Unmanned helicopter sliding mode flight control method based on online neural network

Abstract

The invention aims to provide an unmanned helicopter sliding-mode flight control method based on an online neural network. The unmanned helicopter sliding-mode flight control method is specifically implemented according to the following steps: step 1, designing a helicopter attitude and height dynamic nonlinear model; 2, designing a nonlinear disturbance observer and a neural network estimator, and designing a sliding mode robust controller based on a backstepping method; and step 3, stability analysis is carried out through a Lyapunov function, and the stability of the helicopter system facing interference and uncertainty is ensured. According to the method, the problem existing in robust flight control of keeping attitude and height stability of the unmanned helicopter under interference and uncertainty in the prior art is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned helicopter control, and particularly relates to a sliding mode flight control method for unmanned helicopters based on an online neural network. Background Art

[0002] Due to its vertical takeoff and landing, hovering, and maneuvering flight capabilities, unmanned helicopters play an important role in both military and civilian fields. However, due to the complexity, nonlinearity, and highly coupled dynamic characteristics of the unmanned helicopter system, and the inevitable challenges of uncertainty, external interference, actuator failures, and input saturation in practical applications, the design of its control system has become particularly difficult. Therefore, the research on helicopter flight control has received attention in the academic community.

[0003] Historically, the field of flight control has been deeply studied. Traditional control methods, such as PID control, sliding mode control, and control methods based on LMI or observers, usually rely on simplifying complex helicopter nonlinear models into linear models or ignoring the coupling relationship between Euler angle rates and helicopter angular velocities. Although these methods simplify the control model, they also lead to a decrease in control accuracy and suboptimal performance. To overcome these limitations, researchers have begun to combine traditional control methods with intelligent control strategies, such as fuzzy logic and neural networks, to develop more advanced and effective controllers. For example, Chinese scholars have combined backstepping, neural networks, and disturbance observers, which not only retains the ability of backstepping to efficiently handle nonlinear systems but also effectively addresses system uncertainty and external interference. Similarly, foreign researchers have significantly improved the performance of sliding mode control by combining adaptive control and sliding mode control methods. Although sliding mode control exhibits robustness in the face of system uncertainty and external interference, it often causes significant chattering in complex environments. Neural networks, with their powerful function approximation ability, effectively solve the problem of system uncertainty. By integrating neural networks with observers, system uncertainty can be more effectively handled, while external interference is handled by a nonlinear disturbance observer. Combining sliding mode control with these observers not only effectively solves the problems of system uncertainty and external interference but also reduces the chattering of the controller, enhancing the robustness and accuracy of the system. Summary of the Invention

[0004] The purpose of the present invention is to provide a sliding mode flight control method for unmanned helicopters based on an online neural network, which solves the problems existing in the robust flight control of maintaining attitude and altitude stability of unmanned helicopters under interference and uncertainty in the prior art.

[0005] The technical solution adopted by the present invention is a sliding mode flight control method for unmanned helicopters based on an online neural network, which is specifically implemented according to the following steps:

[0006] Step 1: Design a dynamic non-linear model for the helicopter's attitude and altitude;

[0007] Step 2: Design a non-linear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method;

[0008] Step 3: Conduct a stability analysis through the Lyapunov function to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0009] The features of the present invention also lie in that,

[0010] Step 1 is specifically implemented according to the following steps:

[0011] For the variables appearing in the following formula, the explanations are as follows: represents the first derivative of the function f(x), represents the second derivative of the function f(x), A T represents the transpose matrix of matrix A, A -1 represents the inverse matrix of matrix A, |A| represents the determinant of matrix A, represents the n-dimensional vector space, I n×n represents the n-order identity matrix;

[0012] Step 1.1: Design a dynamic model for the helicopter's attitude and altitude:

[0013]

[0014] where h(t) and v(t) are the altitude position and its climbing speed of the unmanned helicopter in the inertial coordinate system, m is the mass of the unmanned helicopter, g 0 is the acceleration due to gravity, Ω(t) = (φ(t) θ(t) ψ(t)) T represents the attitude angle of the unmanned helicopter, where φ(t), θ(t) and ψ(t) represent the roll angle, pitch angle and yaw angle respectively, W(t) = (p(t) q(t) r(t)) T represents the angular velocity vector, where p(t), q(t) and r(t) represent the roll angular velocity, pitch angular velocity and yaw angular velocity respectively, J = diag{J xx J yy J zz} represents the inertia matrix of the unmanned helicopter, where, J xx 、J yy and J zz represent the roll moment of inertia, pitch moment of inertia and yaw moment of inertia respectively, H 0 (t) is the attitude motion matrix:

[0015]

[0016] where sin(·), cos(·), tan(·) and sec(·) represent the sine function, cosine function, tangent function and secant function in trigonometric functions respectively;

[0017] W(t) × represents the cross product operator matrix:

[0018]

[0019] T m (t) and τ 0 (t) are the pulling force and control moment of the main rotor of the helicopter. They are the control inputs of the altitude attitude system of the unmanned helicopter. x = (x 1 , x 2 ) T is the state of the system. x 1 (t) = (h(t) Ω T (t)) T represents the state vector. x 2 (t) = (v(t) W T (t)) T represents the velocity vector, and represent the interference force and interference moment in the vertical direction respectively, and represent the uncertain terms of the system;

[0020] Step 1.2. Based on the above helicopter attitude and altitude model, rewrite the system:

[0021]

