Nonlinear super-spiral robust control method for tilt rotorcraft

Abstract

The invention relates to flight control of a tilt rotorcraft, in particular to a nonlinear super-spiral robust control method for the tilt rotorcraft, and aims to realize nonlinear control of the tilt rotorcraft on the basis of not simplifying or linearizing a dynamical model and quickly track expected speed and attitude instructions, and the technical scheme adopted by the invention is that the nonlinear super-spiral robust control method for the tilt rotorcraft comprises a nonlinear super-spiral robust control method for the tilt rotorcraft. Establishing a tilting rotorcraft dynamic model; and designing a super-spiral attitude control law based on the rotation matrix to obtain a control moment of the aircraft, then carrying out real-time approximation on an inverse model of the dynamic model by using an approximation characteristic of an RBF neural network, and calculating an actual control quantity of the aircraft by using the control moment so as to realize automatic control of the tilt rotorcraft. The method is mainly applied to design, manufacturing and flight control occasions of tilt rotorcrafts.

Description

Technical Field

[0001] The present invention relates to the flight control of a tiltrotor aircraft. Aiming at the complex non-linear aerodynamic model of the tiltrotor aircraft, a non-linear robust control method based on an online Radial Basis Function (RBF) neural network and a Super Twisting (STW) algorithm is proposed. This method avoids linearization, simplification, and order reduction of the non-linear model at different working points, realizes non-linear control design and verification on a high-fidelity non-linear model, and can quickly track position and attitude commands with high precision. Specifically, it relates to the non-linear pose tracking control of a tiltrotor aircraft. Background Art

[0002] A tiltrotor aircraft has the rotors of a helicopter and the aerodynamic control surfaces of a fixed-wing aircraft, and can switch between two modes by nacelle tilting, with the capabilities of vertical takeoff and landing, hovering in the air, and high-speed cruising. This type of aircraft combines the advantages of traditional helicopters and fixed-wing aircraft and has broad application prospects in military and civilian fields. Its structural schematic diagram is as Figure 1 shown. However, the complex and variable mechanical structure, the mutual interference between components, and the coupling effect between different channels make the aerodynamic characteristics of the aircraft very complex (monograph: The history of the XV-15 tilt rotor research aircraft: from concept to flight; author: Martin D Maisel, Demo J Giulianetti and Daniel C Dugan; publication date: March 2000), which poses a severe challenge to the design of the control system.

[0003] The high-fidelity dynamic model of a tilt-rotor aircraft is very complex, which contains a large number of differential equations and look-up table interpolation operations, making it difficult to carry out control design. Therefore, researchers usually linearize or simplify it. At present, most control designs are still linear control algorithms, which rely on linearizing the dynamic model of the aircraft at different operating points and then adjusting parameters for each operating point. The design process is cumbersome and it is difficult to ensure system stability. There is relatively little research on the nonlinear control of tilt-rotor aircraft, and it is necessary to simplify or reduce the order of the dynamic model, resulting in deviations in the dynamic characteristics of the system and having certain limitations (Journal: ISA transactions; Authors: Daniel N Cardoso, Sergio Esteban and Guilherme V Raffo; Publication date: July 2020; Article title: A new robust adaptive mixing control for trajectory tracking with improved forward flight of a tilt-rotor UAV; Pages: 86-104).

[0004] In summary, the nonlinear dynamic model of a tilt-rotor aircraft is complex. The existing control designs based on model linearization or simplification have limited applicability and strong limitations, and it is difficult to meet the requirements of high precision and stability. Therefore, it is very necessary to carry out nonlinear control design and verification based on the high-fidelity nonlinear model to achieve the pose tracking control of a tilt-rotor aircraft with high precision and large flight envelope. Summary of the Invention

[0005] To overcome the deficiencies of the prior art, the present invention aims to propose a nonlinear control method based on super-twisting and RBF neural network. Without simplifying or linearizing the dynamic model, the nonlinear control of a tilt-rotor aircraft is realized, and it can quickly track the desired speed and attitude commands. To this end, the technical solution adopted by the present invention is a nonlinear super-twisting robust control method for a tilt-rotor aircraft, which establishes a dynamic model of the tilt-rotor aircraft; designs a super-twisting attitude control law based on the rotation matrix to obtain the control torque of the aircraft, and then uses the approximation characteristics of the RBF neural network to approximate the inverse model of the dynamic model in real time, and calculates the actual control amount of the aircraft from the control torque, so as to realize the automatic control of the tilt-rotor aircraft.

[0006] The detailed steps are as follows:

[0007] Step (1) Establish a dynamic model of a tilt-rotor aircraft

[0008] A nonlinear dynamic model of a tilt-rotor aircraft is established, including rotor, wing, horizontal tail, vertical tail and fuselage subsystems. The rotor part includes an induced velocity model, a flapping motion model and a calculation part of aerodynamic force based on Pitt-Peters dynamic inflow theory; the wing part considers the influence of the rotor wake and models the slipstream region and the free stream region respectively; when modeling the tail fins, the influence of the rotor and wing wakes is considered, and at the same time, the downwash effect of the rotor on the horizontal tail and the sidewash effect of the fuselage on the vertical tail are considered; the fuselage part is modeled similarly to a fixed-wing aircraft, and the aerodynamic force is calculated through wind tunnel test data.

