CN114815861A - Fault-tolerant flight control method based on space-time radial basis function neural network - Google Patents
Fault-tolerant flight control method based on space-time radial basis function neural network Download PDFInfo
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Abstract
The invention discloses a novel time-space radial basis function neural network fault-tolerant control method with a new fusion kernel for faults of an actuator of a multi-rotor aircraft. A novel radial basis function neural network with space-time information expansion is utilized to process signals with time dynamic characteristics and space nonlinearity, and the advantage of higher signal estimation precision is achieved compared with the traditional radial basis function neural network for processing one-dimensional signals. Aiming at the problems of uncertainty of a multi-rotor aircraft model, actuator faults and gust interference, the parameter output of a time-space radial basis function neural network is used for designing a fault-tolerant control law of an integral backstepping sliding mode controller, so that the robust control of a system is improved, and the track of a fault aircraft can turn to a balance point in a short time. The invention is used for fault-tolerant flight control of an aircraft containing multi-rotor aircraft multi-actuator faults, model uncertainty and gust disturbance.
Description
Technical Field
The invention relates to a fault-tolerant flight control method based on a space-time radial basis function neural network, and belongs to the technical field of fault-tolerant control of an uncertain nonlinear system.
Background
As the state of the art in aircraft and spacecraft development has increased, many highly integrated, engineered aircraft have been manufactured and are widely used in various industry areas of human development. Under the background of the rapid development of information technology, various aircrafts are visible everywhere, and are applied to the fields of agriculture, security monitoring, material transportation, storage inspection, civil aerial photography and the like, but not only used in the fields of national defense, civil aviation, disaster relief and the like. In recent years, as the number of tasks and working environments performed by lightweight multi-rotor aircraft has increased, the component structures thereof have also become more complex. They are typically composed of various subsystems such as navigation systems, power systems, control systems, functional components, and the like. Due to the requirements for high performance and intelligent functions of the aircraft, the safety and reliability of the flight of the aircraft under the conditions of faults or performance degradation caused by collision, motor entrainment into particle objects, electromagnetic interference, temperature and the like are generally considered during the design of the multi-rotor aircraft.
Since multi-rotor aircraft are typically under-actuated systems, maintaining stability performance of the attitude control subsystem in the event of a fault is a major issue of research by many scholars and researchers. Generally, a multi-rotor aircraft is powered by a plurality of rotors, and compared with an aircraft in the form of a fixed wing or a single propeller, when the multi-rotor aircraft is interfered by the outside world, collided or fails to lose power, the multi-rotor aircraft is difficult to realize gliding or reduce the falling speed by utilizing a variable pitch by depending on the body structure of the multi-rotor aircraft. In recent years, researchers have proposed methods such as fault detection and isolation, robust control, reconfigurable control, artificial intelligence, predictive analysis and the like for improving the control performance of aerospace vehicles. However, as the integration level and complexity of the aerospace engineering system are increased, the number of nonlinear parameters to be considered and designed is increased, and particularly after a fault occurs, the uncertainty and disturbance of a model can generate more adverse effects on the system. Therefore, the research on the fusion of the intelligent control under the complex system and the traditional nonlinear control method, especially the stability research on the attitude system under the aircraft fault state, is a challenging and promising task, which is also a hot spot of research of many researchers in recent years.
Because many rotor unmanned aerial vehicle when the trouble condition takes place, if the discernment trouble that can not be timely accurate, just can directly lead to unmanned aerial vehicle to take place the crash. An effective method for improving the controllability of the system after the system fails is to use a controller with fault diagnosis and fault tolerance as a solution for the failed system. With the development of the field of fault-tolerant control, many researchers have attempted to make attempts to fault-tolerant control algorithms in the event of actuator failure. Passive fault-tolerant control, also known as passive fault-tolerant control, researchers can exploit a class of predictable faults to achieve a limited fault-tolerance of the control system. In contrast, the active fault tolerance method can detect and identify a fault occurring in the system, and can achieve better system control performance through a designed corresponding controller. Sliding mode control techniques can be used to design active fault-tolerant schemes that can achieve compensation for actuator faults. In practice the model uncertainty of multi-rotor drones is widespread in engineering applications. Along with the increase of many rotor unmanned aerial vehicle load equipment, many rotor unmanned aerial vehicle's system model is more complicated, and the non-linear parameter also increases in the model thereupon. Neural networks are ideal choices considered to solve function approximations in complex nonlinear systems and find application in various intelligent control systems.
Therefore, the invention combines the advantages of the radial basis function neural network with space-time information expansion and the backstepping sliding mode controller, fully utilizes the capability of the space-time radial basis function neural network approaching fusion parameters containing nonlinear terms and error terms to process the system fault and modeling uncertainty aiming at the conditions of deviation fault and gain fault existing in an actuator and gust disturbance of an aircraft, utilizes the self-adaptive backstepping sliding mode controller as the integral control of the system, and further optimizes the control response of the system.
At present, many scholars propose a novel control method of the radial basis function neural network, but few more intensive researches are carried out on the problem that the system has a fault condition. Therefore, the invention is applied to the fault-tolerant control of the multi-rotor aircraft on the basis of the space-time radial basis function neural network.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems of deviation fault and gain fault of an actuator of a multi-rotor aircraft, the conditions of model uncertainty and gust disturbance in a system are considered, and a novel active fault-tolerant control method based on the combination of a self-adaptive space-time radial basis function neural network and a backstepping sliding mode controller is designed. In the method, identification of fusion parameters containing faults and uncertainties is processed by using a radial basis function neural network with time and space information expansion; and using the network for estimating the gust disturbance parameters; a fusion kernel with self-adaptive parameter adjustment is designed, so that the accuracy of the neural network estimation parameters is improved; a backstepping sliding mode controller is used as the overall control of the system, and estimation parameters of the neural network are introduced into the backstepping sliding mode controller, so that a fault-tolerant control law is designed, and the overall robustness and anti-interference performance are guaranteed.