[0022] where, represents the control input of the system: u 1 (t) = cosφ(t)cosθ(t)T m (t) - mg 0 , u 2 (t) = τ 0 (t); f(x 1 ) and f(x 2 ) represent the parameter matrices related to x 1 (t) and x 2 (t) respectively. The specific forms are as follows: g and are constant matrices related to mass and moment of inertia. The specific expression forms are as follows: d(t) and Δf(x) represent the interference and uncertainty of the system:

[0023] To handle the uncertainty of the system, define the continuous function P(x):

[0024]

[0025] Among them, \(L = \text{diag}\{l 1 , l 2 , l 3 , l 4}\}>0\) is the gain coefficient matrix, and \(l 1 , l 2 , l 3 and \(l 4 are its four gain coefficients respectively;

[0026] The radial basis function neural network is used to approximate the continuous function \(P(x)\), and the form is as follows:

[0027] \(P(x)=W *T H(x)+\varepsilon * \ (4)

[0028] Among them, \(H(x)\) is the basis function of the neural network, and \(W * is its optimal weight, and \(\varepsilon * is the optimal approximation error;

[0029] According to formula (3) and formula (4), we have Therefore, formula (2) can be further rewritten as:

[0030]

[0031] Among them represents the composite disturbance composed of the external disturbance of the system and the approximation error of the neural network.

[0032] Step 2 is specifically implemented according to the following steps:

[0033] Step 2.1, Design of the nonlinear disturbance observer:

[0034] The disturbance observer equation is designed as:

[0035]

[0036] Among them, is the disturbance estimated value, is the estimated value of the optimal weight \(W * \), and \(\delta(t)\) is the constructed function;

[0037] Define the disturbance estimation error value as Then the dynamics of the disturbance estimation error is given by the following formula:

[0038]

[0039] Among them is the weight estimation error;

[0040] Step 2.2, Design of neural network disturbance observer:

[0041] The neural network disturbance observer is designed as:

[0042]

[0043] where, Π(t) is the state vector of the observer, η(t) is the construction function, Λ = diag{λ 1 , λ 2 , λ 3 , λ 4} > 0 is the gain coefficient matrix, and λ 1 , λ 2 , λ 3 and λ 4 are its 4 gain coefficients respectively;

[0044] Define the nominal estimation error e n (t) = x 2 (t) - Π(t), then the dynamic representation of the error is:

[0045]

[0046] Select the adaptive rate as:

[0047]

[0048] where, γ > 0 and σ > 0 are gain coefficients, and s(t) is the sliding mode surface to be designed later;

[0049] Step 2.3, Design of sliding mode controller based on backstepping method.

[0050] Step 2.3 is specifically implemented according to the following steps:

[0051] Step 2.3.1, Define the altitude attitude angle error;

[0052] Step 2.3.2, Define the velocity and attitude angular velocity error terms;

[0053] Step 2.3.3, Define the sliding mode surface;

[0054] Step 2.3.4, Design the controller.

[0055] Step 2.3.1 is specifically implemented according to the following steps:

[0056] Define the altitude attitude angle error e 1 (t):

[0057] e 1 (t) = x1 (t)-x d (t) (3)

[0058] Among them, x d (t) is the desired tracking trajectory of the altitude attitude;

[0059] According to formula (5), the dynamics of the altitude attitude error is expressed as:

[0060]

[0061] Define the candidate Lyapunov function V 1 (t) as:

[0062]

[0063] According to equations (11) and (12), the derivative of equation (13) is:

[0064]

[0065] Among them, α 1 (t) is the virtual control rate, e 2 (t) is the speed and attitude angular velocity error term,

[0066] Since |f 1 (x 1 )| = secθ(t) ≠ 0, so f 1 (x 1 ) is an invertible matrix. To ensure the negative definiteness of formula (14), design α 1 (t) as:

[0067]

[0068] Among them, K 1 = diag{k 11 , k 12 , k 13 , k 14} > 0 is the gain coefficient matrix, k 11 , k 12 , k 13 and k 14 are its 4 gain coefficients respectively;

[0069] According to equations (14) and (15), rewrite as:

[0070]

[0071] Step 2.3.2 is specifically implemented according to the following steps:

[0072] Define the velocity and attitude angular velocity error terms e 2 (t):

[0073] e 2 (t) = x 2 (t) - α 1 (t) (9)

[0074] According to formula (5), the dynamic expressions of the altitude attitude error, velocity, and attitude angular velocity errors are as follows:

[0075]

[0076] where

[0077] Step 2.3.3 is specifically implemented according to the following steps:

[0078] Step 2.3.3, define the sliding surface s(t):

[0079] s(t) = c 1 e 1 (t) + e 2 (t) (11)

[0080] where c 1 > 0 is the gain coefficient;

[0081] Combining equations (12), (15), (17), (18), and (19), the derivative of s(t) is:

[0082]

[0083] Define the candidate Lyapunov function V 2 (t) as:

[0084]

[0085] According to equations (16), (19), and (20), the derivative of the candidate Lyapunov equation V 2 (t) is:

[0086]

[0087] Step 2.3.4 is specifically implemented according to the following steps:

[0088] Design the controller u(t):

[0089] Similar to Step 2.3.1, obviously g is an invertible matrix. To ensure the negative definiteness of equation (22), design the controller u(t) as follows:

[0090]

[0091] where m 1 > 0 and n 1 > 0 are gain parameters, sign(s(t)) is the sign function of s(t), which is a discontinuous switching function in sliding mode control and is defined as:

[0092]

[0093] The boundary layer formula is as follows:

[0094]

[0095] where Φ > 0 is the boundary layer thickness. Therefore, the feedback control law becomes:

[0096]

[0097] where sat(s(t) / Φ) is the saturation function and is defined as:

[0098]

[0099] According to Eqs. (22) and (25), rewritten as:

[0100]

[0101] Step 3 is specifically implemented according to the following steps:

[0102] Perform stability analysis on the designed controller:

[0103] To ensure the stability of the helicopter system, consider the Lyapunov function V(t) as:

[0104]

[0105] Combining Eqs. (27) and (7), the derivative of V(t) is:

[0106]

[0107] Since:

[0108]

[0109] where H(x) is a bounded function ||H(x)|| < τ, ε 1 , ε 2 , ε 3 , ε 4 > 0 are design parameters; therefore, according to Eqs. (29), (30), assume and consider the following equation:

[0110]

[0111] The following inequality relations are obtained:

[0112]

[0113] wherein,

[0114]

[0115] For the helicopter attitude and altitude dynamic system described by formula (2), a neural network flight controller designed in the form of formula (25) is designed, and the relevant parameters of the controller satisfy:

[0116]

[0117] After the above analysis, under the action of the online neural network unmanned helicopter sliding mode flight control method, the tracking error of the helicopter can converge to the desired bounded range, realizing effective tracking of the tracking target.

[0118] The beneficial effects of the present invention are as follows. Based on the online neural network unmanned helicopter sliding mode flight control method, by adopting the neural network-based unmanned helicopter sliding mode flight control method and combining a nonlinear disturbance observer and a neural network estimator, the stability and robustness of the unmanned helicopter in the face of interference and uncertainty are significantly improved. When designing the sliding mode controller, by introducing a saturation function, the control chattering is effectively eliminated, making the control input smoother, thereby increasing the feasibility of the control system. Through Matlab / Simulink simulation, it is proved that the method of the present invention can effectively control the altitude and attitude of the unmanned helicopter, enabling it to quickly and accurately track the preset trajectory, thereby improving the tracking performance of the helicopter. BRIEF DESCRIPTION OF THE DRAWINGS

[0119] Figure 1 is the flowchart of the online neural network unmanned helicopter sliding mode flight control method of the present invention;

[0120] Figure 2 is the state tracking trajectory curve of the unmanned aerial vehicle altitude and attitude system, including altitude tracking trajectory, roll angle tracking trajectory, pitch angle tracking trajectory, and yaw angle tracking trajectory;

[0121] Figure 3 is the state tracking trajectory error curve of the unmanned aerial vehicle altitude and attitude system, including altitude tracking trajectory error, roll angle tracking trajectory error, pitch angle tracking trajectory error, and yaw angle tracking trajectory error;

[0122] Figure 4It is the speed tracking trajectory curve of the UAV altitude and attitude system, including the climb speed tracking trajectory, roll angular velocity tracking trajectory, pitch angular velocity tracking trajectory, and yaw angular velocity tracking trajectory;

[0123] Figure 5 It is the total disturbance and its estimation curve of the UAV altitude and attitude system, including the disturbance force curve and three disturbance torque curves;

[0124] Figure 6 It is the control input curve of the UAV altitude and attitude system, including the main rotor thrust and three resultant external torques. Specific implementation manner

[0125] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0126] The present invention is based on an online neural network sliding mode flight control method for an unmanned helicopter, and the flowchart is as Figure 1 shown, and it is specifically implemented according to the following steps:

[0127] Step 1: Design the dynamic nonlinear model of the helicopter attitude and altitude;

[0128] Step 1 is specifically implemented according to the following steps:

[0129] For the variables appearing in the following formulas, the explanations are as follows: represents the first derivative of the function f(x), represents the second derivative of the function f(x), A T represents the transpose matrix of matrix A, A -1 represents the inverse matrix of matrix A, |A| represents the determinant of matrix A, represents the n-dimensional vector space, I n×n represents the n-order identity matrix;

[0130] Step 1.1: Design the dynamic model of the helicopter attitude and altitude:

[0131]

[0132] Among them, h(t) and v(t) are the altitude position and climb speed of the unmanned helicopter in the inertial coordinate system, m is the mass of the unmanned helicopter, g 0 is the acceleration due to gravity, Ω(t) = (φ(t) θ(t) ψ(t)) T represents the attitude angle of the unmanned helicopter, where φ(t), θ(t), and ψ(t) represent the roll angle, pitch angle, and yaw angle respectively, W(t) = (p(t) q(t) r(t)) T represents the angular velocity vector, where p(t), q(t), and r(t) represent the roll angular velocity, pitch angular velocity, and yaw angular velocity respectively, J = diag{Jxx J yy J zz} represents the inertia matrix of the unmanned helicopter, where J xx 、J yy and J zz represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia respectively, and H 0 (t) is the attitude motion matrix:

[0133]

[0134] where sin(·), cos(·), tan(·), and sec(·) represent the sine function, cosine function, tangent function, and secant function in trigonometric functions respectively;

[0135] W(t) × represents the cross product operator matrix:

[0136]

[0137] T m (t) and τ 0 (t) are the thrust and control moment of the main rotor of the helicopter. They are the control inputs of the altitude attitude system of the unmanned helicopter. x = (x 1 , x 2 ) T is the state of the system, x 1 (t) = (h(t) Ω T (t)) T represents the state vector, x 2 (t) = (v(t) W T (t)) T represents the velocity vector, and represent the disturbing force and disturbing moment in the vertical direction respectively, and represent the uncertain terms of the system;