[0009] Define two right-handed orthogonal coordinate systems: (1) Inertial coordinate system {I} = {O I , X I , Y I , Z I}, where the coordinate origin O I is located on the ground, X I points north, Y I points east, and Z I points vertically downward; (2) Body coordinate system {B} = {O B , X B , Y B , Z B}, where the coordinate origin O B is located at the center of gravity of the tilt-rotor aircraft, X B points forward of the body, Y B points to the right of the body, and Z B is perpendicular to the fuselage and points downward. The six-degree-of-freedom nonlinear dynamic model of the tilt-rotor aircraft is described as

[0010]

[0011] where u, x, and y represent the control input vector, state vector, and output vector respectively, and are expanded as

[0012]

[0013] In the formula, (x, y, z) represents the position of the aircraft in the inertial coordinate system {I}, (u, v, w) represents the three-axis velocity in the body coordinate system {B}, (φ, θ, ψ) are the Euler angles, and (p, q, r) represents the angular velocity in the body coordinate system {B}. The eight control inputs are: collective pitch δ col , collective pitch differential δ colc , longitudinal cyclic pitch δ lon , longitudinal cyclic pitch differential δ lonc , aileron δ ail , elevator δ ele , rudder δ rud and nacelle tilt angle β m , where β mWhen it is 0°, it is in helicopter mode, and β m When it is 90°, it is in fixed-wing mode;

[0014] The attitude dynamics model of a tiltrotor aircraft based on the rotation matrix is expressed as

[0015]

[0016] where represents the inertia matrix of the aircraft, is defined in the body coordinate system {B} and represents the resultant moment generated by the rotor, wing, fuselage, horizontal tail, and vertical tail, represents the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, represents the skew-symmetric matrix spanned by ω. The specific expressions of R and S(ω) are as follows:

[0017]

[0018]

[0019] In the formula, s* represents sin(*), c* represents cos(*), φ, θ, and ψ respectively represent the roll angle, pitch angle, and yaw angle of the aircraft;

[0020] Step (2) Pose control law design

[0021] Let the control torque to be designed be Define the error e τ = τ * - τ, then Equation (3) can be written as

[0022]

[0023] Define the attitude error e R and the angular velocity error e ω in the following form:

[0024]

[0025] where represents the rotation matrix corresponding to the desired attitude, represents the desired angular velocity, and (·) ∨ represents the inverse transformation of S(·). Differentiating e R yields:

[0026]

[0027] In the formula, tr(·) represents the trace of the matrix. Differentiating e ω and substituting Equation (6) gives:

[0028]

[0029] Design the sliding mode surface \(s\) as

[0030]

[0031] where \(s_1\), \(s_2\) and \(s_3\) represent the sliding mode surfaces of the three attitude channels respectively, is the matrix to be designed, \(k\) Ri (\(i = 1,2,3\)) are positive constants. Take the derivative of \(s\), and then substitute Eqs. (8) and (9) and simplify to get:

[0032]

[0033] where \(\Omega\) represents the terms related to known and measurable quantities, and \(D\) represents the terms related to unknown and unmeasurable quantities. Their expressions are as follows:

[0034]

[0035] \(D = J\) -1 \(e\) τ (13)

[0036] For Eq. (11), design the control torque based on the super-twisting control algorithm as:

[0037] \(\tau\) * \(= J(X + \Omega)\) (14)

[0038] where the expression of \(X\) is as follows:

[0039]

[0040] In the formula, \(sgn(\cdot)\) represents the sign function, \(k\) ij (\(i = 1,2, j = 1,2,3\)) are positive gains;

[0041] After the attitude controller outputs the control torque (14), the actual control quantity needs to be calculated. In the helicopter mode, it is the collective differential \(\delta\) colc , the longitudinal cyclic pitch \(\delta\) lon and the longitudinal cyclic differential \(\delta\) lonc . Use the online radial basis function neural network to approximate the inverse model in real time, and calculate the corresponding control quantity from the desired torque. Analyzing the internal structure of the model, it can be obtained that the torque \(\tau\) is the collective \(\delta\) col , the collective differential \(\delta\) colc , the longitudinal cyclic pitch \(\delta\) lon , the longitudinal cyclic differential \(\delta\) lonc , the three-axis velocity \(V\) in the body coordinate system \(\{B\}\) b \(= [u, v, w]\) T and the angular velocity \(\omega = [p, q, r]\)T For the pitch channel in the helicopter mode of a tilt-rotor aircraft, the pitch moment is mainly adjusted by the longitudinal cyclic pitch δ lon , so its inverse model is expressed as:

[0042] δ lon = g(τ, δ col , V b , ω) (16)

[0043] A neural network is used to approximate it, and the radial basis function is designed as

[0044]

[0045] where is the true value of the neural network weight, ε lon is the estimation error of the neural network, and h(τ, δ col , V, ω) is the Gaussian basis function. The estimator based on the RBF neural network is designed as

[0046]

[0047] where is the estimated neural network weight, h i represents the output of the i-th neuron, b i is the width parameter of the kernel function, c i is the center value, and the superscript "-" represents the normalization process. The gradient descent method is used to adjust the weights online through the pitch moment error e τy , and the update law is

[0048]

[0049] In the formula, k lon is the parameter to be designed. Similarly, the neural networks for the roll and yaw channels can be designed respectively. Their structures are the same as that of the pitch channel. The differences are the weight update laws and the output quantities. For the roll channel, the roll moment is mainly adjusted by the collective pitch differential δ colc ; for the yaw channel, the yaw moment is mainly adjusted by the longitudinal cyclic pitch differential δ lonc . The weight update laws for adjusting the neural networks of the roll and yaw channels are respectively:

[0050]

[0051] where k colc and k lonc are the parameters to be designed, e τx and e τx are the errors of the roll and yaw moments respectively;

[0052] The position loop adopts a PID controller to obtain the collective pitch input and the desired roll angle and pitch angle. In helicopter mode, the collective pitch is δ col Adjusted according to the altitude error e z to obtain the desired roll angle φ d Adjusted according to the lateral velocity error e v to obtain the desired pitch angle θ d Adjusted according to the longitudinal velocity error e u to obtain the position control expression as follows:

[0053]

[0054] where and are the proportional, integral, and derivative coefficients of the collective pitch PID controller respectively; and are the proportional, integral, and derivative coefficients of the desired roll angle PID controller respectively; and are the proportional, integral, and derivative coefficients of the desired pitch angle PID controller respectively.

[0055] For the control design of fixed-wing mode, the super-twisting attitude control part is the same as that of the tilt-rotor mode. Only the RBF network part needs to be adjusted to the control surfaces of the fixed-wing mode, namely the aileron δ ail , elevator δ ele and rudder δ rud to perform roll, pitch, and yaw control respectively. For the position loop, due to the tilting of the nacelle, the longitudinal and vertical channels are switched. In fixed-wing mode, the collective pitch δ col is adjusted according to the longitudinal velocity error e u to obtain the desired roll angle φ d is adjusted according to the lateral velocity error e v to obtain the desired pitch angle θ d is adjusted according to the altitude error e z For the transition between tilt-rotor mode and fixed-wing mode, a longitudinal and vertical channel switching strategy and an allocation strategy between the two sets of control surfaces need to be designed. In the switching strategy, the channel switching coefficients are designed as

[0056]

[0057] k2 = sin(β m ), k4 = cos(β m ) (25)

[0058] The two sets of control surfaces are allocated according to the speed magnitude: Let the initial speed of the tilt transition be V1, the final speed be V2, and the forward flight speed be V. The moment distribution coefficient of the control surfaces during the transition process is designed as

[0059]

[0060] Then the torques of the rotor and the aerodynamic control surface are respectively

[0061]

[0062] The features and beneficial effects of the present invention are as follows:

[0063] The present invention conducts non - linear control design for a tilt - rotor aircraft, and proposes an attitude control method based on a super - twisting attitude control law and an online RBF neural network. Without linearizing or simplifying the non - linear dynamic model of the tilt - rotor aircraft, it can achieve accurate tracking of commands. Through Simulink simulation comparison with a linear PID - LQR attitude control algorithm, the effectiveness and superiority of the non - linear control law proposed in this paper are verified. Brief Description of the Drawings

[0064] Figure 1 is a schematic diagram of the coordinate system of the tilt - rotor aircraft adopted by the present invention;

[0065] Figure 2 is the STW - RBF attitude control flow chart proposed by the present invention;

[0066] Figure 3 is a schematic diagram of the switching of the longitudinal - vertical channel in the transition mode;

[0067] Figure 4 is the linear PID - LQR attitude control flow chart for comparative simulation experiments;

[0068] Figure 5 is the comparison of the speed and altitude error curves of the simulation experiments;

[0069] Figure 6 is the comparison of the attitude curves of the simulation experiments;

[0070] Figure 7 is the comparison of the control input curves of the simulation experiments. Detailed Embodiment

[0071] The present invention proposes a control method based on a super-twisting algorithm for attitude control and an online RBF neural network, which avoids the problems in existing research, retains the dynamic characteristics of the aircraft, and realizes the development of non-linear control design and verification on a high-fidelity non-linear model. The specific contents include: (1) Design a super-twisting attitude control law based on the rotation matrix to obtain the control torque of the aircraft. (2) Utilize the approximation characteristics of the RBF neural network to approximate the inverse model of the aerodynamic calculation part in real time, so as to calculate the actual control quantity of the aircraft from the control torque. (3) Conduct numerical simulation experiments on the proposed control algorithm in Simulink, and compare it with a linear PID-LQR attitude control algorithm to verify the superiority of the non-linear control law proposed by the present invention.

[0072] The non-linear super-twisting robust control method of the present invention for a tilt-rotor aircraft establishes a tilt-rotor aircraft dynamics model; designs a super-twisting attitude control law based on the rotation matrix to obtain the control torque of the aircraft, and then utilizes the approximation characteristics of the RBF neural network to approximate the inverse model of the dynamics model in real time, calculates the actual control quantity of the aircraft from the control torque, thereby realizing the automatic control of the tilt-rotor aircraft.

[0073] The detailed steps are as follows:

[0074] Step (1) Establish a tilt-rotor aircraft dynamics model

[0075] Establish a non-linear dynamics model of the tilt-rotor aircraft, including rotor, wing, horizontal tail, vertical tail and fuselage subsystems. The rotor part includes an induced velocity model, a flapping motion model and a calculation part of aerodynamic force based on the Pitt-Peters dynamic inflow theory; the wing part considers the influence of the rotor wake and models the slipstream area and the free stream area respectively; when modeling the tail fins, the influence of the rotor and wing wakes is considered, and at the same time, the downwash effect of the rotor on the horizontal tail and the sidewash effect of the fuselage on the vertical tail are considered; the fuselage part is modeled similarly to a fixed-wing aircraft, and the aerodynamic force is calculated through wind tunnel experiment data.

