned aerial vehicle;
16) designing an auxiliary power system: introducing a rapid nonsingular terminal sliding mode surface and designing an auxiliary power system;
17) designing a finite time attitude tracking controller: designing an anti-saturation finite time attitude tracking controller of the rotor type plant protection unmanned aerial vehicle according to the introduced fast nonsingular terminal sliding mode surface, the constructed auxiliary power system and the finite time expansion observer;
18) the control adjustment of rotor type plant protection unmanned aerial vehicle gesture: and tracking and controlling the attitude of the rotor type plant protection unmanned aerial vehicle through the attitude angle real-time data and the expected attitude angle data.
The establishment of the complete attitude mathematical model comprises the following steps:
21) based on an Euler Lagrange modeling method, a dynamic mathematical model of the rotary wing type plant protection unmanned aerial vehicle is established according to the inherent characteristics of the rotary wing type plant protection unmanned aerial vehicle and the influence of actuator saturation and wind disturbance factors during flying, and the specific expression of the dynamic mathematical model is as follows:
wherein Ω is [ Ω ]1,Ω2,Ω3]TRepresents an attitude angular velocity vector in the inertial coordinate system, J ═ diag (J)1,J2,J3) Representing a positive definite symmetric inertia matrix, the actual input signal sat (u) ═ sat (u)1),sat(u2),sat(u3)]TIs expressed in the form of
Wherein u ismaxRepresenting the control signal uiUpper bound of (c), sign function sign (u)i) Is defined as
Wind disturbance D ═ D in natural environment1,D2,D3]TIs expressed in the form of
Wherein the content of the first and second substances,
representing the static wind disturbance constant, ajRepresenting the amplitude, w, of a sinusoidal signaljRepresenting the frequency of a sinusoidal signal, bjRepresenting a phase shift of a sinusoidal signal;
symbol (·)×Represents a skew symmetric matrix which satisfies the following form:
22) based on an Euler Lagrange modeling method, a kinematic attitude mathematical model of the rotary wing type plant protection unmanned aerial vehicle is established, and the mathematical expression of the mathematical model is as follows:
wherein, theta is [ phi, theta, psi ═ phi]TRepresenting an attitude angle vector under a coordinate system of the rotor-type plant protection unmanned aerial vehicle, phi, theta and psi respectively representing a roll angle degree, a pitch angle degree and a yaw angle degree, and defining a matrix W as
W＝R1(θ)R2(φ)
Wherein the content of the first and second substances,
23) based on rotor formula plant protection unmanned aerial vehicle's dynamics gesture mathematical model and motion gesture mathematical model, obtain rotor formula plant protection unmanned aerial vehicle's complete gesture mathematical model through basic transformation, its mathematical expression as follows:
wherein M is1(Θ) is a symmetric positive definite matrix, whose specific expression is as follows:
wherein the content of the first and second substances,
m11＝Ix,m12＝m14＝0,m13＝-Ixsinθ,m15＝Iycos2φ+Izsin2φ,m16＝(Iy-Iz)cosφsinφcosθ,m17＝-Ixsinθ,m18＝(Iy-Iz) cos phi sin phi cos theta and m19＝Ixsin2θ+Iysin2φcos2θ+Izcos2φcos2θ，
Ix,IyAnd IzRepresenting the coefficients of inertia in the x, y and z axes respectively,
the Coriolis centrifugal matrix is represented, and the specific expression form is as follows:
wherein the content of the first and second substances,
m21＝0,
m24＝-m22,
M3(Θ) represents a rotation matrix, which is expressed in the following concrete form:
the establishment of the complete posture mathematical expansion model comprises the following steps:
31) defining an intermediate variable
32) Complete attitude mathematical model and intermediate variable z based on rotor type plant protection unmanned aerial vehicle1Establishing a complete attitude mathematical development model of the rotor type plant protection unmanned aerial vehicle, wherein the specific expression form is as follows:
wherein the content of the first and second substances,
representing a composite disturbance and
the design finite time expansion observer is as follows:
wherein the content of the first and second substances,
and
denotes z1And z2Is observed value of1，ξ2，σ1And σ2Each represents the gain of a finite time evolution observer, which satisfies the following condition: xi1＞0，ξ2＞0，0.5<σ1<1 and σ2＝2σ1-1；
In a finite time extended observer
And
are respectively defined as