[0138] Step 1.2. Based on the above helicopter attitude and altitude model, rewrite the system:

[0139]

[0140] where, represents the control input of the system: u 1 (t) = cosφ(t)cosθ(t)T m (t) - mg 0 , u 2 (t) = τ 0 (t); f(x 1 ) and f(x2 ) represent the parameter matrices related to x 1 (t) and x 2 (t) respectively, and their specific forms are as follows: g and are constant matrices related to mass and moment of inertia, and their specific expressions are as follows: d(t) and Δf(x) represent the disturbances and uncertainties of the system:

[0141] To handle the uncertainties of the system, a continuous function P(x) is defined:

[0142]

[0143] where L = diag{l 1 , l 2 , l 3 , l 4} > 0 is the gain coefficient matrix, and l 1 , l 2 , l 3 and l 4 are its 4 gain coefficients respectively;

[0144] The radial basis function neural network is used to approximate the continuous function P(x), and the form is as follows:

[0145] P(x) = W *T H(x) + ε * (4)

[0146] where H(x) is the basis function of the neural network, W * is its optimal weight, and ε * is the optimal approximation error;

[0147] According to formula (3) and formula (4), we have Therefore, formula (2) can be further rewritten as:

[0148]

[0149] where represents the composite disturbance composed of the external disturbance of the system and the neural network approximation error.

[0150] Step 2: Design a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method;

[0151] Step 2 is specifically implemented according to the following steps:

[0152] Step 2.1: Design of the nonlinear disturbance observer:

[0153] The disturbance observer equation is designed as follows:

[0154]

[0155] Wherein, is the disturbance estimation value, is the estimated value of the optimal weight W * , and δ(t) is a constructed function;

[0156] Define the disturbance estimation error value as Then the dynamics of the disturbance estimation error is given by the following formula:

[0157]

[0158] Where is the weight estimation error;

[0159] Step 2.2, Design of the neural network disturbance observer:

[0160] The neural network disturbance observer is designed as:

[0161]

[0162] Wherein, Π(t) is the state vector of the observer, η(t) is a constructed function, Λ = diag{λ 1 , λ 2 , λ 3 , λ 4} > 0 is the gain coefficient matrix, and λ 1 , λ 2 , λ 3 and λ 4 are its 4 gain coefficients respectively;

[0163] Define the nominal estimation error e n (t) = x 2 (t) - Π(t) of the neural network observer, then the dynamics of the error is expressed as:

[0164]

[0165] Select the adaptive rate as:

[0166]

[0167] Wherein, γ > 0 and σ > 0 are gain coefficients, and s(t) is the sliding mode surface to be designed later;

[0168] Step 2.3, Design of the sliding mode controller based on the backstepping method.

[0169] Step 2.3 is specifically implemented according to the following steps:

[0170] Step 2.3.1: Define the altitude attitude angle error;

[0171] Step 2.3.2: Define the velocity and attitude angular velocity error terms;

[0172] Step 2.3.3: Define the sliding surface;

[0173] Step 2.3.4: Design the controller.

[0174] Step 2.3.1 is specifically implemented according to the following steps:

[0175] Define the altitude attitude angle error e 1 (t):

[0176] e 1 (t) = x 1 (t) - x d (t) (27)

[0177] where x d (t) is the altitude attitude desired tracking trajectory;

[0178] According to formula (5), the dynamics of the altitude attitude error is expressed as:

[0179]

[0180] Define the candidate Lyapunov function V 1 (t) as:

[0181]

[0182] According to equations (11) and (12), the derivative of equation (13) is:

[0183]

[0184] where α 1 (t) is the virtual control rate, e 2 (t) is the velocity and attitude angular velocity error term,

[0185] Since |f 1 (x 1 )| = secθ(t) ≠ 0, so f 1 (x 1 ) is an invertible matrix. To ensure the negativity of formula (14), design α 1 (t) as:

[0186]

[0187] where K 1 = diag{k 11 ,k12 , k 13 , k 14} > 0 is the gain coefficient matrix, k 11 , k 12 , k 13 and k 14 are its 4 gain coefficients respectively;

[0188] According to equations (14) and (15), rewrite as:

[0189]

[0190] Step 2.3.2 is specifically implemented according to the following steps:

[0191] Define the velocity and attitude angular velocity error terms e 2 (t):

[0192] e 2 (t) = x 2 (t) - α 1 (t) (33)

[0193] According to formula (5), the dynamic representations of the altitude attitude error, velocity and attitude angular velocity errors are:

[0194]

[0195] where

[0196] Step 2.3.3 is specifically implemented according to the following steps:

[0197] Step 2.3.3. Define the sliding mode surface s(t):

[0198] s(t) = c 1 e 1 (t) + e 2 (t) (35)

[0199] where c 1 > 0 is the gain coefficient;

[0200] Combining equations (12), (15), (17), (18) and (19), the derivative of s(t) is:

[0201]

[0202] Define the candidate Lyapunov function V 2 (t) as:

[0203]

[0204] According to equations (16), (19) and (20), the derivative of the candidate Lyapunov equation V 2 (t) is:

[0205]

[0206] Step 2.3.4 is specifically implemented according to the following steps:

[0207] Design the controller u(t):