[0076] Define two right-handed orthogonal coordinate systems: (1) Inertial coordinate system {I} = {O I , X I , Y I , Z I}, where the coordinate origin O I is located on the ground, X I points north, Y I points east, and Z I points vertically downward; (2) Body coordinate system {B} = {O B , X B , Y B , Z B}, where the coordinate origin O BLocated at the center of gravity of the tiltrotor, X B Points forward along the fuselage, Y B Points rightward along the fuselage, Z B Perpendicular to the fuselage and downward. The six-degree-of-freedom nonlinear dynamic model of the tiltrotor is described as

[0077]

[0078] where u, x, and y represent the control input vector, state vector, and output vector respectively, and are expanded as

[0079]

[0080] In the formula, (x, y, z) represents the position of the aircraft in the inertial coordinate system {I}, (u, v, w) represents the three-axis velocity in the body coordinate system {B}, (φ, θ, ψ) are the Euler angles, and (p, q, r) represents the angular velocity in the body coordinate system {B}. The eight control inputs are: collective pitch δ col , collective pitch differential δ colc , longitudinal cyclic pitch δ lon , longitudinal cyclic pitch differential δ lonc , aileron δ ail , elevator δ ele , rudder δ rud and nacelle tilt angle β m , where β m = 0° is the helicopter mode, and β m = 90° is the fixed-wing mode.

[0081] The attitude dynamics model of the tiltrotor based on the rotation matrix is expressed as

[0082]

[0083] where represents the inertia matrix of the aircraft, is defined in the body coordinate system {B} and represents the resultant moment generated by the rotor, wing, fuselage, horizontal tail, and vertical tail, represents the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, represents the skew-symmetric matrix spanned by ω. The specific expressions of R and S(ω) are as follows:

[0084]

[0085] In the formula, s* represents sin(*), c* represents cos(*), and φ, θ, and ψ represent the roll angle, pitch angle, and yaw angle of the aircraft respectively.

[0086] Step (2) Pose control law design

[0087] Let the control torque to be designed be Define the error e τ = τ * -τ, then Equation (3) can be written as

[0088]

[0089] Define the attitude error e R and the angular velocity error e ω in the following form:

[0090]

[0091] where represents the rotation matrix corresponding to the desired attitude, represents the desired angular velocity, (·) ∨ represents the inverse transformation of S(·). Differentiating e R yields

[0092]

[0093] where tr(·) represents the trace of the matrix. Differentiating e ω and substituting Equation (6) gives

[0094]

[0095] Design the sliding surface s as

[0096]

[0097] where s1, s2, and s3 respectively represent the sliding surfaces of the three attitude channels, is the matrix to be designed, and k Ri (i = 1, 2, 3) are positive constants. Differentiating s and then substituting Equations (8) and (9) and arranging gives

[0098]

[0099] where Ω represents the terms related to known and measurable quantities, and D represents the terms related to unknown and unmeasurable quantities. Their expressions are as follows:

[0100]

[0101] For Equation (11), based on the super-twisting control algorithm, design the control torque as

[0102] τ * = J(X + Ω) (14)

[0103] where the expression of X is as follows:

[0104]

[0105] where sgn(·) represents the sign function, and k ij (i = 1, 2, j = 1, 2, 3) are positive gains.

[0106] After the attitude controller outputs the control torque (14), it is necessary to calculate the actual control amount, which is the total pitch differential δ colc , longitudinal cyclic pitch δ lon and longitudinal cyclic pitch differential δ lonc in the helicopter mode. The present invention uses an online radial basis function neural network to approximate the inverse model in real time, and calculates the corresponding control amount from the desired torque. Analyzing the internal structure of the model, it is obtained that the torque τ is a function of the total pitch δ col , total pitch differential δ colc , longitudinal cyclic pitch δ lon , longitudinal cyclic pitch differential δ lonc , the three-axis velocity V b = [u, v, w] T and the angular velocity ω = [p, q, r] T in the body coordinate system {B}. For the pitch channel in the helicopter mode of a tilt-rotor aircraft, the pitch torque is mainly adjusted by the longitudinal cyclic pitch δ lon , so its inverse model can be expressed as

[0107] δ lon = g(τ, δ col , V b , ω) (16)

[0108] A neural network is used to approximate it, and the radial basis function is designed as

[0109]

[0110] where is the true value of the neural network weight, ε lon is the estimation error of the neural network, and h(τ, δ col , V, ω) is a Gaussian basis function. The estimator based on the RBF neural network is designed as

[0111]

[0112] where is the estimated neural network weight, h i represents the output of the i-th neuron, b i is the width parameter of the kernel function, c i is the center value, and the superscript "-" represents the normalization process. The gradient descent method is used to pass through the pitch torque error e τyPerform online adjustment of the weights, and the update law is

[0113]

[0114] where k lon is a parameter to be designed. Similarly, neural networks for the roll and yaw channels can be designed respectively. Their structures are the same as that of the pitch channel. The differences are the weight update laws and output quantities. For the roll channel, the roll moment is mainly adjusted by the collective differential δ colc ; for the yaw channel, the yaw moment is mainly adjusted by the longitudinal cyclic differential δ lonc . The weight update laws for adjusting the neural networks of the roll and yaw channels are respectively

[0115]

[0116] where k colc and k lonc are parameters to be designed, and e τx and e τx are the errors of the roll and yaw moments respectively.