And
the design of the auxiliary power system comprises the following steps:
51) introducing a rapid nonsingular terminal sliding mode surface s, wherein the specific expression form is as follows:
wherein, thetae＝[φ-φd,θ-θd,ψ-ψd]T,
m1And m2Is a normal number; l1And p1Is a positive odd constant, and satisfies the condition:
and
in fast nonsingular terminal sliding-form surfaces
And
are respectively defined as
52) an auxiliary power system is designed based on the introduced rapid nonsingular terminal sliding mode surface, and the specific expression form is as follows
Wherein γ represents an auxiliary power system parameter, Δ u-sat (u), ρ1> 1 and ρ2＞0。
The anti-saturation finite time attitude tracking controller of the rotor type plant protection unmanned aerial vehicle is designed as follows:
u＝ua+ub+uc
wherein u isa，ubAnd ucAre respectively
And
The control adjustment of rotor type plant protection unmanned aerial vehicle gesture includes following steps:
71) inputting attitude angle real-time data in the flight data memory into the finite time expansion observer, and outputting real-time attitude angular velocity information and composite disturbance information observed by the finite time expansion observer;
72) inputting the observed real-time attitude angular velocity information and the compound disturbance information as well as expected attitude angle data and real-time attitude angle data in a flight data memory into an anti-saturation finite time attitude tracking controller, and outputting a control signal for adjusting the attitude of the plant protection unmanned aerial vehicle and new real-time attitude angle data;
73) updating and storing the new real-time attitude angle data into a flight data memory;
74) comparing the difference between the expected attitude angle data and the real-time attitude angle data in the flight database memory:
if the sum of the absolute values of the difference values of the three expected attitude angle degrees and the corresponding real-time attitude angle degrees is greater than 1, controlling the parameter m1And m2The value of (A) is increased by 0.2 at the same time until the sum of the absolute values of the differences is less than or equal to 0.5;
if the sum of the absolute values of the differences is less than or equal to 0.5, the parameter m is controlled1And m2The value of (2) is increased by 0.1 at the same time until the sum of the absolute values of the differences is less than or equal to 0.1;
if the sum of the absolute values of the differences is less than or equal to 0.1, the parameter m is controlled1And m2The value of (A) is increased by 0.05 at the same time until the sum of the absolute values of the differences is less than or equal to 0.01;
and if the sum of the absolute values of the difference values is less than or equal to 0.01, the real-time attitude control performance requirement of the rotary wing type plant protection unmanned aerial vehicle is met.
Advantageous effects
Compared with the prior art, the attitude tracking control method of the rotor type plant protection unmanned aerial vehicle based on the anti-saturation limited time can realize that the rotor type plant protection unmanned aerial vehicle tracks an expected attitude angle signal in the limited time, improve the anti-interference and actuator saturation suppression capability of a flight control system, accelerate the convergence speed of tracking error, effectively suppress the jitter phenomenon output by the system, detect the attitude angle speed on line to reduce the design cost of the rotor type plant protection unmanned aerial vehicle, and simultaneously avoid energy loss caused by selecting too large control gain.
The method can ensure that the attitude tracking error of the rotor type plant protection unmanned aerial vehicle is converged to a bounded error area within a limited time; secondly, the method can realize the targets of accurate tracking, jitter elimination and actuator saturation suppression of the attitude track of the rotor type plant protection unmanned aerial vehicle under the condition that wind disturbance and actuator saturation problems exist, and improve the robustness and track tracking quality of the system; then, the method can detect the attitude angular velocity of the rotor type plant protection unmanned aerial vehicle on line and compensate the adverse effect caused by wind disturbance, and meanwhile, the problem of energy loss caused by selecting large control gain due to the fact that the robustness of the system is improved can be avoided.
