Self-disturbance rejection and fault-tolerant control method for unmanned helicopter based on radial basis function neural network

Abstract

The present invention discloses an unmanned helicopter self-disturbance rejection fault-tolerant control method based on radial basis function neural network, which belongs to the technical field of unmanned helicopter fault-tolerant control, and specifically comprises the following steps: step A, constructing a posture model corresponding to the unmanned helicopter according to the 6-DOF motion characteristics of the unmanned helicopter, introducing a sensor fault model on this basis, and establishing an unmanned helicopter posture model including sensor faults; step B, constructing an unmanned helicopter posture fault-tolerant control loop according to real-time target instructions based on the posture model corresponding to the unmanned helicopter, and obtaining the posture control vector of the unmanned helicopter; step C, performing fault-tolerant control on the unmanned helicopter according to the output of the posture control law of the unmanned helicopter; and based on the real-time target instructions, executing the following steps A to C in real time to realize real-time fault-tolerant control of the unmanned helicopter. The present invention solves the problem of fault-tolerant flight control of unmanned helicopters with sensor faults.

Description

Technical Field

[0001] The invention belongs to the technical field of fault-tolerant control of unmanned helicopters, and in particular relates to a self-disturbance rejection fault-tolerant control method of an unmanned helicopter based on a radial basis function neural network. Background Art

[0002] Unmanned helicopters are widely used in military and civilian fields because of their excellent flight characteristics, such as hovering, flying in any direction, and taking off and landing in a small area. As the performance of unmanned helicopters continues to improve, the requirements for sensors in their flight control systems are also getting higher and higher. In addition, the harsh working environment faced by unmanned helicopters can easily cause failures of onboard sensors. If the faulty sensor signal is fed back to the control system, it will inevitably lead to erroneous control, and in severe cases, a crash will occur. At this time, effective sensor fault-tolerant control is the key and prerequisite for achieving safe flight.

[0003] In recent years, research on fault-tolerant control of aircraft sensor failures has attracted attention. Wang et al. proposed a dual adaptive fault-tolerant control strategy for quadrotor aircraft based on adaptive sliding mode control and adaptive boundary layer. This method can compensate for uncertain models and fault information, and adopts the minimum discontinuous control gain, which significantly reduces the control jitter effect. However, different types of external disturbances have not been studied. In the prior art, a method using offline trained deep neural networks to estimate faults is proposed, combined with nonlinear dynamic inversion, which can land aircraft under different fault types and severe wind disturbance conditions. However, this method cannot estimate fault information in real time, and is still a long way from engineering practice.

[0004] Active Disturbance Rejection Control (ADRC) regards the internal and external disturbances of the system as total disturbances, establishes an extended state observer through state expansion, estimates the total disturbance with the expanded state, and uses it for real-time compensation of system control. ADRC does not rely on accurate mathematical models, overcomes the interference of uncertain internal and external disturbances, and makes the control system more robust. It has been strongly verified from the perspectives of engineering practice and theoretical analysis. Due to the excessive number of adjustment parameters of nonlinear active disturbance rejection control technology, the practical application of active disturbance rejection is limited. The prior art also discloses linear active disturbance rejection control (LADRC) technology, which greatly reduces the adjustment workload and greatly promotes the research and application of active disturbance rejection control technology. At the same time, the radial basis function neural network (RBFNN) has strong adaptive ability and can approximate any continuous function. Therefore, the present invention discloses an unmanned helicopter self-disturbance rejection fault-tolerant control method based on the radial basis function neural network, introduces the state output signal integral variable to augment the original system, and on this basis, uses RBFNN to estimate the unknown sensor fault, uses LADRC technology to obtain the unmanned helicopter state quantity and the estimated value of the total internal and external disturbance, and converts the unmanned helicopter system into a standard integral series structure that does not contain disturbance. The method has a simple structure, strong adaptive ability, can solve various types of sensor failure problems, and has high engineering application value. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an unmanned helicopter self-disturbance rejection fault-tolerant control method based on a radial basis function neural network, so as to solve the unmanned helicopter fault-tolerant flight control problem with sensor failure.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions: the present invention designs an unmanned helicopter self-disturbance rejection fault-tolerant control method based on radial basis function neural network, and based on real-time target instructions, the following steps A to C are executed in real time to realize real-time fault-tolerant control of the unmanned helicopter;

[0007] Step A: According to the 6-DOF motion characteristics of the unmanned helicopter, a posture model corresponding to the unmanned helicopter is constructed. On this basis, a sensor fault model is introduced to establish an unmanned helicopter posture model including sensor faults, and then proceed to step B.