[0117] The position loop uses a PID controller to obtain the collective input and the desired roll angle and pitch angle. In the helicopter mode, the collective δ col is adjusted according to the altitude error e z , the desired roll angle φ d is adjusted according to the lateral velocity error e v , and the desired pitch angle θ d is adjusted according to the longitudinal velocity error e u . The position control expressions are as follows:

[0118]

[0119] where and are the proportional, integral, and differential coefficients of the collective PID controller respectively; and are the proportional, integral, and differential coefficients of the desired roll angle PID controller respectively; and are the proportional, integral, and differential coefficients of the desired pitch angle PID controller respectively.

[0120] For the control design of the fixed-wing mode, the super-twisting attitude control part is the same as that of the helicopter mode. Only the RBF network part needs to be adjusted to the control surfaces of the fixed-wing mode, that is, the aileron δ ail , the elevator δ ele and the rudder δ rud, roll, pitch, and yaw controls are performed separately. For the position loop, due to the tilt of the nacelle, the longitudinal and vertical channels are switched. In the fixed-wing mode, the collective pitch δ col is adjusted according to the longitudinal velocity error e u to obtain the desired roll angle φ d is adjusted according to the lateral velocity error e v to obtain the desired pitch angle θ d is adjusted according to the altitude error e z For the transition between the tilt-rotor mode and the fixed-wing mode, a longitudinal and vertical channel switching strategy and a distribution strategy between the two sets of control surfaces need to be designed. In the switching strategy, the channel switching coefficient is designed as

[0121]

[0122] k2 = sin(β m ), k4 = cos(β m ) (25)

[0123] The two sets of control surfaces are distributed according to the speed magnitude: Let the initial speed of the tilt transition be V1, the final speed be V2, and the forward flight speed be V. The moment distribution coefficient of the control surface during the transition process is designed as

[0124]

[0125] Then the moments of the rotor and the aerodynamic control surface are respectively

[0126]

[0127] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0128] The implementation steps of the technical solution adopted by the present invention are as follows:

[0129] (1) Establish a tilt-rotor aircraft dynamics model

[0130] The present invention takes the tilt-rotor aircraft in Figure 1 as the research object and establishes a nonlinear dynamics model, including rotor, wing, horizontal tail, vertical tail, and fuselage subsystems. The rotor part includes an induced velocity model based on the Pitt-Peters dynamic inflow theory, a flapping motion model, and a calculation part of aerodynamic force; the wing part considers the influence of the rotor wake and models the slipstream area and the free-stream area respectively; when modeling the tail fins, the influence of the rotor and wing wakes is considered, and at the same time, the downwash effect of the rotor on the horizontal tail and the sidewash effect of the fuselage on the vertical tail are considered; the fuselage part is modeled similar to a fixed-wing aircraft, and the aerodynamic force is calculated through wind tunnel experiment data.

[0131] For the convenience of subsequent controller design, as Figure 1As shown, two right-handed orthogonal coordinate systems are defined: (1) Inertial coordinate system {I} = {O I , X I , Y I , Z I}, where the coordinate origin O I is located on the ground, X I points north, Y I points east, and Z I points vertically downward; (2) Body coordinate system {B} = {O B , X B , Y B , Z B}, where the coordinate origin O B is located at the center of gravity of the tiltrotor aircraft, X B points forward of the body, Y B points to the right of the body, and Z B is perpendicular to the fuselage and points downward. The six-degree-of-freedom nonlinear dynamic model of the tiltrotor aircraft can be described as

[0132]

[0133] where u, x, and y represent the control input vector, state vector, and output vector, respectively, and are expanded as

[0134]

[0135] In the formula, (x, y, z) represents the position of the aircraft in the inertial coordinate system {I}, (u, v, w) represents the three-axis velocity in the body coordinate system {B}, (φ, θ, ψ) are the Euler angles, and (p, q, r) represents the angular velocity in the body coordinate system {B}. The eight control inputs are: collective pitch δ col , collective pitch differential δ colc , longitudinal cyclic pitch δ lon , longitudinal cyclic pitch differential δ lonc , aileron δ ail , elevator δ ele , rudder δ rud and nacelle tilt angle β m , where β m = 0° is the helicopter mode, and β m = 90° is the fixed-wing mode.

[0136] The attitude dynamics model of the tiltrotor aircraft based on the rotation matrix can be expressed as

[0137]

[0138] where represents the inertial matrix of the aircraft, Defined in the body coordinate system {B}, it represents the resultant moment generated by the rotor, wing, fuselage, horizontal tail, and vertical tail. Represents the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}. Represents the skew-symmetric matrix spanned by ω. The specific expressions of R and S(ω) are as follows:

[0139]

[0140] In the formula, s* represents sin(*), c* represents cos(*), and φ, θ, and ψ respectively represent the roll angle, pitch angle, and yaw angle of the aircraft.

