CN112327926B - Self-adaptive sliding mode control method for unmanned aerial vehicle formation - Google Patents
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Abstract
The invention discloses a self-adaptive sliding mode control method for nonlinear unmanned aerial vehicle formation based on a neural network and an interference observer, which adopts a nonlinear dynamics model capable of reflecting the authenticity of the nonlinear unmanned aerial vehicle formation. In order to enable unmanned aerial vehicle formation to have good tracking performance when a task is executed, the actual flight running condition of the unmanned aerial vehicle is analyzed, and the adverse effects of the uncertainty of the state parameters of an actuator of an unmanned aerial vehicle model and the external electromagnetic wave interference on the tracking performance are considered. An adaptive sliding mode controller is designed, and a radial basis function neural network approximation and disturbance observer approximation are adopted to respectively approximate and compensate the uncertainty of a model and the influence of external disturbance. Meanwhile, the global stability of the formed closed loop system under the action of the controller is ensured, and the method has certain advantages in practical application through simulation experiments.
Description
Technical Field
The invention relates to the field of aviation unmanned aerial vehicle control, in particular to a problem of adaptive unmanned aerial vehicle formation accurate track tracking control.
Background
In recent years, unmanned aerial vehicle control technology has made remarkable progress, and unmanned aerial vehicle formation is widely used in various fields to complete complex and difficult tasks. Particularly plays a great role in high-risk work or military applications, such as mountain reconnaissance, cable patrol, military rescue and the like. Therefore, there is a fundamental problem to be solved in completing these tasks, namely, how to implement the trajectory tracking control of the unmanned aerial vehicle formation with the highest accuracy. Meanwhile, the unmanned aerial vehicle operates in a formation under a complex environment, and the problems of uncertainty of state parameters of a system executor and external interference (air flow, external electromagnetic waves and the like) exist, so that the control performance is greatly reduced. Therefore, it is of practical significance to take advanced controller design methods for solving such problems.
The patent CN110286694a discloses a multi-leader distributed unmanned aerial vehicle formation cooperative control method, which mainly contributes to providing an algorithm for realizing consistent formation flight of unmanned aerial vehicles in a communication delay environment, but the problem of uncertain items and external interference of a system is not solved. The patent CN107807663A discloses an unmanned aerial vehicle formation maintaining control method based on self-adaptive control, aims at an unmanned aerial vehicle formation system, linearizes a nonlinear model of an unmanned aerial vehicle based on a small disturbance principle, and establishes a self-adaptive control system reference model, but the model linear processing method is too ideal and does not accord with the actual running condition of the unmanned aerial vehicle, so that a certain deviation exists in track tracking of the unmanned aerial vehicle formation, and meanwhile, a corresponding solution is not provided for factors such as system uncertainty, interference and the like.
At present, because the control performance of a nonlinear system is greatly influenced by model uncertainty, interference and the like, many scholars at home and abroad have conducted intensive research on the problems, and the combination of an interference observer and a neural network is proved to be capable of effectively and approximately compensating uncertainty items and external interference, and meanwhile, stability and robustness in the global range of the system can be ensured by adopting a sliding mode controller. In addition, the method has no detailed report on other published materials and documents based on unmanned aerial vehicle formation control.
Disclosure of Invention
In view of the defects in the prior art, the invention provides an unmanned aerial vehicle formation self-adaptive sliding mode control method based on a neural network and an interference observer, which comprises the following steps:
step 1, establishing an ith unmanned aerial vehicle power model,
wherein i=1,..n represents the i-th unmanned aerial vehicle, (x) i ，y i ，z i ) Representing displacement distances of the unmanned aerial vehicle in three directions in three dimensions, V i Representing the flight rate, gamma i Represent the flying course angle, χ i Representing the pitch angle of flight.
Wherein T is i For engine propulsion, D i And L i Respectively, flight resistance and aircraft lift, m i G is gravity acceleration, phi is the mass of the machine body i Inclination angle.
Step 2, converting the unmanned aerial vehicle dynamic model in the step 1 into a state space equation, and introducing an uncertain term and interference of a system, wherein the nonlinear model can be described as:
wherein F is i ＝[T i ，L i sinφ i ，L i cosφ i ] T Defined as the control input of the system, p i ＝[x i ，y i ，z i ] T Defined as the spatial location of the drone,defined as the spatial rate of the drone. d, d mi Status uncertainty item, d, representing unmanned aerial vehicle model si Representing the external electromagnetic wave interference term. And wherein:
ε i ＝[0 0 g] T
and 3, mainly designing a self-adaptive sliding mode controller to realize tracking control of the target. The specific process is as follows:
firstly, describing the realization of a system, wherein the unmanned aerial vehicle is required to meet a required formation structure in the formation maneuvering process, and in the invention, the preset position of an ith unmanned aerial vehicle meets the following conditions:
wherein the method comprises the steps ofRepresenting the desired formation centre position, +.>The position of the drone relative to the formation center is indicated, and the controller targets set below are precise trajectory tracking controls that maintain the drone in the desired position.