[0008] Step B: Based on the attitude model corresponding to the unmanned helicopter and according to the real-time target instruction, an attitude fault-tolerant control loop of the unmanned helicopter is constructed to obtain the attitude control vector of the unmanned helicopter; then, step C is entered;

[0009] Step C: performing fault-tolerant control on the unmanned helicopter according to the output of the attitude control law of the unmanned helicopter.

[0010] As a preferred technical solution of the present invention: in the step A, according to the 6-DOF motion characteristics of the unmanned helicopter, the kinematic model corresponding to the unmanned helicopter is constructed as follows:

[0011]

[0012] Where V = [uvw] T is the forward flight speed, lateral speed, and vertical speed of the unmanned helicopter; S = [pqr] T is the roll angular velocity, pitch angular velocity, and yaw angular velocity of the unmanned helicopter; α=[φθψ] T is the roll Euler angle, pitch Euler angle, and yaw Euler angle of the unmanned helicopter; P = [XYZ] T is the ground coordinate of the unmanned helicopter; m is the total mass of the unmanned helicopter; F and M are the total external force and torque of the components of the unmanned helicopter respectively; I is the inertia matrix of the unmanned helicopter, Ω is the antisymmetric matrix of the three-axis angular rate of the unmanned helicopter, R EB is the transformation matrix from the body coordinate system to the ground coordinate system, and E is the transformation matrix from the angular velocity of the unmanned helicopter body to the Euler angular velocity.

[0013] Taking the posture model as an example, equations (1-2) and (1-3) can be expressed as

[0014]

[0015] Where w is the external disturbance, U c =[δ lon δ lat δ TR ] is the control vector composed of the longitudinal pitch, lateral pitch and tail rotor pitch control variables. Combining equations (1-5) and (1-6) gives the second-order attitude model:

[0016]

[0017] Where F3 = dF1 / dt, F1, F2, B are corresponding abbreviations. The internal dynamic characteristics other than α, the control coupling between channels and the external disturbance are regarded as the total disturbance, which is recorded as Then formula (1-7) becomes

[0018]

[0019] In the formula, B 0α is the attitude control gain matrix, the pitch, roll, and yaw channel control quantity U ciWith output y αi =α i It forms a single input-single output relationship.

[0020] Formula (1-8) can be expressed in state space form as

[0021]

[0022] Where, X1=[φ θ ψ] T , Y represents the system output.

[0023] Generally, sensor faults are divided into constant deviation faults, drift faults and constant gain faults. Based on this, the sensor fault model is expressed as follows

[0024] Y=m s X1+Y t (1-10)

[0025] Where Y is the actual measured value output by the system sensor, m s =[m l m a m c ] is the sensor gain coefficient matrix, Y t =[Y l Y a Y c ] is the sensor bias coefficient matrix and Y tmin <Y t <Y tmax , there are upper and lower boundaries.

[0026] Combining equations (1-9) and (1-10), we can get the attitude model of the unmanned helicopter including sensor failure:

[0027]

[0028] In the formula, f g (X1)=(m s -I)X1+Y t .

[0029] As a preferred technical solution of the present invention: in the step B, based on the attitude model corresponding to the unmanned helicopter and according to the real-time target instruction, the attitude fault-tolerant control loop of the unmanned helicopter is constructed as follows to obtain the attitude control vector of the unmanned helicopter;

[0030] Due to the unknown faults of the attitude angle sensor, the system output measurement value cannot be directly applied to the extended state observer of LADRC. Therefore, the state augmentation method is used to transform the extended state observer, and RBFNN is used to estimate the unknown faults of the sensor to solve the impact of the sensor fault on the estimation of the true value of the system state.

[0031] The integral signal of the system output signal is defined as

[0032]

[0033] Combining equations (1-11) and (1-12), we get

[0034]

[0035] For the augmented system (1-13), the following linear extended state observer (LESO) based on RBFNN is designed:

[0036]

[0037] In the formula, are the estimated values ​​of X0, X1, and X2 respectively; is the expansion state, which represents the estimated value of the total disturbance of the system; It indicates the estimation of unknown faults of attitude angle sensor using RBFNN. is the estimated value of the weight coefficient, where:

[0038]

[0039] c j =[c 1j c 2j … c nj ] T (1-16)

[0040] In the formula, c j b is the coordinate vector of the center point of the Gaussian basis function of the jth node neuron in the hidden layer; j is the width of its Gaussian basis function, and n represents the number of input variables.