[0141] (2) Design of the pose control law

[0142] Let the control moment to be designed be Define the error e τ = τ * -τ, then Equation (3) can be written as

[0143]

[0144] Define the attitude error e R and the angular velocity error e ω in the following form:

[0145]

[0146] where represents the rotation matrix corresponding to the desired attitude, represents the desired angular velocity, (*) ∨ represents the inverse transformation of S(·). Differentiating e R yields

[0147]

[0148] In the formula, tr(·) represents the trace of the matrix. Differentiating e ω and substituting Equation (6) gives

[0149]

[0150] Design the sliding surface s as

[0151]

[0152] where s1, s2, and s3 respectively represent the sliding surfaces of the three attitude channels, is the matrix to be designed, and k Ri (i = 1, 2, 3) are positive constants. Differentiating s and then substituting Equations (8) and (9) and arranging gives

[0153]

[0154] Among them, Ω represents the terms related to known and measurable quantities, and D represents the terms related to unknown and unmeasurable quantities. Their expressions are as follows:

[0155]

[0156] D = J -1 e τ (13)

[0157] For equation (11), based on the super-twisting control algorithm, the control torque is designed as

[0158] τ * = J(X + Ω) (14)

[0159] Among them, the expression of X is as follows:

[0160]

[0161] In the formula, sgn(·) represents the sign function, and k ij (i = 1, 2, j = 1, 2, 3) are positive gains.

[0162] After the attitude controller outputs the control torque (14), the actual control quantity needs to be calculated. In the helicopter mode, it is the collective differential δ colc , the longitudinal cyclic pitch δ lon and the longitudinal cyclic pitch differential δ lonc . The present invention uses an online radial basis function neural network to approximate the inverse model in real time, and calculates the corresponding control quantity from the desired torque. For the pitch channel in the helicopter mode of the tilt-rotor aircraft, the pitch torque is mainly adjusted by the longitudinal cyclic pitch δ lon , so its inverse model can be expressed as

[0163] δ lon = g(τ, δ col , V b , ω) (16)

[0164] A neural network is used to approximate it, and the radial basis function is designed as

[0165]

[0166] Among them is the true value of the neural network weight, ε lon is the estimation error of the neural network, and h(τ, δ col , V, ω) is a Gaussian basis function. The estimator based on the RBF neural network is designed as

[0167]

[0168] where are the estimated neural network weights, and h i represents the output of the i-th neuron, and b i is the width parameter of the kernel function, c i is the center value, and the superscript "-" represents the normalization process. The gradient descent method is used to adjust the weights online through the pitch moment error e τy , and the update law is

[0169]

[0170] where k lon is the parameter to be designed. Similarly, the neural networks for the roll and yaw channels can be designed respectively. Their structures are the same as that of the pitch channel, and the differences lie in the weight update laws and output quantities. For the roll channel, the roll moment is mainly adjusted by the collective pitch differential δ colc ; for the yaw channel, the yaw moment is mainly adjusted by the longitudinal cyclic pitch differential δ lonc . The weight update laws for adjusting the neural networks of the roll and yaw channels are respectively

[0171]

[0172] where k colc and k lonc are the parameters to be designed, and e τx and e τx are the errors of the roll and yaw moments respectively. The above attitude control process based on the super-twisting algorithm and RBF neural network is as shown in Figure 2 .

[0173] The position loop adopts a PID controller to obtain the collective pitch input and the desired roll angle and pitch angle. In the helicopter mode, the collective pitch δ col is adjusted according to the altitude error e z , the desired roll angle φ d is adjusted according to the lateral velocity error e v , and the desired pitch angle θ d is adjusted according to the longitudinal velocity error e u . The position control expressions are as follows:

[0174]

[0175] where and are the proportional, integral, and differential coefficients of the collective pitch PID controller respectively; and are the proportional, integral, and differential coefficients of the desired roll angle PID controller respectively; and They are the proportional, integral, and derivative coefficients of the desired pitch angle PID controller respectively.

[0176] For the control design of the fixed-wing mode, the super-twisting attitude control part is the same as that of the helicopter mode. Only the RBF network part needs to be adjusted to the control surfaces of the fixed-wing mode, that is, the aileron δ ail , elevator δ ele and rudder δ rud , for roll, pitch, and yaw control respectively. For the position loop, due to the tilt of the nacelle, the longitudinal and vertical channels are switched. The collective pitch δ col in the fixed-wing mode is adjusted according to the longitudinal velocity error e u . The desired roll angle φ d is adjusted according to the lateral velocity error e v . The desired pitch angle θ d is adjusted according to the altitude error e z . In addition, for the transition between the helicopter mode and the fixed-wing mode, a switching strategy for the longitudinal and vertical channels and a distribution strategy between the two sets of control surfaces need to be designed.

[0177] The tilt of the nacelle in the transition mode changes the direction of the rotor thrust, which in turn leads to changes in the longitudinal control logic of the helicopter mode and the fixed-wing mode. In the helicopter mode, the longitudinal velocity of the tiltrotor is controlled by the pitch angle, and the vertical velocity is controlled by the collective pitch. In the fixed-wing mode, the longitudinal velocity is controlled by the collective pitch, and the vertical velocity is controlled by the pitch angle. Therefore, during the transition process, the vertical and longitudinal channels are severely coupled, and a switching between the control channels is required. The switching strategy is as Figure 3 shown. The channel switching coefficients are designed as

[0178]

[0179] k2 = sin(β m ), k4 = cos(β m ) (25)

[0180] In the early stage of the tilt transition, the forward flight speed is small, and the control moment mainly comes from the rotor. As the tilt angle of the nacelle increases, the forward flight speed gradually increases, and the control moment generated by the aerodynamic control surface also increases continuously. In the later stage of the tilt transition, the control surface is mainly the aerodynamic control surface, and the cyclic pitch of the rotor is supplemented. During the transition process, there is redundancy in the control surfaces of the tiltrotor. Therefore, it is necessary to reasonably distribute the control surfaces to achieve the hybrid control operation of the cyclic pitch and the aerodynamic control surface.