[0208] Similar to Step 2.3.1, obviously g is an invertible matrix. To ensure the negativity of equation (22), design the controller u(t) as follows:

[0209]

[0210] where m 1 > 0 and n 1 > 0 are gain parameters, sign(s(t)) is the sign function of s(t), which is a discontinuous switching function in sliding mode control and is defined as:

[0211]

[0212] The boundary layer formula is as follows:

[0213]

[0214] where Φ > 0 is the boundary layer thickness. Therefore, the feedback control law becomes:

[0215]

[0216] where sat(s(t) / Φ) is the saturation function and is defined as:

[0217]

[0218] According to equations (22) and (25), Rewrite it as:

[0219]

[0220] Step 3. Perform stability analysis through the Lyapunov function to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0221] Step 3 is specifically implemented according to the following steps:

[0222] Conduct stability analysis on the designed controller:

[0223] To ensure the stability of the helicopter system, consider the Lyapunov function V(t) as:

[0224]

[0225] Combining equations (27) and (7), the derivative of V(t) is:

[0226]

[0227] Since:

[0228]

[0229] where H(x) is a bounded function ||H(x)|| < τ, ε 1 , ε 2 , ε 3 , ε 4 > 0 is a design parameter;

[0230] Therefore, according to equations (29) and (30), assuming and considering the following equation:

[0231]

[0232] the following inequality relationship is obtained:

[0233]

[0234] where,

[0235]

[0236] For the helicopter attitude and altitude dynamic system described by formula (2), a neural network flight controller designed in the form of formula (25) is designed, and the relevant parameters of the controller satisfy:

[0237]

[0238] After the above analysis, under the action of the online neural network unmanned helicopter sliding mode flight control method, the tracking error of the helicopter can converge to the desired bounded range, realizing effective tracking of the tracking target.

[0239] Through the above stability analysis, we can obtain that for the helicopter system with uncertainties and disturbances, formula (2), designing the controller (25) and the observers (6) and (8), if there exists a given gain coefficient matrix that satisfies and the gain coefficients satisfy the unmanned helicopter error tracking system, formula (2) can track the desired attitude and altitude, and its closed-loop error can converge to the desired bounded range.

[0240] Example 1

[0241] The present invention is based on an online neural network sliding mode flight control method for an unmanned helicopter, and the flow chart is as Figure 1 shown, and is specifically implemented according to the following steps:

[0242] Step 1: Design a dynamic nonlinear model of the helicopter attitude and altitude;

[0243] Step 2: Design a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method;

[0244] Step 3: Perform stability analysis through the Lyapunov function to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0245] Embodiment 2

[0246] The present invention is based on an online neural network sliding mode flight control method for an unmanned helicopter, and the flow chart is as Figure 1 shown, and is specifically implemented according to the following steps:

[0247] Step 1: Design a dynamic nonlinear model of the helicopter attitude and altitude;

[0248] Step 1 is specifically implemented according to the following steps:

[0249] For the variables appearing in the following formulas, the explanations are as follows: represents the first derivative of the function f(x), represents the second derivative of the function f(x), A T represents the transpose matrix of matrix A, A -1 represents the inverse matrix of matrix A, |A| represents the determinant of matrix A, represents the n-dimensional vector space, I n×n represents the n-order identity matrix;

[0250] Step 1.1: Design a dynamic model of the helicopter attitude and altitude:

[0251]

[0252] where h(t) and v(t) are the altitude position and its climbing speed of the unmanned helicopter in the inertial coordinate system, m is the mass of the unmanned helicopter, g 0 is the acceleration due to gravity, Ω(t) = (φ(t) θ(t) ψ(t)) T represents the attitude angle of the unmanned helicopter, where φ(t), θ(t), and ψ(t) represent the roll angle, pitch angle, and yaw angle respectively, W(t) = (p(t) q(t) r(t)) T represents the angular velocity vector, where p(t), q(t), and r(t) represent the roll angular velocity, pitch angular velocity, and yaw angular velocity respectively, J = diag{J xxJ yy J zz} represents the inertia matrix of the unmanned helicopter, where J xx 、J yy and J zz represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia respectively, and H 0 (t) is the attitude motion matrix:

[0253]

[0254] where sin(·), cos(·), tan(·), and sec(·) represent the sine function, cosine function, tangent function, and secant function in trigonometric functions respectively;

[0255] W(t) × represents the cross product operator matrix:

[0256]

[0257] T m (t) and τ 0 (t) are the thrust and control moment of the main rotor of the helicopter. They are the control inputs of the altitude attitude system of the unmanned helicopter. x = (x 1 , x 2 ) T is the state of the system. x 1 (t) = (h(t) Ω T (t)) T represents the state vector. x 2 (t) = (v(t) W T (t)) T represents the velocity vector. and represent the disturbing force and disturbing moment in the vertical direction respectively. and represent the uncertain terms of the system;

[0258] Step 1.2. Based on the above helicopter attitude and altitude model, rewrite the system:

[0259]

[0260] where, represents the control input of the system: u 1 (t) = cosφ(t)cosθ(t)T m (t) - mg 0 , u 2 (t) = τ 0 (t); f(x 1 ) and f(x 2) respectively represent the parameter matrices related to x 1 (t) and x 2 (t), and the specific forms are as follows: g and are constant matrices related to mass and moment of inertia, and the specific expressions are as follows: d(t) and Δf(x) represent the disturbances and uncertainties of the system:

[0261] To handle the uncertainties of the system, a continuous function P(x) is defined:

[0262]

[0263] where L = diag{l 1 , l 2 , l 3 , l 4} > 0 is the gain coefficient matrix, and l 1 , l 2 , l 3 and l 4 are its 4 gain coefficients respectively;

[0264] The radial basis function neural network is used to approximate the continuous function P(x), and the form is as follows:

[0265] P(x) = W *T H(x) + ε * (4)

[0266] where H(x) is the basis function of the neural network, W * is its optimal weight, and ε * is the optimal approximation error;

[0267] According to formulas (3) and (4), we have Therefore, formula (2) can be further rewritten as:

[0268]

[0269] where represents the composite disturbance composed of the external disturbance of the system and the neural network approximation error.