The method provided by the invention aims to improve the robustness of a flight control system, inhibit the jitter phenomenon, realize the rapid convergence of attitude tracking errors, eliminate the negative influence caused by the saturation of the actuator and avoid the energy loss caused by selecting too large control gain under the flight condition of wind disturbance and actuator saturation of the rotor type plant protection unmanned aerial vehicle, and simultaneously can detect the attitude angular velocity signal on line to reduce the manufacturing cost of the rotor type plant protection unmanned aerial vehicle.
Drawings
FIG. 1 is a sequence diagram of the method of the present invention;
FIG. 2 is a control schematic block diagram of the present invention;
FIG. 3 is a graph of the roll angle real-time tracking response of the present invention;
FIG. 4 is a graph of the pitch real-time tracking response of the present invention;
FIG. 5 is a plot of yaw angle real-time tracking response of the present invention;
FIG. 6 is a graph of attitude angle tracking error response of the present invention;
FIG. 7 is a graph of an actual input response of the present invention;
FIG. 8 is a wind disturbance detection error plot for the limited time extended observer of the present invention;
FIG. 9 is a plot of the attitude angular velocity detection of the limited time development observer 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 and fig. 2, the method for controlling attitude tracking of a rotor type plant protection unmanned aerial vehicle based on anti-saturation finite time according to the present invention includes the following steps:
first, acquisition of desired attitude angle data: and acquiring expected attitude angle data input into a flight data memory of the rotor type plant protection unmanned aerial vehicle, wherein the expected attitude angle data is set according to flight attitude requirements of the rotor type plant protection unmanned aerial vehicle.
And step two, acquiring real-time attitude angle data: gather the real-time data of attitude angle through the attitude sensor that rotor formula plant protection unmanned aerial vehicle carried on to with the real-time attitude angle data storage of gathering in flight data memory, attitude angle real-time data includes: roll angle degree, pitch angle degree and yaw angle degree.
Thirdly, establishing a complete posture mathematical model: according to the inherent characteristics of the rotor type plant protection unmanned aerial vehicle and the influence of actuator saturation and wind disturbance factors during flying, a complete attitude mathematical model of the rotor type plant protection unmanned aerial vehicle is established.
It should be particularly noted that, in the long-time flight or take-off phase of the rotor type plant protection unmanned aerial vehicle, the problem of input saturation is easily caused in the actuator, which may damage the stability of the flight system, and the light person may cause the failure of the mission, or even cause the crash accident. In addition, the rotor type plant protection unmanned aerial vehicle can continuously receive the influence of natural wind disturbance when flying, reduces flight system's stability. Therefore, in the mathematical modeling process of the rotor type plant protection unmanned aerial vehicle, the influence of actuator saturation and wind disturbance factors is considered to be beneficial to enhancing the safety and reliability of the system, but the design difficulty of the control system is greatly increased.
The method specifically comprises the following steps of:
(1) based on an Euler Lagrange modeling method, a dynamic mathematical model of the rotary wing type plant protection unmanned aerial vehicle is established according to the inherent characteristics of the rotary wing type plant protection unmanned aerial vehicle and the influence of actuator saturation and wind disturbance factors during flying, and the specific expression of the dynamic mathematical model is as follows:
wherein Ω is [ Ω ]1,Ω2,Ω3]TRepresents an attitude angular velocity vector in the inertial coordinate system, J ═ diag (J)1,J2,J3) Representing a positive definite symmetric inertia matrix, the actual input signal sat (u) ═ sat (u)1),sat(u2),sat(u3)]TIs expressed in the form of
Wherein u ismaxRepresenting the control signal uiUpper bound of (c), sign function sign (u)i) Is defined as
Wind disturbance D ═ D in natural environment1,D2,D3]TIs expressed in the form of
Wherein the content of the first and second substances,
representing the static wind disturbance constant, ajRepresenting the amplitude, w, of a sinusoidal signaljRepresenting the frequency of a sinusoidal signal, bjRepresenting a phase shift of a sinusoidal signal;