[0181] The control efficiency of the aerodynamic control surface is related to the square of the speed. Therefore, the control surfaces can be distributed according to the speed magnitude. Let the initial speed of the tilt transition be V1, the final speed be V2, and the forward flight speed be V. The moment distribution coefficient of the control surface during the transition process is designed as

[0182]

[0183] Then the torques of the rotor and the aerodynamic control surfaces are respectively

[0184]

[0185] The following gives specific implementation examples:

[0186] The numerical simulation experiment is carried out on the MATLAB / Simulink platform. Taking the attitude control in helicopter mode as an example for the simulation experiment, under the same position loop control structure, a comparative experiment is carried out with a linear PID-LQR controller, and its control process is as Figure 4 shown. Linearize the nonlinear dynamics model of the tiltrotor in the hover state to obtain the state space expression, then set the weight matrix and solve the Riccati equation to obtain the feedback matrix of the LQR control law.

[0187] The vertical position (m), velocity (m / s) and yaw angle (rad) commands given in the simulation are as follows:

[0188] z d =-3t, u d =10, v d =0, ψ d =0.2t (28)

[0189] The parameters set in the simulation are: k R =diag(25, 200, 75), k 11 =100, k 12 =200, k 13 =1000, k 21 =0.5, k 22 =1, k 23 =0.5, and the weight adjustment gains of the neural networks corresponding to the three channels are respectively k colc =1.5×10 -8 ,k lon =-2.5×10 -10 ,k lonc =5×10 -9 。The simulation results are as Figures 5 to 7 shown.

[0190] Figure 4 Shows the errors in the position loop of the two control methods. It can be seen from the figure that both methods can make the errors converge and the system is stable, but the control algorithm proposed in the present invention has a faster convergence speed and a smaller tracking error. Figure 5 Shows the attitude curve of the tiltrotor. It can be seen that the method of the present invention makes the response of the attitude angle faster. Figure 6The control input within a reasonable range indicates the rationality of the control algorithm. Since the position loop control structures are the same, the vertical position error curves and the collective pitch control inputs of the two methods are basically the same.

[0191] To better compare the performance differences between the two methods, the root mean square error (RMSE) of the attitude is calculated, as shown in Table 1. It can be seen from the table that the root mean square errors of the three-axis attitude angles of the control algorithm proposed by the present invention are much smaller than those of the PID-LQR control algorithm, indicating that this non-linear control algorithm has better control performance.

[0192] Table 1 Comparison of root mean square errors

[0193]

[0194] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A nonlinear super-helical robust control method for a tiltrotor aircraft, characterized in that: A dynamic model of a tiltrotor aircraft is established; a superhelical attitude control law is designed based on the rotation matrix to obtain the control torque of the aircraft, and then the approximation characteristics of the RBF neural network are used to approximate the inverse model of the dynamic model in real time, and the actual control amount of the aircraft is calculated from the control torque, thereby realizing automatic control of the tiltrotor aircraft.