The technical scheme is as follows: a novel time-space radial basis function neural network fault-tolerant control method with a new fusion kernel for multi-rotor aircraft actuator faults is characterized in that: 1) the active fault-tolerant control method can be adapted to a multi-rotor flight control system with an actuator fault and an uncertain model at the same time, and the fault-tolerant controller can resist gust disturbance and has a fault-tolerant control effect under a time-varying fault, so that the set parameters can be reduced by adaptively adjusting an uncertain item and a disturbance parameter, and the robustness of the system is improved; 2) the method adopts a novel fusion kernel space-time radial basis function neural network, can quickly estimate fault data and uncertainty parameter values, uses fault flight data for neural network weight parameter training, estimates test data with larger fault values by using a trained model, further carries out iterative training, improves the accurate estimation performance of the network on the fault data, and improves the fault tolerance; 3) the backstepping sliding mode controller is applied to the overall stability control of the system, and the fault value of the actuator can be quickly and accurately estimated by the flight fault-tolerant controller. The method comprises the following specific steps:
step 1) establishing an affine nonlinear system fault model:
step 1.1) for a multi-rotor aircraft in a normal state the following affine non-linear model can be considered,
wherein the state vector
Can be obtained by measurement and calculation, and the system modeling parameter is f (x) epsilon R 12 And g (x) ε R 12×4 ，u(t)∈R 4 The system input quantity. The meaning of the parameter corresponding to the state vector is: position parameter [ x y z ] under inertial coordinate system]Linear velocity of line
Roll angle phi, pitch angle theta, yaw angle psi, corresponding angular velocity
The attitude, angular velocity, position and speed of the multi-rotor aircraft can be measured and calculated through a gyroscope, a magnetometer and other sensor data, and aircraft state data can be obtained. u ═ u 1 u 2 u 3 u 4 ] T Wherein u is 1 For four-rotor lift control, u 2 Inputting control quantity u for roll 3 Inputting control amount for pitch, u 4 The control amount is input for yaw.
Step 1.2) for the definition of force rectangular type of the multi-rotor aircraft in the wind interference environment, the method takes a representative four-rotor aircraft model as an example to represent the following wind interference mathematical model,
wherein d is 1 、d 2 、d 3 、d 4 The wind disturbance quantities of the aircraft in the vertical direction, the transverse rolling shaft, the pitching shaft and the yawing shaft are respectively, and the acting force of the single propeller subjected to wind disturbance is
Wherein ρ, A i Air density and propeller rotation area, V p，i The induced wind speed and condition parameters of the propeller without wind disturbance
V gust，i For gust disturbance terms, m is the aircraft mass, J XX 、J YY 、J ZZ The inertia constants of the aircraft in the roll, pitch and yaw directions are respectively.
Step 1.3) for a multi-rotor aircraft with actuator gain faults and deviation faults, selecting an actuator fault model,
u F ＝α(t)u+τ(t) (3)
wherein α (t) is (0, 1)]τ (t) is a parameter that includes an actuator additive fault. u. of F The input variable of the multi-rotor aircraft affine nonlinear system containing the actuator gain fault and the deviation fault.
Step 1.4) taking into account the conditions existing in the above steps, for a multi-rotor aircraft affine nonlinear system with gust disturbances, actuator gain faults and deviation faults, the mathematical model thereof is represented as
Wherein f is 0 (x) For the system containing the determination of attitude angular velocity and modeling parameters, g 0 (x) For modeling parameter terms, f 0 (x) And g 0 (x) Can be obtained by sensor measurement and experimental data, and Δ f (x) and Δ g (x) are parameter error terms existing in modeling. To facilitate fault-tolerant control law design in a system, parameters are defined
An affine nonlinear system containing gust disturbance, actuator fault and model uncertain parameters can be obtained as
Step 2) designing a space-time radial basis function neural network identifier based on the self-adaptive fusion kernel:
step 2.1) designing a space-time radial basis function neural network
Radial basis function neural networks are generally composed of an input layer, a hidden layer, and an output layer. The space-time radial basis function has the advantages of time dynamic characteristics and space nonlinear (complex) signals, and is provided on the basis of a traditional radial basis function neural network method, and the specific design is as follows:
first layer (input layer): according to the data of the system state variables and the output data of the controller, the input signals of the input layer are aircraft attitude angle, angular velocity and control law signals which can be expressed as aircraft attitude angle, angular velocity and control law signals
Due to the time domain expansion required on the conventional radial basis function neural network, the sampling signal x (t-1) at the previous moment x (t) is added to the input of the network. Thus, the input to the spatio-temporal radial basis function neural network may be expressed as [ x (t) x (t-1)] T Wherein x (t) e R 10 ，x(t-1)∈R 10 。
Second layer (hidden layer): in the design of the nonlinear hidden layer, time expansion is carried out on a kernel space of a neural network in signal processing, and two parallel time layers are designed to correspond to two groups of moments in an input layer and are used for mapping dynamics and nonlinear characteristics of a signal in time. Psi (i，t) The method is a basic function of a hidden layer of a neural network, and adopts a common Gaussian kernel function as follows:
wherein, the first and the second end of the pipe are connected with each other,
is the central value of the neural network, and σ is the standard deviation.
Third layer (output layer): the output layer adopts linear combination output. Method for estimating parameters by considering space-time radial basis function neural network
Defining the expected value of the kth target signal as d (k), and the error between the network estimated value and the network expected value as
The corresponding cost function is:
the overall mapping of the spatio-temporal radial basis function neural network employed herein is given as follows:
wherein the content of the first and second substances,
w (i，t) (k) for the current weight value from hidden layer to output layer, p is the number of neurons in the hidden layer of the neural network, T is the truncation time, and b (k) is the bias term for the output neurons. w is a (i，t) (k) And b (k) will be updated at each iteration of learning.