symbol (·)×Represents a skew symmetric matrix which satisfies the following form:
(2) based on an Euler Lagrange modeling method, a kinematic attitude mathematical model of the rotary wing type plant protection unmanned aerial vehicle is established, and the mathematical expression of the mathematical model is as follows:
wherein, theta is [ phi, theta, psi ═ phi]TRepresenting an attitude angle vector under a coordinate system of the rotor-type plant protection unmanned aerial vehicle, phi, theta and psi respectively representing a roll angle degree, a pitch angle degree and a yaw angle degree, and defining a matrix W as
W＝R1(θ)R2(φ)
Wherein the content of the first and second substances,
(3) based on rotor formula plant protection unmanned aerial vehicle's dynamics gesture mathematical model and motion gesture mathematical model, obtain rotor formula plant protection unmanned aerial vehicle's complete gesture mathematical model through basic transformation, its mathematical expression as follows:
wherein M is1(Θ) is a symmetric positive definite matrix, whose specific expression is as follows:
wherein the content of the first and second substances,
m11＝Ix,m12＝m14＝0,m13＝-Ixsinθ,m15＝Iycos2φ+Izsin2φ,m16＝(Iy-Iz)cosφsinφcosθ,m17＝-Ixsinθ,m18＝(Iy-Iz) cos phi sin phi cos theta and m19＝Ixsin2θ+Iysin2φcos2θ+Izcos2φcos2θ，
Ix,IyAnd IzRepresenting the coefficients of inertia in the x, y and z axes respectively,
the Coriolis centrifugal matrix is represented, and the specific expression form is as follows:
wherein the content of the first and second substances,
m21＝0,
m24＝-m22,
M3(Θ) represents a rotation matrix, which is expressed in the following concrete form:
fourthly, establishing a complete posture mathematical expansion model: based on the complete attitude mathematical model of the rotor type plant protection unmanned aerial vehicle, the complete attitude mathematical expansion model of the rotor type plant protection unmanned aerial vehicle is established.
The method comprises the following specific steps:
(1) defining an intermediate variable
(2) Complete attitude mathematical model and intermediate variable z based on rotor type plant protection unmanned aerial vehicle1Establishing a complete attitude mathematical development model of the rotor type plant protection unmanned aerial vehicle, wherein the specific expression form is as follows:
wherein the content of the first and second substances,
representing a composite disturbance and
fifthly, designing the finite time expansion observer: designing a finite time expansion observer based on a complete attitude mathematical expansion model of the rotor type plant protection unmanned aerial vehicle;
wherein the content of the first and second substances,
and
denotes z1And z2Is observed value of1，ξ2，σ1And σ2Each represents the gain of a finite time evolution observer, which satisfies the following condition: xi1＞0，ξ2＞0，0.5<σ1<1 and σ2＝2σ1-1；
In a finite time extended observer
And
are respectively defined as
And
what should be particularly noted is that, compared with the conventional observer, the finite time expansion observer designed by the invention not only can effectively compensate the adverse effect caused by the composite disturbance, but also can accurately detect the attitude angular velocity information, and more importantly, can realize the finite time convergence of the observation system and improve the detection performance of the observation system.
Sixthly, designing an auxiliary power system: and introducing a quick nonsingular terminal sliding mode surface and designing an auxiliary power system.
The design of the auxiliary power system comprises the following steps:
(1) introducing a rapid nonsingular terminal sliding mode surface s, wherein the specific expression form is as follows:
wherein, thetae＝[φ-φd,θ-θd,ψ-ψd]T,
m1And m2Is a normal number; l1And p1Is a positive odd constant, and satisfies the condition:
and
in fast nonsingular terminal sliding-form surfaces
And
are respectively defined as
Psi dn1sign psi-psi dT and
(2) an auxiliary power system is designed based on the introduced rapid nonsingular terminal sliding mode surface, and the specific expression form is as follows
Wherein γ represents an auxiliary power system parameter, Δ u-sat (u), ρ1> 1 and ρ2＞0。
What needs to be particularly noted is that the designed fast nonsingular terminal sliding mode surface can improve the convergence speed of the system state after reaching the sliding mode surface and avoid the singularity problem; the designed auxiliary power system does not require that the control signal be bounded and the system is time-limited to converge, which improves the input saturation rejection quality of the flight system; in addition to this, the control parameter ρ may be increased1And ρ2To increase the speed of eliminating input saturation.