The graph theory is a very important part in formation flight, the undirected graph G= (v, E, A) is adopted in the invention, v represents a set of n non-empty nodes, E is a set of ordered edge pairs of the nodes, and the adjacent Laplace matrix A meets the following conditions:
wherein:
the known dispersion synchronization errors of the ith unmanned aerial vehicle are as follows:
wherein the method comprises the steps ofa ij For Laplace adjacency matrixElements in A.
Defining a sliding mode surface according to tracking errors:
definition sat(s) i ) The buffeting phenomenon can be effectively avoided as a saturation function, and the following conditions are satisfied:
is a positive boundary layer.
And 4, performing approximate compensation on the model uncertain item parameters by utilizing RBFNN, and designing an interference observer to solve the interference problem.
First, the buffeting phenomenon can be avoidedRepresenting RBFNN output value d mi Can be expressed as:
wherein the method comprises the steps of
h i (p)＝[h i (p)] T
Representing the estimation error of RBFNN, which satisfies:
the RBFNN adaptation law can then be defined as:
representing d in disturbance observer si Wherein the disturbance observer is designed to compensate for the disturbance term, can be expressed as:
wherein the method comprises the steps of
As a reversible constant matrix, m i And L i Is constant, thus P can be obtained i Is the derivative of:
as an estimation error of external disturbance, its derivative form can be expressed as:
the observed error function can be obtained from the above expression as:
due to d mi And d si Is bounded and therefore mu i Is bounded, and the solution is obtained:
it is known that the disturbance observation error is limited when t→infinity.
Combining with an unmanned aerial vehicle dynamic model to obtain a self-adaptive control law F i ：
And 5, verifying the stability of closed-loop control of the unmanned aerial vehicle formation system.
According to the described sliding mode self-adaptive control method for unmanned aerial vehicle formation, the stability of unmanned aerial vehicle system state and uncertain item and interference item estimation error and the signal limitation need to be proved;
selecting Lyapunov function V i The method comprises the following steps:
V i ＝V mi +V di
wherein the method comprises the steps of
Wherein the method comprises the steps ofV i The derivative form of (a) is:
the equivalent transformation is not difficult to obtain:
let xi i Satisfy the following requirementsConsider ||s i The I is less than or equal to delta and S i Both cases of || > Δ can be derived:
wherein the method comprises the steps ofAnd r is a positive definite matrix, the known interference observation error is bounded, so the self-adaptive sliding mode controller is asymptotically stable to the system state and uncertainty and the estimation error of interference.
The invention considers the uncertainty factor of the model state parameter and the external disturbance at the same time, and the adopted nonlinear model is more in line with the actual running condition of the unmanned aerial vehicle than the traditional model, and has more advantages in practice.
Drawings
FIG. 1 is a block diagram of an adaptive sliding mode unmanned aerial vehicle formation controller based on RBFNN and disturbance observer
Fig. 2 is a simulation diagram of position tracking performance of unmanned aerial vehicle formation
Fig. 3 is a rate tracking performance simulation graph of unmanned aerial vehicle formation
Fig. 4 is a position tracking error simulation diagram of unmanned aerial vehicle formation
Fig. 5 is a rate tracking error simulation diagram of unmanned aerial vehicle formation
Detailed Description
The invention will be explained in further detail below with reference to the drawings and embodiments. The specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order that those skilled in the art can better understand the implementation of the present invention, the present invention will employ Matlab2014a software to simulate unmanned aerial vehicle formation tracking control to verify its reliability. We consider the situation of four unmanned aerial vehicle formations.
The mass of the unmanned aerial vehicle is respectively m 1 ＝1.5kg，m 2 ＝2kg，m 3 ＝1.8kg，m 4 =1.6 kg. Wherein the resistance experienced by the unmanned aerial vehicle is expressed as:
wherein g=9.81 kg/m 2 For gravity, ρ=1.225 kg/m 3 For air density, wing area s=1.37 m 2 ，C D0 =0.02 is zero lift drag coefficient, k d =0.1 is the inductive drag coefficient, k n =1 is the payload factor validity, V wi For gusts, its model can be expressed as:
the initial positions and speed states of the four unmanned aerial vehicles are shown in table 1:
| unmanned aerial vehicle numbering | x/m | y/m | z/m | Vx(m/s) | Vy(m/s) | Vz(m/s) |
| 1 | -56 | 60 | 580 | 10 | 15 | 18 |
| 2 | -60 | 58 | 576 | 6 | 12 | 16 |
| 3 | -58 | -58 | 420 | 8 | 15 | 17 |
| 4 | 56 | 60 | 400 | 4 | 9 | 14 |
The desired location and rate of the drone queuing center is expressed as:
simultaneously, the positions of the four unmanned aerial vehicles from the formation center are all arranged according to a preset formation, and the four unmanned aerial vehicles are operated cooperatively under control input, wherein the control input F of the ith unmanned aerial vehicle i The method comprises the following steps:
on the premise of meeting the stability and the limitation of the closed-loop system, constant parameters in the controller are respectively set as follows: k (k) i ＝2，k i0 ＝3，ξ i =4; parameters in the saturation function are set as: delta = kappa = 0.1, zeta = 4; other parameters were taken separately: delta i ＝2，λ i ＝0.5。
External interference can be modeled as:
by designing the system model state parameter uncertainty term to prove the robustness of the controller, it can be expressed as:
simulation results show that unmanned aerial vehicle formation simulation results are shown in figures 2-5. As can be seen from fig. 4, the position tracking error of the unmanned aerial vehicle eventually converges to around zero, indicating that the control target is satisfied. Meanwhile, as shown in fig. 5, the speed tracking errors of the four unmanned aerial vehicles in three directions are rapidly attenuated to be near zero within 5 seconds, so that the convergence speed is better in performance while stability is met. Fig. 2-3 show the control states of the positions and the speed tracks of the four unmanned aerial vehicles at the respective terminal moments, which meet the expectations.