[0270] Step 2: Design a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method;

[0271] Step 3: Conduct a stability analysis through the Lyapunov function to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0272] Example 3

[0273] The present invention is based on an online neural network sliding mode flight control method for an unmanned helicopter, and the flow chart is as shown in Figure 1 and is specifically implemented according to the following steps:

[0274] Step 1: Design a dynamic nonlinear model of the helicopter attitude and altitude;

[0275] Step 2: Design a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method;

[0276] Step 2 is specifically implemented according to the following steps:

[0277] Step 2.1: Design of the nonlinear disturbance observer:

[0278] The disturbance observer equation is designed as:

[0279]

[0280] where is the disturbance estimated value, is the estimated value of the optimal weight W * and δ(t) is a constructed function;

[0281] Define the disturbance estimation error value as Then the dynamics of the disturbance estimation error is given by the following formula:

[0282]

[0283] where is the weight estimation error;

[0284] Step 2.2: Design of the neural network disturbance observer:

[0285] The neural network disturbance observer is designed as:

[0286]

[0287] where Π(t) is the state vector of the observer, η(t) is a constructed function, Λ = diag{λ 1 , λ 2 , λ 3 , λ 4} > 0 is the gain coefficient matrix, and λ 1 , λ 2 , λ 3 and λ 4 are its 4 gain coefficients respectively;

[0288] Define the nominal estimation error e n (t) = x 2 (t) - Π(t) of the neural network observer, then the dynamics of the error is expressed as:

[0289]

[0290] Select the adaptation rate as:

[0291]

[0292] where γ > 0 and σ > 0 are gain coefficients, and s(t) is the sliding mode surface to be designed later;

[0293] Step 2.3. Design a sliding mode controller based on the backstepping method.

[0294] Step 3. Conduct a stability analysis through the Lyapunov function to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0295] Embodiment 4

[0296] The present invention relates to an online neural network-based sliding mode flight control method for an unmanned helicopter, and the flow chart is as Figure 1 shown, and is specifically implemented according to the following steps:

[0297] Step 1. Design a dynamic nonlinear model of the helicopter attitude and altitude;

[0298] Step 2. Design a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method;

[0299] Step 3. Conduct a stability analysis through the Lyapunov function to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0300] Step 3 is specifically implemented according to the following steps:

[0301] Step 3 is specifically implemented according to the following steps:

[0302] Conduct a stability analysis on the designed controller:

[0303] To ensure the stability of the helicopter system, consider the Lyapunov function V(t) as:

[0304]

[0305] Combining equations (27) and (7), the derivative of V(t) is:

[0306]

[0307] Since:

[0308]

[0309] where H(x) is a bounded function ||H(x)|| < τ, ε1 , ε 2 , ε 3 , ε 4 >0 is a design parameter;

[0310] Therefore, according to equations (29) and (30), assuming and considering the following equation:

[0311]

[0312] the following inequality relationship is obtained:

[0313]

[0314] where

[0315]

[0316] For the helicopter attitude and altitude dynamic system described by formula (2), a neural network flight controller designed in the form of formula (25) is designed, and the relevant parameters of the controller satisfy:

[0317]

[0318] Through the above analysis, under the action of the online neural network unmanned helicopter sliding mode flight control method, the tracking error of the helicopter can converge to the desired bounded range, realizing effective tracking of the tracking target.

[0319] Example 5

[0320] The present invention is based on an online neural network unmanned helicopter sliding mode flight control method, and the flow chart is as Figure 1 shown, and is specifically implemented according to the following steps:

[0321] Step 1: Design a helicopter attitude and altitude dynamic nonlinear model;

[0322] Step 2: Design a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method;

[0323] Step 2 is specifically implemented according to the following steps:

[0324] Step 2.1: Design of the nonlinear disturbance observer:

[0325] The disturbance observer equation is designed as:

[0326]

[0327] where is the disturbance estimated value, is the optimal weight W *The estimated value, where δ(t) is a construction function;

[0328] Define the interference estimation error value as Then the dynamics of the interference estimation error are given by the following equation:

[0329]

[0330] where is the weight estimation error;

[0331] Step 2.2, Design of the neural network interference observer:

[0332] The neural network interference observer is designed as:

[0333]

[0334] where Π(t) is the state vector of the observer, η(t) is the construction function, Λ = diag{λ 1 , λ 2 , λ 3 , λ 4} > 0 is the gain coefficient matrix, and λ 1 , λ 2 , λ 3 and λ 4 are its 4 gain coefficients respectively;

[0335] Define the nominal estimation error e n (t) = x 2 (t) - Π(t) of the neural network observer, then the dynamics of the error are expressed as:

[0336]

[0337] Select the adaptation rate as:

[0338]

[0339] where γ > 0 and σ > 0 are gain coefficients, and s(t) is the sliding mode surface to be designed later;

[0340] Step 2.3, Design of the sliding mode controller based on the backstepping method.