And seventhly, designing a finite time attitude tracking controller: according to the introduced fast nonsingular terminal sliding mode surface, the constructed auxiliary power system and the limited time expansion observer, the anti-saturation limited time attitude tracking controller of the rotor type plant protection unmanned aerial vehicle is designed.
The anti-saturation finite time attitude tracking controller of the rotor type plant protection unmanned aerial vehicle is designed as follows:
u＝ua+ub+uc
wherein u isa，ubAnd ucAre respectively
And
Eighth step, the control adjustment of rotor type plant protection unmanned aerial vehicle gesture: and tracking and controlling the attitude of the rotor type plant protection unmanned aerial vehicle through the attitude angle real-time data and the expected attitude angle data.
(1) Inputting attitude angle real-time data in the flight data memory into the finite time expansion observer, and outputting real-time attitude angular velocity information and composite disturbance information observed by the finite time expansion observer;
(2) inputting the observed real-time attitude angular velocity information and the compound disturbance information as well as expected attitude angle data and real-time attitude angle data in a flight data memory into an anti-saturation finite time attitude tracking controller, and outputting a control signal for adjusting the attitude of the plant protection unmanned aerial vehicle and new real-time attitude angle data;
(3) updating and storing the new real-time attitude angle data into a flight data memory;
(4) comparing the difference between the expected attitude angle data and the real-time attitude angle data in the flight database memory:
if the sum of the absolute values of the difference values of the three expected attitude angle degrees and the corresponding real-time attitude angle degrees is greater than 1, controlling the parameter m1And m2The value of (A) is increased by 0.2 at the same time until the sum of the absolute values of the differences is less than or equal to 0.5;
if the sum of the absolute values of the differences is less than or equal to 0.5, the parameter m is controlled1And m2The value of (2) is increased by 0.1 at the same time until the sum of the absolute values of the differences is less than or equal to 0.1;
if the sum of the absolute values of the differences is less than or equal to 0.1, the parameter m is controlled1And m2The value of (A) is increased by 0.05 at the same time until the sum of the absolute values of the differences is less than or equal to 0.01;
and if the sum of the absolute values of the difference values is less than or equal to 0.01, the real-time attitude control performance requirement of the rotary wing type plant protection unmanned aerial vehicle is met.
In order to prove that the tracking error signal of the rotary wing type plant protection unmanned aerial vehicle converges to a bounded region in a limited time range, the following composite Lyapunov function is designedNumber V1：
For the composite Lyapunov function V1Solving a first derivative, and bringing the designed fast nonsingular terminal sliding mode surface, the auxiliary power system and the anti-saturation finite time attitude tracking controller into the first derivative to obtain:
wherein the content of the first and second substances,
and
if case 1 is satisfied:
then the composite Lyapunov function V1First derivative of
Can be changed into
Therein, Ψ1＝min{λmin(H1-H3s-1),σ1-1},Ψ2＝min{λmin(H2),σ2And
according to Lyapunov finite timeThe stability principle can be known, and the composite Lyapunov function V1At a finite time t1Converging to zero. In this case, the finite time t1Is calculated by
If case 2 is satisfied:
then the composite Lyapunov function V1First derivative of
Can be changed into
Therein, Ψ3＝min{λmin(H1),σ1-1},
According to the Lyapunov finite time stability principle, the composite Lyapunov function V1At a finite time t1Converging to zero. In this case, the finite time t2Is calculated by
Combining case 1 and case 2, the fast nonsingular terminal sliding mode surface s is in the limited time t3Converge into the following bounded region Λ:
wherein the finite time t3Is t3＝min{t1,t2}。
Based on designed fast nonsingular sliding mode surface s and bounded region LambdaTracking error of attitude angle thetaeAt a finite time t4Converge to the following bounded area Δ:
wherein the finite time t4Is calculated by
It is to be noted that in particular,
is a gaussian hypergeometric function. If it is not
Middle alpha1，α2And alpha3Are all positive numbers, α4Is a negative number and satisfies the condition alpha3-α2-α1If greater than 0, then
Is a convergence function. Thus, a finite time t can be obtained4Is convergence.