[0041] The output Uc of the LADRC control law is:

[0042]

[0043] In the formula, w c Expressed as controller bandwidth, v1=v, When the system input v is a constant value, v2=0, v3=0.

[0044] The posture model (1-11) is transformed into the control law (1-17)

[0045]

[0046] Under the extended state estimation compensation, the system becomes an integral series linear controlled object, that is,

[0047]

[0048] The part of the system (1-13) that is different from the standard integral series type is regarded as the total disturbance (including internal and external disturbances) and estimated by LESO. As the compensation of the control law, the nonlinear system with disturbance is processed into a standard integral series type system in the form of formula (1-20), realizing the dynamic compensation linearization of the nonlinear controlled object. Estimation of sensor fault f by RBFNN g (X1) The system output information is transmitted to the LESO series structure without sensor fault information, ensuring is the estimated value of the actual X1.

[0049] The unmanned helicopter self-disturbance rejection fault-tolerant control method based on radial basis function neural network of the present invention adopts the above technical scheme and has the following technical effects compared with the prior art:

[0050] The present invention designs an unmanned helicopter self-disturbance rejection and fault-tolerant control method based on radial basis function neural network, establishes an attitude model of the unmanned helicopter, and designs a linear extended state observer based on RBFNN to estimate sensor failures and internal and external total disturbances. Based on this, an unmanned helicopter fault-tolerant control method is constructed, which can effectively prevent the unmanned helicopter attitude control system from being affected by sensor failures and unable to stably control the flight attitude. The unmanned helicopter self-disturbance rejection and fault-tolerant control method based on radial basis function neural network proposed in this patent can effectively overcome the influence of sensor failures, and has strong anti-interference ability and good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a block diagram of the linear active disturbance rejection controller of the present invention;

[0052] Figure 2 It is the RBF neural network structure of the present invention;

[0053] Figure 3 A linear auto-disturbance rejection fault-tolerant controller based on a radial basis function neural network according to the present invention;

[0054] Figure 4 is the attitude control loop of the present invention;

[0055] Figure 5 is the pitch angle response curve of the present invention; wherein (a) is the pitch angle command tracking curve, and (b) is the sensor fault estimation;

[0056] Figure 6 is the roll angle response curve of the present invention; wherein (a) is the roll angle command tracking curve, and (b) is the sensor fault estimation;

[0057] Figure 7It is the yaw angle response curve of the present invention; wherein, (a) is the yaw angle command tracking curve, and (b) is the sensor fault estimation. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solution and effect of the present invention clearer and more specific, the present invention is further described in detail by enumerating examples below. It should be noted that the specific implementation described here is only used to explain the present invention and is not used to limit the present invention.

[0059] With the in-depth application of neural network control methods in the field of intelligent control, the radial basis function neural network (RBFNN), as a commonly used three-layer feedforward network, has the characteristics of simple structure, fast learning speed, and excellent performance approximation. It can be used to design an extended state observer to achieve accurate estimation of sensor faults. The design of linear active disturbance rejection control law helps to improve the adaptability and robustness of the control system and enhance the control performance of the controller.

[0060] In summary, the present invention proposes an unmanned helicopter self-disturbance rejection fault-tolerant control method based on radial basis function neural network.

[0061] The equation of motion for the unmanned helicopter flight dynamics is:

[0062]

[0063] Where V = [uvw] T is the linear velocity; S = [pqr] T is the angular velocity; α=[φθψ] T are Euler angles, namely roll angle, pitch angle and yaw angle; P = [XYZ] T is the ground coordinate; m is the mass of the whole aircraft; F and M are the resultant external forces and moments of the components of the whole aircraft (rotor, tail rotor, fuselage, vertical tail, horizontal tail, etc., including gravity); I is the moment of inertia matrix, Ω is the angular velocity cross product vector operator, R EB is the transformation matrix from body coordinates to ground coordinates, that is:

[0064]

[0065] E is the conversion matrix from the body angular velocity to the Euler angular velocity, that is:

[0066]

[0067] Taking the posture model as an example, equations (2) and (3) can be expressed as

[0068]

[0069] Where w is the external disturbance, U c =[δ lon δ lat δ TR ] is the control vector composed of the longitudinal pitch change, lateral pitch change and tail rotor pitch change control variables. Combining equations (8) and (9) gives the second-order attitude model:

[0070]

[0071] Where F3 = dF1 / dt, F1, f2, and B are corresponding abbreviations. The internal dynamic characteristics other than α, the control coupling between channels, and the external disturbance are regarded as the total disturbance, which is recorded as Then equation (46) becomes

[0072]

[0073] In the formula, B 0α is the attitude control gain matrix, the pitch, roll, and yaw channel control quantity U ci With output y αi =α i It forms a single input-single output relationship.