[0341] Step 2.3 is specifically implemented according to the following steps:

[0342] Step 2.3.1, Define the altitude and attitude angle error;

[0343] Step 2.3.2, Define the velocity and attitude angular velocity error terms;

[0344] Step 2.3.3, Define the sliding mode surface;

[0345] Step 2.3.4, design the controller.

[0346] Step 3, perform stability analysis through the Lyapunov function to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0347] Embodiment 6

[0348] Next, the present invention will be further described with reference to the accompanying drawings and a specific example.

[0349] Verify the simulation of the unmanned helicopter system in the Matlab / Simulink environment by referring to the following physical parameters of the unmanned helicopter:

[0350] m = 9 kg, g = 9.8 N / kg

[0351] J xx = 0.26 kg·m 2 , J yy = 0.35 kg·m 2 , J zz = 0.29 kg·m 2

[0352] The gains of the controller, sliding mode gain, nonlinear disturbance observer gain, and neural network observer gain of the unmanned helicopter system are selected as:

[0353] k 11 = 6, k 12 = 6, k 13 = 6, k 14 = 6, l 1 = 20, l 2 = 10, l 3 = 10, l 4 = 10,

[0354] λ 1 = 20, λ 2 = 10, λ 3 = 10, λ 4 = 10, c 1 = 3, m 1 = 3, n 1 = 3, γ = 0.1, σ = 1, Φ = 0.3

[0355] The disturbance of the unmanned helicopter system is given by the following formula:

[0356]

[0357] The uncertainty terms of the unmanned helicopter system are given by the following formula:

[0358]

[0359] The initial state of the unmanned helicopter is (50, 10, 10, 1), and the tracking trajectory x d (t) is as follows:

[0360]

[0361] The state variable x of the unmanned helicopter 1 (t) tracking simulation curve is as Figure 2 shown, and the trajectory tracking error simulation curve is as Figure 3 shown. The simulation results show that the altitude and attitude of the unmanned helicopter can quickly track the preset desired trajectory. The proposed control strategy effectively reduces chattering, realizes smooth control actions, and maintains performance under various operating conditions. This shows that the system has good robustness and its potential in practical applications.

[0362] The state variable x of the unmanned helicopter 2 (t) tracking simulation curve is as Figure 4 shown. It can be seen from the figure that the climbing speed, roll angular velocity, pitch angular velocity, and yaw angular velocity of the unmanned helicopter can quickly track the preset tracking trajectory.

[0363] As Figure 5 shown, the nonlinear disturbance observer well estimates the disturbances existing in the system. The control input of the unmanned helicopter system is as Figure 6 shown. It can be seen from the figure that using the saturation function when designing the sliding mode controller can effectively eliminate chattering and make the control curve smoother.

Claims

1. The sliding mode flight control method of unmanned helicopter based on online neural network is characterized by: Follow the steps below to implement it: Step 1, design the helicopter attitude and altitude dynamic nonlinear model; Step 2: Design a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method; Step 3: Perform stability analysis through Lyapunov function to ensure the stability of the helicopter system in the face of interference and uncertainty.

2. The sliding mode flight control method of an unmanned helicopter based on an online neural network according to claim 1 is characterized in that: The step 1 is specifically implemented according to the following steps: The variables that appear in the following formula are explained as follows: represents the first-order derivative of the function f(x), represents the second-order derivative of the function f(x), A T represents the transposed matrix of matrix A, A -1 represents the inverse matrix of matrix A, |A| represents the determinant of matrix A, represents n-dimensional vector space, I n×n represents the n-order identity matrix; Step 1.1, design helicopter attitude and altitude dynamic model: Where h(t) and v(t) are the height position and climbing speed of the unmanned helicopter in the inertial coordinate system, m is the mass of the unmanned helicopter, g0 is the acceleration of gravity, Ω(t) = (φ(t)θ(t)ψ(t)) T represents the attitude angle of the unmanned helicopter, where φ(t), θ(t) and ψ(t) represent the roll angle, pitch angle and yaw angle respectively, W(t) = (p(t)q(t)r(t)) T represents the angular velocity vector, where p(t), q(t) and r(t) represent the roll angular velocity, pitch angular velocity and yaw angular velocity respectively, J = diag{J xx J yy J zz } represents the inertia matrix of the unmanned helicopter, where J xx , J yy and J zz They represent the rolling moment of inertia, pitch moment of inertia and yaw moment of inertia respectively, and H0(t) is the attitude motion matrix: Among them, sin(·), cos(·), tan(·) and sec(·) represent the sine function, cosine function, tangent function and cosecant function in trigonometric functions respectively; W(t) × Represents the cross product operator matrix: T m (t) and τ0(t) are the thrust and control torque of the helicopter main rotor, which are the control inputs of the altitude attitude system of the unmanned helicopter, x = (x1, x2) T is the state of the system, x1(t)=(h(t)Ω T (t)) T represents the state vector, x2(t)=(v(t)W T (t)) T represents the velocity vector, and They represent the disturbance force and disturbance moment in the vertical direction, and Represents the uncertainty of the system; Step 1.2: Based on the above helicopter attitude and altitude model, rewrite the system: in, Represents the control input of the system: u1(t)=cosφ(t)cosθ(t)T m (t)-mg0, u2(t)=τ0(t); f(x1) and f(x2) represent the parameter matrices of x1(t) and x2(t), respectively. The specific form is as follows: g and is a constant matrix related to mass and moment of inertia, and its specific expression is as follows: d(t) and Δf(x) represent the disturbance and uncertainty of the system: In order to deal with the uncertainty of the system, a continuous function P(x) is defined: Wherein, L=diag{l1,l2,l3,l4}>0 is the gain coefficient matrix, l1,l2,l3 and l4 are its four gain coefficients respectively; The radial basis function neural network is used to approximate the continuous function P(x), which is as follows: P(x)=W *T H(x)+ε * (4) Among them, H(x) is the basis function of the neural network, W * is its optimal weight, ε * is the optimal approximation error; According to formula (3) and formula (4), we have Therefore, formula (2) can be further rewritten as: in Represents the composite interference composed of the external interference of the system and the approximation error of the neural network.