In conclusion, under the influence of wind disturbance and actuator saturation of the rotor type plant protection unmanned aerial vehicle, the designed anti-saturation finite time attitude tracking controller can ensure the finite time stability of the whole closed-loop system, improve the robustness of the system and the anti-saturation capacity of the actuator, accelerate the error convergence speed, effectively inhibit the jitter phenomenon, detect the attitude angular speed on line to reduce the design cost of the rotor type plant protection unmanned aerial vehicle, and simultaneously avoid energy loss caused by selecting too large control gain.
In order to verify the effectiveness of the controller provided by the invention, in a specific embodiment, a rotor type plant protection unmanned aerial vehicle attitude tracking control system is built on a MATLAB/Simulink simulation platform.
In an embodiment of the present invention, the desired attitude angle trajectory is adopted as
(unit: rad),
the inertia matrix is J ═ diag (0.055,0.055,0.098) (unit: kg · m2)，
Wind disturbance in natural environment is
6+3sin4 pi T5+710+3sin pi T4+410,3+2sin3 pi T5+310+6cos pi T4+410T (unit: N.m), and the upper bound value of the actual input signal is umax0.3 (unit: N · m).
In addition, in order to better simulate the actual flight environment, sensor noise was added to the simulation, and the value was set to 0.1. The selected control parameters are as follows: n is1＝2.5，l1＝9,p1＝5,l2＝5,p2＝9,m1＝25,m2＝0.6,h1＝10,h2＝15,σ1＝0.6,σ20.4 and xi1＝ξ235. The sampling time is t ═ 0.01 (unit: s). Fig. 3 is a roll angle real-time tracking response graph, fig. 4 is a pitch angle real-time tracking response graph, fig. 5 is a yaw angle real-time tracking response graph, fig. 6 is an attitude angle tracking error response graph, fig. 7 is an actual input response graph, fig. 8 is a wind disturbance detection error graph of a limited time extended observer, and fig. 9 is an attitude angular velocity detection graph of the limited time extended observer. As can be seen from fig. 3 to 5, under the influence of external wind disturbance and input saturation, the real-time roll angle signal, the real-time pitch angle signal and the real-time yaw angle signal of the rotor-type plant protection unmanned aerial vehicle can accurately track the upper expected roll angle signal, the upper expected pitch angle signal and the upper expected yaw angle signal respectively. From fig. 6, the present invention can be seenThe attitude control method designed by the invention can ensure that the attitude angle error signal is converged to be close to 0. It can be seen from fig. 7 that the actual control signal is within the saturation range (-0.3) and no chattering occurs. It can be seen from fig. 8 that the limited time expansion observer designed by the present invention can ensure that the detection error of the complex disturbance thereof is within a small range. It can be seen from fig. 9 that the finite time expansion observer designed by the present invention can effectively detect the real-time attitude angle signal.
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 (7)
1. A method for tracking and controlling the attitude of a rotary wing type plant protection unmanned aerial vehicle based on anti-saturation finite time is characterized by comprising the following steps:
11) acquisition of desired attitude angle data: acquiring expected attitude angle data input into a flight data memory of the rotor type plant protection unmanned aerial vehicle, wherein the expected attitude angle data is set according to flight attitude requirements of the rotor type plant protection unmanned aerial vehicle;
12) acquiring real-time attitude angle data: gather the real-time data of attitude angle through the attitude sensor that rotor formula plant protection unmanned aerial vehicle carried on to with the real-time attitude angle data storage of gathering in flight data memory, attitude angle real-time data includes: roll angle degree, pitch angle degree and yaw angle degree;
13) establishing a complete posture mathematical model: establishing a complete attitude mathematical model of the rotor type plant protection unmanned aerial vehicle according to the inherent characteristics of the rotor type plant protection unmanned aerial vehicle and the influence of actuator saturation and wind disturbance factors during flying;
14) establishing a complete posture mathematical expansion model: establishing a complete attitude mathematical expansion model of the rotor type plant protection unmanned aerial vehicle based on the complete attitude mathematical model of the rotor type plant protection unmanned aerial vehicle;
15) designing a limited time extended observer: designing a finite time expansion observer based on a complete attitude mathematical expansion model of the rotor type plant protection unmanned aerial vehicle;
16) designing an auxiliary power system: introducing a rapid nonsingular terminal sliding mode surface and designing an auxiliary power system;
17) designing a finite time attitude tracking controller: designing an anti-saturation finite time attitude tracking controller of the rotor type plant protection unmanned aerial vehicle according to the introduced fast nonsingular terminal sliding mode surface, the constructed auxiliary power system and the finite time expansion observer;
18) the control adjustment of rotor type plant protection unmanned aerial vehicle gesture: and tracking and controlling the attitude of the rotor type plant protection unmanned aerial vehicle through the attitude angle real-time data and the expected attitude angle data.