[0074] Formula (11) can be expressed in state space form as

[0075]

[0076] Where, X1=[φ θ ψ] T , Y represents the system output.

[0077] Generally, sensor faults are divided into constant deviation faults, drift faults and constant gain faults. Based on this, the sensor fault model is expressed as follows

[0078] Y=m s X1+Y t (13)

[0079] Where Y is the actual measured value output by the system sensor, m s =[m l m a m c ] is the sensor gain coefficient matrix, Y t =[Y l Y a Y c ] is the sensor bias coefficient matrix and Y tmin <Y t <Y tmax , there are upper and lower boundaries. Just choose different m s ,Y tThe combination can represent different sensor fault forms. The specific fault description is shown in Table 1.

[0080] Table 1 Sensor failure types

[0081]

[0082] Combining equations (12) and (13), we can get the attitude model of the unmanned helicopter including sensor failure:

[0083]

[0084] In the formula, f g (X1)=(m s -I)X1+Y t .

[0085] Fault-tolerant controller design:

[0086] Assuming the total disturbance Differentiable, and assuming System (12) can be expressed in the form of an expanded system as follows:

[0087]

[0088] Construct a linear extended state observer LESO for system (14), namely

[0089]

[0090] In the formula, and are the observed values ​​of the system respectively; β1, β2 and β3 are the observer control parameters, which can be selected as [β1 β2 β3] = [3w0 3w 2 0 w 3 0].

[0091] The control law is designed as:

[0092]

[0093] In the formula, w c Expressed as controller bandwidth, v1=v, When the system input v is a constant value, v2 = 0, v3 = 0. This constitutes the LADRC controller, such as Figure 1 shown.

[0094] In actual engineering, attitude angle and angular rate signals are directly measured by inertial measurement elements, and these sensors are easily affected by changes in the surrounding environment and their own processes, resulting in inaccurate measurement results. Therefore, a state observer is introduced to estimate the flight state information. LESO has the characteristics of being able to observe the system state and disturbance at the same time, and uses expansion thinking to estimate the total internal and external disturbances. At the same time, this section introduces RBF neural network to approximate sensor failures.

[0095] RBF neural network has the ability to approximate any continuous unknown function. It consists of a three-layer feedforward neural network, including an input layer, a hidden layer, and an output layer. Figure 2 shown.

[0096] x=[x i ] T is the network input vector, the jth hidden layer node h j Expressed as

[0097]

[0098] c j =[c 1j c 2j … c nj ] T (20)

[0099] In the formula, c j b is the coordinate vector of the center point of the Gaussian basis function of the jth node neuron in the hidden layer; j is the width of its Gaussian basis function, n represents the number of input variables, and m represents the number of hidden layer nodes.

[0100] The weight between the hidden layer and the output layer is W = [w1,…,w m ] T The network output is

[0101] y(t)=W T h=w1h1+w2h2+…+w m h m (twenty one)

[0102] If the sensor fails, g (X1) consists of a sufficient number of hidden layer nodes, then f g (X1) is expressed as the network output:

[0103] f g (X1)=W *T h(X1)+ε (22)

[0104] Where W * is the ideal weight, ε is the output of the neural network and fg (X1) Bounded error between true values.

[0105] Taking attitude fault-tolerant control as an example, due to the unknown fault of the attitude angle sensor, the system output measurement value cannot be directly applied to LESO. Therefore, the state augmentation method is used to transform LESO, and the RBF neural network is used to estimate the unknown fault of the sensor to solve the impact of the sensor fault on the estimation of the true value of the system state.

[0106] The integral signal of the system output signal is defined as

[0107]

[0108] Combining equations (14) and (23), we get

[0109]

[0110] The augmented system (23) is designed as follows RBFNN-LESO

[0111]

[0112] In the formula, are the estimated values ​​of X0, X1, and X2 respectively; is the expansion state, which represents the estimated value of the total disturbance of the system; It indicates the estimation of unknown faults of attitude angle sensor using RBF neural network. It is W * Therefore, the linear active disturbance rejection fault-tolerant controller based on radial basis function neural network (RBFNN-LADRC) is as follows: Figure 3 shown.