The gradient descent learning algorithm for designing the radial basis function neural network based on the space-time expansion comprises the following steps:
wherein, w (i，t) (k +1) is the updated weight value, η step In order to learn the step size of the step,
for conventional derivatives, the estimation can be done by the differential chain rule
For the convenience of calculation, the partial derivative can be further taken as:
substituting the formula (10) into the formula (9) can obtain
w (i，t) (k+1)＝w (i，t) (k)+η step ψ (i，t) (x，c (i，t) )e(k) (11)
Similarly, the learning rule of b (k) is designed as follows:
b(k+1)＝b(k)+η step e(k) (12)
step 2.2) design of novel adaptive fusion nucleus
In order to improve the estimation precision of the radial basis function neural network, the method optimizes the requirement of the initial weight value of the space-time radial basis function neural network by utilizing the advantage that Euclidean and cosine distance measurement can adaptively adjust the weight of the kernel, and a new fusion kernel is expressed as follows:
ψ i (x，c (i，t) )＝Υ 1 ψ i1 (||x-c (i，t) ||)+Υ 2 ψ i2 (x.c (i，t) ) (13)
wherein the Gaussian kernel function ψ i1 (||x-c (i，t) I | I) is Euclidean kernel, cosine kernel ψ i2 (x.c (i，t) ) Can be expressed as:
wherein, iota → 0 + Is a normal amount. Novel parameter gamma in fused nucleus 1 And upsilon 2 Weight coefficients corresponding to Euclidean kernel and cosine kernel respectively, and existing | γ 1 (k)|+|Υ 2 (k) 1. Therefore, the cost function in (4.14) needs to be redefined as:
in order to obtain the learning rule in the new kernel, the weight coefficient γ is designed with reference to the design method in formula (11) 1 And upsilon 2 The gradient learning descent algorithm is as follows:
similarly, the chain derivative method can be used to obtain
Accordingly, γ may be obtained after taking the partial derivative of the formula 1 (k) The update rule of (1) is:
similarly, γ 2 (k) The update rule of (1) is:
step 3) design of fault-tolerant controller
Step 3.1) defining the reference input signal of the system controller as x according to the mathematical model of the affine nonlinear system ref The system tracking error is defined as:
wherein epsilon 1 And ε 2 Respectively, the tracking errors of the attitude angle and the angular speed of the system, and mu is the introduced virtual control quantity. Defining virtual control quantities
(κ 1 > 0), further, it can be deduced
From this, ε can be derived 2 Another expression form of (A) is
In order to enable the system to better realize the sliding mode, the integral sliding mode surface of the system is selected as follows:
and 3.2) in order to design a control law finally to stabilize the system, an adaptive method is adopted in the method to estimate unknown parameters in the system. The self-adaptive law for defining the related parameters of the uncertainty term, the gust disturbance term and the fault parameter term involved in the control law can be designed as follows:
wherein, γ i (i ═ 1, …, 4) is a normal number, ξ > 0, and the parameters
Are respectively the output of the neural network, and exist
And, the parameters
Disturbance d for gusts w Is alternatively represented, i.e.
For parameter
In other words, a in different value ranges has the following inequality relationship
Meanwhile, in order to satisfy the system stability condition, it needs to be defined as
Step 3.3) designing a complete fault-tolerant control law for a nonlinear system with actuator faults, modeling uncertainty and gust disturbance according to the parameter settings
Wherein iota is normal number and kappa is present 3 ＝(1-h 1 )ι|s|。
Has the advantages that: aiming at the situation that the multi-rotor aircraft may have actuator gain faults, deviation faults and gust disturbance in various complex environments, the modeling error item in the system modeling process is considered, and the method designs a novel time-space radial basis function neural network fault-tolerant control method with a new fusion kernel for the actuator faults of the multi-rotor aircraft. The designed space-time radial basis function neural network utilizes the concept of space-time orthogonality, and can approach nonlinear parameter items containing faults and modeling errors in the system, so that the designed fault-tolerant flight controller can actively compensate the adverse effect of the faults of the actuator on the aircraft, can estimate wind disturbance parameters, and improves the disturbance resistance of the aircraft. A self-adaptive backstepping sliding mode controller is used in the design, the system robustness is enhanced, and the finally completed fault-tolerant flight controller can still stably fly under the condition that an actuator fails. The method has the following advantages;
(1) considering that the traditional space-time radial basis function has higher prediction precision in processing one-dimensional data, but has lower precision in processing time signal sequences of time domain signals and space signals, a novel space-time radial basis function neural network structure with a self-adaptive fusion kernel is provided; the time signal (dynamics) and nonlinear (complexity) prediction precision is improved by utilizing the space-time radial basis function neural network; the method utilizes the reciprocating characteristics of Euclidean kernels and cosine kernels, and is superior to the prediction precision of artificial fusion kernels in three main estimation problems of nonlinear system identification, mode classification and function approximation. The framework utilizes a gradient descent method to dynamically adjust the weights of the participating kernels, thereby reducing the need for predetermined weights.
(2) An active fault-tolerant control scheme is provided, and the unmanned aerial vehicle flight control system with actuator faults and uncertain models can be adapted simultaneously. In addition, the fault-tolerant controller can resist gust disturbance and has a good fault-tolerant control effect under time-varying faults. When the system has actuator failure or interference, the adaptive backstepping sliding mode controller only needs to adaptively adjust the uncertainty item and the disturbance parameter to enable the system to reach the sliding mode surface, thereby reducing the set parameters and improving the robustness of the system.
(3) The radial basis function neural network in the method adopts a weight updating rule with rapid gradient descent, and can rapidly estimate fault data and uncertainty parameter values. In the method, the fault flight data is used for neural network weight parameter training, the trained model is used for estimating test data with a larger fault value, iterative training is further performed, the accurate estimation performance of the network on the fault data is improved, and the fault tolerance is improved.