The self-adaptive sliding mode controller provided by the invention can effectively control uncertainty and interference of a system, can well realize formation flying target control, and has good tracking performance.
Finally, it is not intended that the present invention be limited to the specific embodiments disclosed as the best mode contemplated for carrying out the present invention, but rather that the present invention shall be construed according to the appended claims.
Claims (4)
1. A self-adaptive sliding mode control method for nonlinear unmanned aerial vehicle formation based on a neural network and an interference observer comprises the following steps:
step 1, establishing an ith unmanned aerial vehicle power model;
step 2, converting the unmanned aerial vehicle dynamic model in the step 1 into a state space equation, and introducing uncertain items and interference of a system;
step 3, designing an adaptive sliding mode controller to obtain an adaptive control law;
step 4, adopting RBFNN to approximately compensate the model uncertain item parameters, and designing an interference observer to solve the interference problem;
step 5, verifying the stability of closed-loop control of the unmanned aerial vehicle formation system;
firstly, describing the realization of a system, wherein the unmanned aerial vehicle is required to meet a required formation structure in the formation maneuvering process, and in the invention, the preset position of an ith unmanned aerial vehicle meets the following conditions:
wherein the method comprises the steps ofRepresenting the desired formation centre position, +.>The position of the unmanned aerial vehicle relative to the formation center is represented, and the following set controller targets are accurate track tracking control for enabling the unmanned aerial vehicle to keep a required position;
the graph theory is a very important part in formation flight, the undirected graph G= (v, E, A) is adopted, v represents a set of n non-empty nodes, E is a set of ordered edge pairs of the nodes, and the adjacent Laplace matrix A meets the following conditions:
wherein:
the known dispersion synchronization errors of the ith unmanned aerial vehicle are as follows:
wherein the method comprises the steps ofa ij Is an element in the laplace adjacency matrix a;
defining a sliding mode surface according to tracking errors:
definition sat(s) i ) The buffeting phenomenon can be effectively avoided as a saturation function, and the following conditions are satisfied:
for positive boundary layers, κ and ζ are positive tunable parameters.
2. The adaptive sliding mode control method for nonlinear unmanned aerial vehicle formation based on the neural network and the interference observer according to claim 1, wherein the power model of the ith unmanned aerial vehicle in the step 1 is as follows:
wherein i=1,..n represents the i-th unmanned aerial vehicle, (x) i ，y i ，z i ) Representing position coordinates of the unmanned aerial vehicle in three directions in a three-dimensional space, V i Representing the flight rate, gamma i Represent the flying course angle, χ i Representing the flying pitch angles, respectively:
wherein T is i For engine propulsion, D i And L i Respectively, flight resistance and aircraft lift, m i G is gravity acceleration, phi is the mass of the machine body i Inclination angle.
3. The adaptive sliding mode control method for nonlinear unmanned aerial vehicle formation based on the neural network and the interference observer according to claim 2, wherein the nonlinear model of uncertainty and interference terms introduced into the system in step 2 can be described as:
wherein F is i ＝[T i ，L i sinφ i ，L i cosφ i ] T Defined as the control input of the system, p i ＝[x i ，y i ，z i ] T Defined as the spatial location of the drone,defined as the space velocity of the unmanned aerial vehicle, d mi Status uncertainty item, d, representing unmanned aerial vehicle model si Representing an ambient interference term, wherein:
ε i ＝[0 0 g] T ，
4. the adaptive sliding mode control method for forming a nonlinear unmanned aerial vehicle based on a neural network and an interference observer according to claim 3, wherein the design process of the sliding mode controller in the step 3 is as follows:
the known dispersion synchronization errors of the ith unmanned aerial vehicle are as follows:
wherein the method comprises the steps ofa ij Is an element in the laplace adjacency matrix a;
defining a sliding mode surface according to the synchronization error:
combining with an unmanned aerial vehicle dynamic model to obtain a self-adaptive control law F i ：
Wherein sat(s) i ) The buffeting phenomenon can be effectively avoided as a saturation function, and the following conditions are satisfied:
for positive boundary layers, κ and ζ are positive tunable parameters.
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