[0113] The system (25) is transformed into

[0114]

[0115] Under the extended state estimation compensation, the system becomes an integral series linear controlled object, that is,

[0116]

[0117] The part of system (24) that is different from the standard integral series type is regarded as the total disturbance (including internal and external disturbances) and estimated by LESO as the compensation of the control law. The nonlinear system with disturbance is processed into a standard integral series type system in the form of formula (27), realizing the dynamic compensation linearization of the nonlinear controlled object. g (X1) The system output information is transmitted to the LESO series structure without sensor fault information, ensuring is the estimated value of the actual X1.

[0118] Attitude control loop design:

[0119] The pitch, roll, and yaw attitude control loops are all designed as second-order RBFNN-LADRC control structures, such as Figure 4 As shown. The pitch angle and roll angle attitude commands are given by the speed control loop, the yaw angle command comes directly from the task command, and the attitude control loop output control increment is superimposed with the reference value to form [δ lon δ lat δ TR ] variable pitch control amount, and δ col The total moment control variables act together on the unmanned helicopter.

[0120] From the above analysis, we can see that the pitch channel control δ lon Designed for

[0121]

[0122] In the formula, θ r is the output signal from the longitudinal velocity loop, θ is the pitch angle signal with sensor failure, is the longitudinal control trim, b 0θ To control the gain, is the total disturbance estimate of the RBF neural network output.

[0123] Roll channel control δ lat and heading channel control δ TR The design is the same and will not be described in detail.

[0124] To verify the effectiveness of the RBF-LADRC fault-tolerant controller designed in this paper, an attitude control simulation experiment is carried out in the MATLAB / Simulink environment. The controlled object is a single-rotor unmanned helicopter with a tail rotor, and its parameters are shown in Table 2. The model contains gust disturbances, and the output attitude response contains Gaussian noise with an intensity of 0.003db as an external interference signal.

[0125] Table 2 Main parameters of unmanned helicopter

[0126]

[0127] During the simulation, a 0.5 rad command signal is applied to the three attitude angles of the unmanned helicopter, and the sensor fault is set in the following modes:

[0128] 1) The pitch angle sensor has a constant gain failure, and the gain m c =2;

[0129] 2) The roll angle sensor has a drift fault, and the drift is a sinusoidal signal with an amplitude of 0.3rad;

[0130] 3) The yaw angle sensor has a constant deviation fault, and the constant output value is 0.3rad.

[0131] The parameter values ​​of the RBF-LADRC controller are shown in Table 3, where the number of hidden layer nodes of the RBF network of each control loop is 12, and the network width b of the Gaussian basis function is j =2.

[0132] Figures 5 to 7 It shows the response process of the system after the attitude sensor fails. It can be seen that no matter what kind of fault occurs in the sensor, the extended state observer can effectively estimate the true state value of the system, and the observation error is small. At the same time, the RBF neural network can estimate the sensor fault value more accurately, so the true attitude angle of the system can quickly stabilize to the set command value. The above simulation shows that when there is a sensor fault in the system, the neural network extended state observer designed in this paper can effectively estimate the unmeasurable state value of the unmanned helicopter in real time. The design of the fault-tolerant controller is completed by combining the RBF neural network with the anti-disturbance controller, and the unmanned helicopter attitude angle can quickly track the command signal under the condition of sensor failure, achieving the design purpose of the controller.

[0133] Table 3 Controller parameter values

[0134]