(4) Compared with a fault observer based on a model, the method aims at the change of nonlinear term parameters in the model, estimates parameter values by utilizing a space-time radial basis function neural network with rapid gradient descent, and simultaneously applies a backstepping sliding mode controller to the overall stability control of the system, thereby realizing the rapid and accurate estimation of nonlinear fusion parameters by the flight fault-tolerant controller.
Drawings
FIG. 1 is a flow chart of the system operation of the method of the present invention;
FIG. 2 is a block diagram of a platform of a test and experiment system;
FIG. 3 is a schematic view of a quad-rotor aircraft model and its coordinate system;
FIG. 4 is a mean square error test curve;
FIG. 5 is a prediction of spatio-temporal radial basis function neural networks and conventional radial basis function neural networks;
FIG. 6 is a prediction error for a spatio-temporal radial basis function neural network and a conventional radial basis function neural network;
FIG. 7 is an attitude tracking angle of the Qball-X4 UAV without external wind disturbance and actuator failure;
FIG. 8 shows attitude tracking errors of the Qball-X4 UAV without external wind disturbance and actuator failure;
FIG. 9 is an attitude tracking angle of the Qball-X4 UAV with external wind disturbance and without actuator failure;
FIG. 10 shows attitude tracking errors of a Qball-X4 UAV with external wind disturbance and without actuator failure;
FIG. 11 is an attitude tracking angle of the Qball-X4 UAV with external wind disturbance and actuator failure;
FIG. 12 shows attitude tracking errors of a Qball-X4 UAV with external wind disturbances and actuator failure;
FIG. 13 is a neural network recognizer parameter estimation.
Detailed Description
The invention is further explained below with reference to the drawings.
As shown in fig. 1, considering the situation that a nonlinear system with uncertainty has an actuator fault and external wind disturbance, a space-time radial basis function neural network is combined with an adaptive backstepping sliding mode controller, the sliding mode controller is used for realizing the global stability of the system, the state data of an aircraft is used for the input of the neural network, the output of the aircraft is used for fault-tolerant processing in the system according to the characteristics of rapidity and accuracy of approximation of the space-time radial basis function neural network to the nonlinear function, and finally the design of the fault-tolerant flight controller is completed. The method comprises the following specific steps:
step 1) establishing an affine nonlinear system fault model:
step 1.1) for a multi-rotor aircraft in a normal state the following affine non-linear model can be considered,
wherein the state vector
Can be obtained by measurement and calculation, and the system modeling parameter is f (x) epsilon R 12 And g (x) ε R 12×4 ，u(t)∈R 4 The system inputs the quantity. The meaning of the parameter corresponding to the state vector is: position parameter [ x y z ] under inertial coordinate system]Linear velocity of line
Roll angle phi, pitch angle theta, yaw angle psi, corresponding angular velocity
The attitude, angular velocity, position and speed of the multi-rotor aircraft can be measured and calculated through a gyroscope, a magnetometer and other sensor data, and aircraft state data can be obtained. u ═ u 1 u 2 u 3 u 4 ] T Wherein u is 1 For four-rotor lift control, u 2 Inputting control quantity u for roll 3 For pitch input of control quantity, u 4 The control amount is input for yaw.
Step 1.2) for the definition of force rectangular type of the multi-rotor aircraft in the wind interference environment, the method takes a representative four-rotor aircraft model as an example to represent the following wind interference mathematical model,
wherein d is 1 、d 2 、d 3 、d 4 The wind disturbance quantities of the aircraft in the vertical direction, the transverse rolling shaft, the pitching shaft and the yawing shaft are respectively, and the acting force of the single propeller subjected to wind disturbance is
Wherein ρ, A i Air density and propeller rotation area, V p，i The induced wind speed and condition parameters of the propeller without wind disturbance
V gust，i For gust disturbance terms, m is the aircraft mass, J XX 、J YY 、J ZZ The inertia constants of the aircraft in the roll, pitch and yaw directions are respectively.
Step 1.3) for a multi-rotor aircraft with actuator gain faults and deviation faults, selecting an actuator fault model,
u F ＝α(t)u+τ(t) (3)
wherein α (t) ∈ (0, 1)]τ (t) is a parameter that includes an actuator additive fault. u. u F The input variable of the multi-rotor aircraft affine nonlinear system containing the actuator gain fault and the deviation fault.
Step 1.4) taking into account the conditions existing in the above steps, for a multi-rotor aircraft affine nonlinear system with gust disturbances, actuator gain faults and deviation faults, the mathematical model thereof is represented as
Wherein f is 0 (x) For the system containing the determination of the attitude angular velocity and the modeling parameters, g 0 (x) For modeling parameter terms, f 0 (x) And g 0 (x) Can be obtained by sensor measurement and experimental data, and Δ f (x) and Δ g (x) are parameter error terms existing in modeling. To facilitate fault-tolerant control law design in a system, parameters are defined
An affine nonlinear system containing gust disturbance, actuator fault and model uncertain parameters can be obtained as
Step 2) designing a space-time radial basis function neural network identifier based on the self-adaptive fusion kernel:
step 2.1) designing a space-time radial basis function neural network
Radial basis function neural networks are generally composed of an input layer, a hidden layer, and an output layer. The space-time radial basis function has the advantages of time dynamic characteristics and space nonlinear (complex) signals, and is provided on the basis of a traditional radial basis function neural network method, and the specific design is as follows:
first layer (input layer): according to the data of the system state variables and the output data of the controller, the input signals of the input layer are aircraft attitude angle, angular velocity and control law signals which can be expressed as aircraft attitude angle, angular velocity and control law signals
Due to the time domain expansion required on the conventional radial basis function neural network, the sampling signal x (t-1) at the previous moment x (t) is added to the input of the network. Thus, the input to the spatio-temporal radial basis function neural network can be expressed as [ x (t) x(t-1)] T Wherein x (t) e R 10 ，x(t-1)∈R 10 。
Second layer (hidden layer): according to the invention, time expansion is carried out on a kernel space of a neural network in signal processing is considered in nonlinear hidden layer design, and two parallel time layers are designed to correspond to two groups of moments in an input layer and are used for mapping dynamics and nonlinear characteristics of signals in time. Psi (i，t) The method is a basic function of a hidden layer of a neural network, and adopts a common Gaussian kernel function as follows:
wherein the content of the first and second substances,
is the central value of the neural network, and σ is the standard deviation.