2. The nonlinear super-helical robust control method for a tiltrotor aircraft according to claim 1, characterized in that: The detailed steps are as follows: Step (1) Establishing the dynamic model of the tiltrotor aircraft A nonlinear dynamic model of a tiltrotor aircraft is established, which includes the rotor, wing, horizontal tail, vertical tail and fuselage subsystems. The rotor part includes the induced velocity model based on the Pitt-Peters dynamic inflow theory, the flapping motion model and the aerodynamic calculation part; the wing part considers the influence of the rotor wake, and models the slipstream area and the freestream area respectively; when modeling the tail, the influence of the rotor and wing wake is considered, and the downwash effect of the rotor on the horizontal tail and the sidewash effect of the fuselage on the vertical tail are considered; the modeling of the fuselage part is similar to that of fixed-wing aircraft, and the aerodynamic force is calculated through wind tunnel experimental data. Define two right-handed orthogonal coordinate systems: (1) Inertial coordinate system {I} = {O I ,X I ,Y I ,Z I }, where the coordinate origin O I Located on the ground, X I Pointing north, Y I Pointing east, Z I Vertically downward; (2) Body coordinate system {B} = {O B ,X B ,Y B ,Z B }, where the coordinate origin O B Located at the center of gravity of the tiltrotor, X B Point to the front of the aircraft, Y B Point to the right of the body, Z B Vertically downward from the fuselage. The six-degree-of-freedom nonlinear dynamic model of the tiltrotor aircraft is described as Where u, x and y represent the control input vector, state vector and output vector respectively, which can be expanded into Where (x, y, z) represents the position of the aircraft in the inertial coordinate system {I}, (u, v, w) represents the three-axis velocity in the body coordinate system {B}, (φ, θ, ψ) is the Euler angle, (p, q, r) represents the angular velocity in the body coordinate system {B}, and the eight control inputs are: col , total distance differential δ colc 、Longitudinal periodic pitch δ lon , longitudinal periodic variable distance differential δ lonc 、Aileron δ ail 、Elevator δ ele 、Rudder δ rud and the nacelle inclination angle β m , where β m =0° is helicopter mode, β m =90° is fixed-wing mode; The attitude dynamics model of the tiltrotor aircraft based on the rotation matrix is ​​expressed as in represents the inertia matrix of the aircraft, Defined in the body coordinate system {B}, it represents the resultant moment generated by the rotor, wing, fuselage, horizontal tail and vertical tail, represents the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, Represents the antisymmetric matrix spanned by ω, and the specific expressions of R and S(ω) are as follows: Where s* represents sin(*), c* represents cos(*), φ, θ and ψ represent the roll angle, pitch angle and yaw angle of the aircraft respectively; Step (2) Design of posture control law Assume the control torque to be designed is Definition error e τ =τ * -τ, then equation (3) can be written as Define the attitude error e R and angular velocity error e ω In the following form: in represents the rotation matrix corresponding to the desired posture, represents the desired angular velocity, (·) ∨ represents the inverse transformation of S(·). R The derivative is: Where tr(·) represents the trace of the matrix. ω Derivative and substitute equation (6) into it to obtain: The designed sliding surface s is in s1, s2 and s3 represent the sliding surfaces of the three attitude channels respectively. is the matrix to be designed, k Ri (i=1,2,3) is a positive constant, take the derivative of s, and then substitute equation (8) and equation (9) into it to get: Where Ω represents the term related to known and measurable quantities, and D represents the term related to unknown and unmeasurable quantities. The expressions of the two are as follows: D=J -1 e τ (13) According to formula (11), the control torque designed based on the super-helical control algorithm is: t * =J(X+Ω) (14) The expression of X is as follows: Where sgn(·) represents the sign function, k ij (i=1,2,j=1,2,3) is positive gain; After the attitude controller outputs the control torque (14), the actual control quantity needs to be calculated. In helicopter mode, it is the total distance differential δ colc 、Longitudinal periodic pitch δ lon and longitudinal periodic differential δ lonc , the inverse model is approximated in real time using an online radial basis function neural network, and the corresponding control quantity is calculated from the desired torque. By analyzing the internal structure of the model, we can obtain: the torque τ is the total distance δ col , total distance differential δ colc 、Longitudinal periodic pitch δ lon , longitudinal periodic variable distance differential δ lonc 、Three-axis velocity V in the body coordinate system {B} b =[u,v,w] T and angular velocity ω=[p,q,r] T For the pitch channel of the tiltrotor helicopter mode, the pitch moment is mainly generated by the longitudinal cyclic pitch variation δ lon Adjustment, so its inverse model is expressed as: d lon =g(τ,δ col ,V b ,oh) (16) A neural network is used to approximate it, and the radial basis function is designed as in is the true value of the neural network weight, ε lon is the estimation error of the neural network, h(τ,δ col ,V,ω) is the Gaussian basis function. The estimator based on RBF neural network is designed as in is the estimated neural network weight, h i represents the output of the i-th neuron, b i is the width parameter of the kernel function, c i is the center value, the superscript "" indicates normalization, and the gradient descent method is used to calculate the pitch moment error e τy The weights are adjusted online, and the update law is Where k lon is the parameter to be designed. Similarly, the neural networks of the roll and yaw channels can be designed respectively. Their structures are the same as those of the pitch channel. The difference is the update law of the weights and the output. For the roll channel, the roll moment is mainly calculated by the total distance differential δ colc Adjustment; For the yaw channel, the yaw moment is mainly adjusted by the longitudinal periodic pitch differential δ lonc Adjustment: The neural network weight update laws for adjusting the roll channel and yaw channel are: where k colc and k lonc is the parameter to be designed, e τx and e τx are the errors of rolling and yaw moments respectively; The position loop uses a PID controller to obtain the total pitch input and the desired roll and pitch angles. In helicopter mode, the total pitch δ col According to the height error e z Adjust to get the desired roll angle φ d According to the lateral velocity error e v Adjust to get the desired pitch angle θ d According to the longitudinal velocity error e u After adjustment, the position control expression is as follows: in and They are the proportional, integral and differential coefficients of the collective PID controller respectively; and are the proportional, integral and differential coefficients of the desired roll angle PID controller respectively; and are the proportional, integral and differential coefficients of the desired pitch angle PID controller respectively.

3. The nonlinear super-helical robust control method for a tiltrotor aircraft according to claim 1, characterized in that: For the control design of the fixed-wing mode, the super-helical attitude control part is the same as that of the tilt-rotor mode. It only needs to adjust the RBF network part to the control surface of the fixed-wing mode, that is, the aileron δ ail 、Elevator δ ele and rudder δ rud , respectively, for roll, pitch and yaw control. For the position loop, the longitudinal and vertical channels are switched due to the tilting of the nacelle. In the fixed-wing mode, the total distance δ col According to the longitudinal velocity error e u Adjust to get the desired roll angle φ d According to the lateral velocity error e v Adjust to get the desired pitch angle θ d According to the height error e z It is found that for the transition between the tiltrotor mode and the fixed-wing mode, it is necessary to design a longitudinal and vertical channel switching strategy and a distribution strategy between the two sets of control surfaces. The channel switching coefficient in the switching strategy is designed as: k2=sin(β m ),k4=cos(β m ) (25) The two sets of control surfaces are distributed according to the speed: the initial speed of the tilt transition is V1, the final speed is V2, the forward flight speed is V, and the moment distribution coefficient of the control surface during the transition process is designed to be The moments of the rotor and the aerodynamic control surface are

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