[0135] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0136] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A self-disturbance rejection fault-tolerant control method for an unmanned helicopter based on a radial basis function neural network, characterized in that: The method described is: Step A: According to the 6-DOF motion characteristics of the unmanned helicopter, a posture model corresponding to the unmanned helicopter is constructed. On this basis, a sensor fault model is introduced to establish an unmanned helicopter posture model including sensor faults, and then proceed to step B. Step B: Based on the attitude model corresponding to the unmanned helicopter and according to the real-time target instruction, an attitude fault-tolerant control loop of the unmanned helicopter is constructed to obtain the attitude control vector of the unmanned helicopter; then, step C is entered; Step C, performing fault-tolerant control on the unmanned helicopter according to the output of the attitude control law of the unmanned helicopter; Based on the real-time target command, the following steps A to C are executed in real time to realize real-time fault-tolerant control of the unmanned helicopter; The step A is specifically as follows: according to the 6-DOF motion characteristics of the unmanned helicopter, a kinematic model corresponding to the unmanned helicopter is constructed as follows: Where V = [uvw] T is the forward flight speed, lateral speed, and vertical speed of the unmanned helicopter; S = [pqr] T is the roll angular velocity, pitch angular velocity, and yaw angular velocity of the unmanned helicopter; α=[φ θ ψ] T is the roll Euler angle, pitch Euler angle, and yaw Euler angle of the unmanned helicopter; P = [XYZ] T is the ground coordinate of the unmanned helicopter; m is the total mass of the unmanned helicopter; F and M are the total external force and torque of the components of the unmanned helicopter respectively; I is the inertia matrix of the unmanned helicopter, Ω is the antisymmetric matrix of the three-axis angular rate of the unmanned helicopter, R EB is the conversion matrix from the body coordinate system to the ground coordinate system, and E is the conversion matrix from the angular velocity of the unmanned helicopter body to the Euler angular velocity; In the posture model, equations (1-2) and (1-3) can be expressed as: Where w is the external disturbance, U c =[δ lon δ lat δ TR ] is the control vector composed of the longitudinal pitch change, lateral pitch change and tail rotor pitch change control variables; the combined equations (1-5) and (1-6) can obtain the second-order attitude model: Where F3 = dF1 / dt, F1, F2, B are corresponding abbreviations; the internal dynamic characteristics other than α, the control coupling between channels and the external disturbance are regarded as the total disturbance, which is recorded as Then formula (1-7) becomes: In the formula, B 0α is the attitude control gain matrix, the pitch, roll, and yaw channel control quantity U ci With output y αi =α i Constitute a single input-single output relationship; Formula (1-8) can be expressed in state space form as: Where, X1=[φ θ ψ] T , Y represents the system output; Sensor faults are divided into constant deviation faults, drift faults and constant gain faults; based on this, the sensor fault model is expressed as follows: Y=m s X1+Y t (1-10) Where Y is the actual measured value output by the system sensor, m s =[m l m a m c ] is the sensor gain coefficient matrix, Y t =[Y l Y a Y c ] is the sensor bias coefficient matrix and Y tmin <Y t <Y tmax , there are upper and lower boundaries; Combining equations (1-9) and (1-10), we can get the attitude model of the unmanned helicopter including sensor failure as follows: where f g (X1) = (m s - I)X1 + Y t ; The step B is specifically as follows: based on the attitude model corresponding to the unmanned helicopter and according to the real-time target instruction, an attitude fault-tolerant control loop of the unmanned helicopter is constructed to obtain the attitude control vector of the unmanned helicopter; an RBFNN is used to estimate the unknown fault of the sensor to solve the influence of the sensor fault on the estimation of the true value of the system state; The integral signal of the system output signal is defined as: Combining equations (1-11) and (1-12), we get: For the augmented system (1-13), the following RBFNN-based linear extended state observer is designed, denoted as LESO; In the formula, are the estimated values ​​of X0, X1, and X2 respectively; is the expansion state, which represents the estimated value of the total disturbance of the system; It indicates the estimation of unknown faults of attitude angle sensor using RBFNN. is the estimated value of the weight coefficient, where: c j =[c 1j c 2j …c nj ] T (1-16) In the formula, c j b is the coordinate vector of the center point of the Gaussian basis function of the jth node neuron in the hidden layer; j is the width of its Gaussian basis function, and n represents the number of input variables; The output Uc of the LADRC control law is: In the formula, w c Expressed as controller bandwidth, v1=v, When the system input v is a constant value, v2=0, v3=0. The posture model (1-11) is transformed into: Under the extended state estimation compensation, the system becomes an integral series linear controlled object, that is: The part of the system (1-13) that is different from the standard integral series type is regarded as the total disturbance and estimated by LESO as the compensation of the control law. The nonlinear system with disturbance is processed into a standard integral series type system in the form of formula (1-20), realizing the dynamic compensation linearization processing of the nonlinear controlled object, in which the total disturbance includes internal disturbance and external disturbance. Estimation of sensor fault f by RBFNN g (X1) The system output information is transmitted to the LESO series structure without sensor fault information, ensuring is the estimated value of the actual X1.

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