Third layer (output layer): the output layer adopts linear combination output. Method for estimating parameters by considering space-time radial basis function neural network
Defining the expected value of the kth target signal as d (k), and the error between the network estimated value and the network expected value as
The corresponding cost function is:
the overall mapping of the spatio-temporal radial basis function neural network employed by the present invention is given as follows:
wherein the content of the first and second substances,
w (i，t) (k) for the current weight value from hidden layer to output layer, p is the number of neurons in the hidden layer of the neural network, T is the truncation time, and b (k) is the bias term for the output neurons. w is a (i，t) (k) And b (k) will be updated at each iterative learning.
The gradient descent learning algorithm for designing the radial basis function neural network based on the space-time expansion comprises the following steps:
wherein, w (i，t) (k +1) is the updated weight value, η step In order to learn the step size,
for conventional derivatives, the estimation can be done by the differential chain rule
For the convenience of calculation, the partial derivative can be further taken as:
substituting the formula (10) into the formula (9) can obtain
w (i，t) (k+1)＝w (i，t) (k)+η step ψ (i，t) (x，c (i，t) )e(k) (11)
Similarly, the learning rule of b (k) is designed as follows:
b(k+1)＝b(k)+η step e(k) (12)
step 2.2) design of novel adaptive fusion nucleus
In order to improve the estimation precision of the radial basis function neural network, the method optimizes the requirement of the initial weight value of the space-time radial basis function neural network by utilizing the advantage that Euclidean and cosine distance measurement can adaptively adjust the weight of the kernel, and a new fusion kernel is expressed as follows:
ψ i (x，c (i，t) )＝Υ 1 ψ i1 (||x-c (i，t) ||)+Υ 2 ψ i2 (x.c (i，t) ) (13)
wherein the Gaussian kernel function ψ i1 (||x-c (i，t) I | I) is Euclidean kernel, cosine kernel ψ i2 (x.c (i，t) ) Can be expressed as:
wherein, iota → 0 + Is a normal amount. The parameter y in the new fusion nucleus 1 And upsilon 2 Weight coefficients corresponding to Euclidean kernel and cosine kernel respectively, and existing | γ 1 (k)|+|Υ 2 (k) 1. Therefore, the cost function in (4.14) needs to be redefined as:
in order to obtain the learning rule in the new kernel, the weight coefficient γ is designed with reference to the design method in formula (11) 1 And upsilon 2 The gradient learning descent algorithm is as follows:
similarly, the chain derivative method can be used to obtain
Accordingly, γ may be obtained after taking the partial derivative of the formula 1 (k) The update rule of (1) is:
similarly, γ 2 (k) The update rule of (1) is:
step 3) design of fault-tolerant controller
Step 3.1) defining the reference input signal of the system controller as x according to the mathematical model of the affine nonlinear system ref The system tracking error is defined as:
wherein epsilon 1 And ε 2 Respectively, the tracking errors of the attitude angle and the angular speed of the system, and mu is the introduced virtual control quantity. Defining virtual control quantities
(κ 1 > 0), further, it can be deduced
From this, ε can be derived 2 Another expression form of (A) is
In order to enable the system to better realize the sliding mode, the integral sliding mode surface of the system is selected as follows:
and 3.2) in order to design a control law finally to stabilize the system, an adaptive method is adopted in the method to estimate unknown parameters in the system. The self-adaptive law for defining the related parameters of the uncertainty term, the gust disturbance term and the fault parameter term involved in the control law can be designed as follows:
wherein, γ i (i ═ 1, …, 4) is a normal number, ξ > 0, and the parameters
Are respectively the output of the neural network, and exist
And, the parameters
Disturbance d for gusts w Is alternatively represented, i.e.
For parameter
In other words, a in different value ranges has the following inequality relationship
Meanwhile, in order to satisfy the system stability condition, it needs to be defined as
Step 3.3) designing a complete fault-tolerant control law for a nonlinear system with actuator faults, modeling uncertainty and gust disturbance according to the parameter settings
Wherein iota is normal number and kappa is present 3 ＝(1-h 1 )ι|s|。
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
The effectiveness of the implementation is illustrated in the following by a practical case simulation.
In order to verify the effectiveness of the method, a platform frame of a test experiment system for carrying out physical test flight in the method is shown in fig. 2, and in order to realize in-loop simulation of hardware, a control board replacing Qpall-X4 in the experiment is a PixHawk4 flight controller, and an onboard computer is replaced by a Jetson Nano. The values of the initial model parameters of the redesigned quad-rotor drone are shown in table 1. In the experiment, the real-time control and state monitoring of the aircraft are realized by using a TCP/IP communication protocol through an airborne computer and a computer-end ground station.