2. The anti-saturation finite time-based attitude tracking control method for rotor-type plant protection unmanned aerial vehicle according to claim 1, wherein the establishment of the complete attitude mathematical model comprises the following steps:
21) based on an Euler Lagrange modeling method, a dynamic mathematical model of the rotary wing type plant protection unmanned aerial vehicle is established according to the inherent characteristics of the rotary wing type plant protection unmanned aerial vehicle and the influence of actuator saturation and wind disturbance factors during flying, and the specific expression of the dynamic mathematical model is as follows:
wherein Ω is [ Ω ]1，Ω2，Ω3]TRepresents an attitude angular velocity vector in the inertial coordinate system, J ═ diag (J)1，J2，J3) Representing a positive definite symmetric inertia matrix, the actual input signal sat (u) ═ sat (u)1)，sat(u2)，sat(u3)]TIs expressed byIn the form of
Wherein u ismaxRepresenting the control signal uiUpper bound of (c), sign function sign (u)i) Is defined as
Wind disturbance D ═ D in natural environment1，D2，D3]TIs expressed in the form of
Wherein the content of the first and second substances,
representing the static wind disturbance constant, ajRepresenting the amplitude, w, of a sinusoidal signaljRepresenting the frequency of a sinusoidal signal, bjRepresenting a phase shift of a sinusoidal signal;
symbol (·)×Represents a skew symmetric matrix which satisfies the following form:
22) based on an Euler Lagrange modeling method, a kinematic attitude mathematical model of the rotary wing type plant protection unmanned aerial vehicle is established, and the mathematical expression of the mathematical model is as follows:
wherein, theta is [ phi, theta, psi ═ phi]TExpressed in rotor type plant protection unmanned planeThe attitude angle vector under the machine coordinate system, phi, theta and psi respectively represent the roll angle degree, the pitch angle degree and the yaw angle degree, and the matrix W is defined as
W＝R1(θ)R2(φ)
Wherein the content of the first and second substances,
23) based on rotor formula plant protection unmanned aerial vehicle's dynamics gesture mathematical model and motion gesture mathematical model, obtain rotor formula plant protection unmanned aerial vehicle's complete gesture mathematical model through basic transformation, its mathematical expression as follows:
wherein M is1(Θ) is a symmetric positive definite matrix, whose specific expression is as follows:
wherein the content of the first and second substances,
m11＝Ix，m12＝m14＝0，m13＝-Ixsinθ，m15＝Iycos2φ+Izsin2φ，m16＝(Iy-Iz)cosφsinφcosθ，m17＝-Ixsinθ，m18＝(Iy-Iz) cos phi sin phi cos theta and m19＝Ixsin2θ+Iysin2φcos2θ+Izcos2φcos2θ，
Ix，IyAnd IzRepresenting the coefficients of inertia in the x, y and z axes respectively,
the Coriolis centrifugal matrix is represented, and the specific expression form is as follows:
wherein the content of the first and second substances,
m21＝0，
m24＝-m22，
M3(Θ) represents a rotation matrix, which is expressed in the following concrete form:
3. the anti-saturation finite time-based attitude tracking control method for the rotary-wing type plant protection unmanned aerial vehicle according to claim 1, wherein the establishment of the complete attitude mathematical expansion model comprises the following steps:
31) defining an intermediate variable
32) Complete attitude mathematical model and intermediate variable z based on rotor type plant protection unmanned aerial vehicle1Establishing a complete attitude mathematical development model of the rotor type plant protection unmanned aerial vehicle, wherein the specific expression form is as follows:
wherein the content of the first and second substances,
representing a composite disturbance and
4. the attitude tracking control method of the anti-saturation finite time-based rotor type plant protection unmanned aerial vehicle according to claim 1, wherein the design finite time expansion observer is as follows:
wherein the content of the first and second substances,
and
denotes z1And z2Is observed value of1，ξ2，σ1And σ2Each represents the gain of a finite time evolution observer, which satisfies the following condition: xi1＞0，ξ2＞0，0.5＜σ1< 1 and σ2＝2σ1-1；
In a finite time extended observer
And
are respectively defined as
5. the attitude tracking control method of the anti-saturation finite time-based rotor type plant protection unmanned aerial vehicle according to claim 1, wherein the design of the auxiliary power system comprises the following steps:
51) introducing a rapid nonsingular terminal sliding mode surface s, wherein the specific expression form is as follows:
wherein, thetae＝[φ-φd，θ-θd，ψ-ψd]T，
m1And m2Is a normal number; l1And p1Is a positive odd constant, and satisfies the condition:
and
in fast nonsingular terminal sliding-form surfaces
And
are respectively defined as
52) an auxiliary power system is designed based on the introduced rapid nonsingular terminal sliding mode surface, and the specific expression form is as follows
Wherein γ represents an auxiliary power system parameter, Δ u-sat (u), ρ1> 1 and ρ2＞0。
6. The attitude tracking control method of the rotor type plant protection unmanned aerial vehicle based on anti-saturation limited time according to claim 1, wherein the anti-saturation limited time attitude tracking controller of the rotor type plant protection unmanned aerial vehicle is designed to:
u＝ua+ub+uc
wherein u isa，ubAnd ucAre respectively
And
wherein the matrix A1And A2Are respectively defined as
And
l2and p2Is a positive odd number and satisfies the condition l2＜p2；h1And h2Is a normal number.
7. The method for tracking and controlling the attitude of the rotor type plant protection unmanned aerial vehicle based on the anti-saturation finite time according to claim 1, wherein the control and adjustment of the attitude of the rotor type plant protection unmanned aerial vehicle comprises the following steps:
71) inputting attitude angle real-time data in the flight data memory into the finite time expansion observer, and outputting real-time attitude angular velocity information and composite disturbance information observed by the finite time expansion observer;
72) inputting the observed real-time attitude angular velocity information and the compound disturbance information as well as expected attitude angle data and real-time attitude angle data in a flight data memory into an anti-saturation finite time attitude tracking controller, and outputting a control signal for adjusting the attitude of the plant protection unmanned aerial vehicle and new real-time attitude angle data;
73) updating and storing the new real-time attitude angle data into a flight data memory;
74) comparing the difference between the expected attitude angle data and the real-time attitude angle data in the flight database memory:
if the sum of the absolute values of the difference values of the three expected attitude angle degrees and the corresponding real-time attitude angle degrees is greater than 1, controlling the parameter m1And m2The value of (A) is increased by 0.2 at the same time until the sum of the absolute values of the differences is less than or equal to 0.5;
if the sum of the absolute values of the differences is less than or equal to 0.5, the parameter m is controlled1And m2The value of (2) is increased by 0.1 at the same time until the sum of the absolute values of the differences is less than or equal to 0.1;
if the sum of the absolute values of the differences is less than or equal to 0.1, the parameter m is controlled1And m2The value of (A) is increased by 0.05 at the same time until the sum of the absolute values of the differences is less than or equal to 0.01;
and if the sum of the absolute values of the difference values is less than or equal to 0.01, the real-time attitude control performance requirement of the rotary wing type plant protection unmanned aerial vehicle is met.
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