TABLE 1 Qball-X4 Multi-rotor aircraft parameters
For a general dynamic model of a multi-rotor aircraft, in the example of the method, a four-rotor aircraft is taken as an example, the aircraft schematic model in fig. 3 is defined as a standard four-rotor airframe model, and an airframe coordinate system (Body Frame) is established on the basis of the four rotors of an X-shaped structural Frame to be O b -x b y b z b The inertial Frame of the quadrotor is O i -x i y i z i . Wherein, the inertia system is a coordinate system of the northeast earth, and the coordinate axes are consistent with the east, north and local directions of the earth, namely O i -x i North direction, O, axially directed to the geographical location i -y i Axially in the east direction of the geographical position, O i -z i The axial direction is directed perpendicular to the ground downward direction. Machine for workingThe body coordinate system is a coordinate system established by the central point of the aircraft and is a right-hand system fixedly connected with the fuselage of the aircraft, O b -x b The axis pointing from the centre point of the fuselage in the direction of the aircraft nose, O b -y b The axis is parallel to the plane of the fuselage and O from the central point of the fuselage b -x b With the axis directed perpendicularly to the right side of the aircraft fuselage, O b -z b The axis is directed downward perpendicular to the fuselage plane starting from the fuselage center point. An X-shaped frame is used and a three-dimensional axis coordinate system is built, and the ground coordinate system of the four rotors is O g -X g Y g Z g 。O b -X b Y b Z b
Typically, the attitude of an aircraft is represented by three Euler angles [ φ θ ψ ]] T Roll angle phi, pitch angle theta and yaw angle psi, respectively, and the dynamic equation which can be introduced into the system is as follows:
wherein J is diag [ J ═ d x J y J z ]Is the inertia matrix of the aircraft, J RP The total moment of inertia of the motor rotor and the propeller around the shaft and the total residual angular velocity of the rotor, m is the mass of the aircraft, g is 9.81N/kg is the acceleration of gravity, u is the acceleration of gravity 1 For four rotor lift control, l is the distance from the rotor center to the four rotor center, u 2 Inputting control quantity u for roll 3 Inputting control amount for pitch, u 4 For yaw input control quantity, input matrix U of X-type quadrotor aircraft belongs to R 4 The definition is as follows: omega g
Parameter omega i Is rotor angular velocity (rad/s) (i ═ 1, 2, 3, 4), F i Is the tension (N), c) to which the rotor is subjected T，i Is the comprehensive tension coefficient of a single propeller, c y，i The single-blade torque coefficient. The angle signal given by the remote controller end of the ground station in the example simulation isA desired attitude signal. To better represent the performance of the attitude controller, the pitch subsystems chosen in this example are as follows:
wherein the parameters
And parameters
The parameter b is a part of the system which needs parameter fusion estimation. State variables in the training of spatio-temporal radial basis function neural networks
And a control quantity [ u ] 1 u 2 u 3 u 4 ]As input to the model training, the collected data is used as parameters and for subsequent calculations. The raw data set is a combination of standard flight data and fault data for the fault injection test aircraft. In the simulation of the example, each group of experimental data is collected at a sampling frequency of 1ms, each group of data comprises 60000 continuous time sequence data, and the training data and the test data are divided according to a ratio of 25: 5. Hidden layer neurons comprising two parallel time layers are designed, each group comprises 10 neurons, and the learning step length of gradient descent is preset to be 0.01. According to the weight updating rule of the novel adaptive kernel space-time radial basis function neural network in the method, iterative training is carried out on the neural network. Finally, the trained network model is embedded into the controller in the experiment, and a good effect is obtained. As shown in FIG. 4, by performing verification comparison on a given set of 500 sample data, the mean square error obtained by the space-time radial basis function neural network based on the novel adaptive kernel proposed in the method is superior to that obtained by the conventional radial basis function neural network. According to the figures 5 and 6, it is easy to find the prediction sample data of the space-time radial basis function neural network trackingThe method has the advantages that the method is more accurate than the traditional radial basis function neural network, and the numerical value of the tracking error is slightly smaller than that of the traditional radial basis function neural network.
In the effect verification stage of the fault-tolerant controller, the method mainly provides expected signals theta of pitching and rolling postures through a ground-end remote controller ref And phi ref And comparing the experimental result with the traditional radial basis function neural network. In order to verify the effectiveness of the proposed fault-tolerant controller, the invention selects a multi-rotor aircraft with modeling uncertainty, and considers three flight simulation scenarios for qualitatively analyzing the control performance of the controller:
scene 1: testing the flight effect of the active disturbance rejection fault-tolerant controller of the neural network based on the space-time radial basis function neural network prediction under the environment without external wind disturbance and actuator fault;
scene 2: the numerical simulation simulates 3-9m/s of horizontal gust disturbance. Analyzing the performance of the controller by the effect of the aircraft in wind disturbance situations lasting for a period of time;
scene 3: under the environment of gust disturbance in scene 2, a specified fault value is further injected into the No. 1-4 motor of the aircraft through the fault-tolerant control system of the aircraft, and corresponding gain fault and deviation fault data are shown in table 2. Meanwhile, in the experiment, the fault data is added with 80 decibel white gaussian noise interference:
TABLE 2 Qball-X4 Multi-rotor aircraft Fault injection data
Experimental data of scene 1 are shown in fig. 7 and 8, and compared with the performances of the conventional radial basis function neural network and the spatio-temporal radial basis function neural network controller, the flight controller designed by the invention can realize good attitude tracking control with the controller based on the conventional radial basis function neural network. However, compared with the variation of the tracking error curve in fig. 8, the controller of the present invention has better tracking performance and smaller error, which can be seenIn addition, the conventional radial basis function neural network does not give a more accurate estimation value in the process of the aircraft shaking. Fig. 9 and 10 show the effect of controlling the attitude of the aircraft during gust disturbances in scene 2. Under the condition of interference, the controller based on the traditional radial basis function neural network and the backstepping sliding mode controller based on the space-time radial basis function neural network have good tracking performance, but the tracking performance of the space-time radial basis function neural network provided by the invention is better when the aircraft has larger action change as can be found through the graph 10. Comparing the tracking effect of the pitch and roll controllers in fig. 11 and fig. 12, it is obvious that the tracking error of the aircraft is greatly changed when the fault is injected in the 40 th second by the controller of the conventional radial basis function neural network, and the aircraft tends to be out of control, but the fault-tolerant controller provided by the invention still maintains the stable tracking effect after the fault is injected. Parameter 1, parameter 2 and gust disturbance curves in fig. 13 show the parameter for the pitch and roll controllers, respectively, in the test of scene 3
And
an estimate of (d). The fault-tolerant controller provided by the invention can provide attitude control parameter supplement in the takeoff stage of the airplane, and can quickly and accurately estimate fault data when an actuator fails.
Claims (3)
1. The method designs a fault-tolerant control algorithm of a nonlinear system with model uncertainty and actuator faults, and is characterized in that: in consideration of the fault-tolerant control process of the multi-rotor aircraft with actuator deviation fault, gain fault and external gust disturbance, the aircraft is difficult to realize stable control effect by virtue of a backstepping sliding mode controller, and the out-of-control condition is easy to occur. Considering that the traditional radial basis function only processes signals in a time domain and is difficult to predict signals with time dynamic characteristics and spatial nonlinearity, the method provides a radial basis function neural network with a new fusion kernel and for processing space-time expansion signals, and improves the output accuracy of the neural network. The fault-tolerant control law design aiming at the nonlinear system of the multi-rotor aircraft containing the deviation fault, the gain fault and the gust disturbance of the actuator comprises the following steps:
step 1) establishing an affine nonlinear system fault model:
step 1.1) for a multi-rotor aircraft in a normal state the following affine non-linear model can be considered,
wherein the state vector
Can be obtained by measurement and calculation, and the system modeling parameter is f (x) epsilon R 12 And g (x) ε R 12×4 ，u(t)∈R 4 The system inputs the quantity. The meaning of the parameter corresponding to the state vector is as follows: position parameter [ x y z ] under inertial coordinate system]Linear velocity of line
Roll angle phi, pitch angle theta, yaw angle psi, corresponding angular velocity
The attitude, angular velocity, position and speed of the multi-rotor aircraft can be measured and calculated through a gyroscope, a magnetometer and other sensor data, and aircraft state data can be obtained. u ═ u 1 u 2 u 3 u 4 ] T Wherein u is 1 For four-rotor lift control, u 2 Inputting control quantity u for roll 3 Inputting control amount for pitch, u 4 The control amount is input for yaw.
Step 1.2) for the definition of force rectangular type of the multi-rotor aircraft in the wind interference environment, the method takes a representative four-rotor aircraft model as an example to represent the following wind interference mathematical model,
wherein d is 1 、d 2 、d 3 、d 4 The wind disturbance quantities of the aircraft in the vertical direction, the transverse rolling shaft, the pitching shaft and the yawing shaft are respectively, and the acting force of the single propeller subjected to wind disturbance is
Where ρ, A i Air density and propeller rotation area, V p，i The condition parameter l is the induced wind speed of the propeller without wind disturbance i ＝v gust，i /v p，i ，(l i ∈(0，0.1))，V gust，i For gust disturbance terms, m is the aircraft mass, J XX 、J YY 、J ZZ The inertia constants of the aircraft in the roll, pitch and yaw directions are respectively.
Step 1.3) for a multi-rotor aircraft with actuator gain faults and deviation faults, selecting an actuator fault model,
u F ＝α(t)u+τ(t) (3)
wherein α (t) ∈ (0, 1)]τ (t) is a parameter that contains an actuator additive fault. u. of F The input variable of the multi-rotor aircraft affine nonlinear system containing the actuator gain fault and the deviation fault.
Step 1.4) taking into account the conditions existing in the above steps, for a multi-rotor aircraft affine nonlinear system with gust disturbances, actuator gain faults and deviation faults, the mathematical model thereof is represented as
Wherein, f 0 (x) For the system containing the determination of attitude angular velocity and modeling parameters, g 0 (x) For modeling parameter terms, f 0 (x) And g 0 (x) Can be obtained by sensor measurement and experimental data, and Δ f (x) and Δ g (x) are parameter error terms existing in modeling. To facilitate fault-tolerant control law design in a system, parameters are defined
An affine nonlinear system containing gust disturbance, actuator fault and model uncertain parameters can be obtained as
Step 2) designing a space-time radial basis function neural network identifier based on the self-adaptive fusion kernel:
step 2.1) designing a space-time radial basis function neural network
Radial basis function neural networks are generally composed of an input layer, a hidden layer, and an output layer. The space-time radial basis function has the advantages of time dynamic characteristics and space nonlinear (complex) signals, and is provided on the basis of a traditional radial basis function neural network method, and the specific design is as follows:
first layer (input layer): according to the data of the system state variables and the output data of the controller, the input signals of the input layer are aircraft attitude angle, angular velocity and control law signals which can be expressed as aircraft attitude angle, angular velocity and control law signals
Due to the fact that time domain expansion needs to be carried out on a traditional radial basis function neural network, x (t) is added to the input of the networkThe sampled signal x (t-1) at the previous time instant. Thus, the input to the spatio-temporal radial basis function neural network may be expressed as [ x (t) x (t-1)] T Wherein x (t) e R 10 ，x(t-1)∈R 10 。
Second layer (hidden layer): in the design of the nonlinear hidden layer, time expansion is carried out on a kernel space of a neural network in signal processing, and two parallel time layers are designed to correspond to two groups of moments in an input layer and are used for mapping dynamics and nonlinear characteristics of a signal in time. Psi (i，t) The method is a basic function of a hidden layer of a neural network, and adopts a common Gaussian kernel function as follows:
wherein the content of the first and second substances,
is the central value of the neural network, and σ is the standard deviation.
Third layer (output layer): the output layer adopts linear combination output. Method for estimating parameters by considering space-time radial basis function neural network
Defining the expected value of the kth target signal as d (k), and the error between the network estimated value and the network expected value as
The corresponding cost function is:
the overall mapping of the spatio-temporal radial basis function neural network employed herein is given as follows:
wherein the content of the first and second substances,
w (i，t) (k) for the current weight value from hidden layer to output layer, p is the number of neurons in the hidden layer of the neural network, T is the truncation time, and b (k) is the bias term for the output neurons. w is a (i，t) (k) And b (k) will be updated at each iteration of learning.
The gradient descent learning algorithm for designing the radial basis function neural network based on the space-time expansion comprises the following steps:
wherein, w (i，t) (k +1) is the updated weight value, η step In order to learn the step size,
for conventional derivatives, the estimation can be done by the differential chain rule
For the convenience of calculation, the partial derivative can be further taken as:
substituting the formula (10) into the formula (9) can obtain
w (i，t) (k+1)＝w (i，t) (k)+η step ψ (i，t) (x，c (i，t) )e(k) (11)
Similarly, the learning rule of b (k) is designed as follows:
b(k+1)＝b(k)+η step e(k) (12)
step 2.2) design of novel self-adaptive fusion nucleus
In order to improve the estimation precision of the radial basis function neural network, the method optimizes the requirement of the initial weight value of the space-time radial basis function neural network by utilizing the advantage that Euclidean and cosine distance measurement can adaptively adjust the weight of the kernel, and a new fusion kernel is expressed as follows:
ψ i (x，c (i，t) )＝Υ 1 ψ i1 (||x-c (i，t) ||)+Υ 2 ψ i2 (x.c (i，t) ) (13)
wherein the Gaussian kernel function ψ i1 (||x-c (i，t) I | I) is Euclidean kernel, cosine kernel ψ i2 (x.c (i，t) ) Can be expressed as:
wherein, iota → 0 + Is a normal amount. Novel parameter gamma in fused nucleus 1 And upsilon 2 Weight coefficients corresponding to Euclidean kernel and cosine kernel respectively, and existing | γ 1 (k)|+|Υ 2 (k) 1. Therefore, the cost function in (4.14) needs to be redefined as:
in order to obtain the learning rule in the new kernel, the weight coefficient γ is designed with reference to the design method in formula (11) 1 And upsilon 2 The gradient learning descent algorithm is as follows:
similarly, it can be obtained by chain differential method
Accordingly, γ may be obtained after taking the partial derivative of the formula 1 (k) The update rule of (1) is:
similarly, γ 2 (k) The update rule of (1) is:
step 3) design of fault-tolerant controller
Step 3.1) defining the reference input signal of the system controller as x according to the mathematical model of the affine nonlinear system ref The system tracking error is defined as:
wherein epsilon 1 And ε 2 Respectively, the tracking errors of the attitude angle and the angular speed of the system, and mu is the introduced virtual control quantity. Defining virtual control quantities
Further, it can be deduced
From this, ε can be derived 2 Another expression form of (A) is
In order to enable the system to better realize the sliding mode, the integral sliding mode surface of the system is selected as follows:
and 3.2) in order to design a control law finally to stabilize the system, an adaptive method is adopted in the method to estimate unknown parameters in the system. The self-adaptive law for defining the related parameters of the uncertainty term, the gust disturbance term and the fault parameter term involved in the control law can be designed as follows:
wherein, γ i (i ═ 1, …, 4) is a normal number, ξ > 0, and the parameters
Are respectively the output of the neural network, and exist
And, the parameters
Disturbance d for gusts w Is alternatively represented, i.e.
For parameter
In other words, a in different value ranges has the following inequality relationship
Meanwhile, in order to satisfy the system stability condition, it needs to be defined as
Step 3.3) designing a complete fault-tolerant control law for a nonlinear system with actuator faults, modeling uncertainty and gust disturbance according to the parameter settings
Wherein iota is normal number and kappa is present 3 ＝(1-h 1 )ι|s|。
2. The method according to claim 1, wherein the error term Δ g (x) in the system modeling in step 1.4) satisfies the following condition
Then, g can be calculated 0 (x)/g(x)∈(0.5，2)。
3. The method of claim 1, wherein the parameters of step 3.2) are selected from the group consisting of actuator bias fault, gain fault, and gust disturbance
And h is 1 ＜1。
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| CN115437244A (en) * | 2022-11-08 | 2022-12-06 | 西北工业大学 | Airplane flight fault-tolerant control system and method for nonlinear sensor fault |
| CN115755988A (en) * | 2023-01-10 | 2023-03-07 | 广东工业大学 | Pure orientation passive positioning method and system for unmanned aerial vehicle cluster and storage medium |
| CN117163281A (en) * | 2023-08-30 | 2023-12-05 | 南京航空航天大学 | Fault-tolerant control method under fault condition of gliding aircraft actuator |
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| CN115437244A (en) * | 2022-11-08 | 2022-12-06 | 西北工业大学 | Airplane flight fault-tolerant control system and method for nonlinear sensor fault |
| CN115437244B (en) * | 2022-11-08 | 2023-05-12 | 西北工业大学 | Nonlinear sensor fault-oriented aircraft flight fault-tolerant control system and method |
| CN115755988A (en) * | 2023-01-10 | 2023-03-07 | 广东工业大学 | Pure orientation passive positioning method and system for unmanned aerial vehicle cluster and storage medium |
| CN117163281A (en) * | 2023-08-30 | 2023-12-05 | 南京航空航天大学 | Fault-tolerant control method under fault condition of gliding aircraft actuator |
| CN117163281B (en) * | 2023-08-30 | 2024-03-08 | 南京航空航天大学 | Fault-tolerant control method under fault condition of gliding aircraft actuator |
| CN117687308A (en) * | 2024-02-02 | 2024-03-12 | 北京理工大学 | Variant aircraft fault-tolerant control method based on fixed-time neural network observer |
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