3. The sliding mode flight control method of an unmanned helicopter based on online neural network according to claim 2 is characterized in that: The step 2 is specifically implemented according to the following steps: Step 2.1, nonlinear disturbance observer design: The disturbance observer equation is designed as: in, is the interference estimate, is the optimal weight W * The estimated value of , δ(t) is the constructor; The interference estimation error is defined as The dynamics of the disturbance estimation error is then given by: in is the weight estimation error; Step 2.2, neural network disturbance observer design: The neural network disturbance observer is designed as: Where Π(t) is the state vector of the observer, η(t) is the constructor, Λ=diag{λ1,λ2,λ3,λ4}>0 is the gain coefficient matrix, and λ1,λ2,λ3 and λ4 are its four gain coefficients respectively; Define the nominal estimation error e of the neural network observer n (t) = x2(t)-Π(t), then the dynamic expression of the error is: Select the adaptive rate: Among them, γ>0 and σ>0 are gain coefficients, and s(t) is the sliding surface to be designed later; Step 2.3: Design a sliding mode controller based on the backstepping method.

4. The sliding mode flight control method of an unmanned helicopter based on online neural network according to claim 3 is characterized in that: The step 2.3 is specifically implemented according to the following steps: Step 2.3.1, define the height attitude angle error; Step 2.3.2, define the velocity and attitude angular velocity error terms; Step 2.3.3, define the sliding surface; Step 2.3.

4. Design the controller.

5. The sliding mode flight control method of an unmanned helicopter based on online neural network according to claim 4 is characterized in that: The step 2.3.1 is specifically implemented according to the following steps: Define the altitude attitude angle error e1(t): e1(t)=x1(t)-x d (t) (3) Among them, x d (t) is the expected tracking trajectory of the altitude attitude; According to formula (5), the dynamics of the height attitude error is It is expressed as: Define the candidate Lyapunov function V1(t) as: According to equations (11) and (12), the derivative of equation (13) is: Where α1(t) is the virtual control rate, e2(t) is the speed and attitude angular velocity error term, Since |f1(x1)|=secθ(t)≠0, f1(x1) is a reversible matrix. In order to ensure the negative definiteness of formula (14), α1(t) is designed as: where K1 = diag{k 11 ,k 12 ,k 13 ,k 14 }>0 is the gain coefficient matrix, k 11 ,k 12 ,k 13 and k 14 They are the 4 gain coefficients respectively; According to formula (14) and formula (15), Re-write as:

6. The sliding mode flight control method of an unmanned helicopter based on online neural network according to claim 5 is characterized in that: The step 2.3.2 is specifically implemented according to the following steps: Define the velocity and attitude angular velocity error term e2(t): e2(t)=x2(t)-α1(t) (9) According to formula (5), the dynamic expression of height attitude error, velocity and attitude angular velocity error is: in 7. The sliding mode flight control method of an unmanned helicopter based on online neural network according to claim 6 is characterized in that: The step 2.3.3 is specifically implemented according to the following steps: Step 2.3.3, define the sliding surface s(t): s(t)=c1e1(t)+e2(t) (11) Where c1>0 is the gain coefficient; Combining equations (12), (15), (17), (18) and (19), the derivative of s(t) is: Define the candidate Lyapunov function V2(t) as: According to equations (16), (19) and (20), the derivative of the candidate Lyapunov equation V2(t) is:

8. The sliding mode flight control method of an unmanned helicopter based on online neural network according to claim 7 is characterized in that: The step 2.3.4 is specifically implemented according to the following steps: Design controller u(t): Similar to step 2.3.1, it is obvious that g is a reversible matrix. In order to ensure the negative definiteness of equation (22), the controller u(t) is designed as follows: Where m1>0 and n1>0 are gain parameters, sign(s(t)) is the sign function of s(t), which is a discontinuous switching function in sliding mode control and is defined as: The boundary layer formula is as follows: Where Φ>0 is the boundary layer thickness, so the feedback control law becomes: where sat(s(t) / Φ) is the saturation function, defined as: According to equations (22) and (25), Re-write as:

9. The sliding mode flight control method of an unmanned helicopter based on online neural network according to claim 8 is characterized in that: The step 3 is specifically implemented according to the following steps: Perform stability analysis on the designed controller: In order to ensure the stability of the helicopter system, the Lyapunov function V(t) is considered as: Combining equations (27) and (7), the derivative of V(t) is: because: Where H(x) is a bounded function ||H(x)||<τ, ε1,ε2,ε3,ε4>0 are design parameters; Therefore, according to equations (29) and (30), assuming And consider the following: The following inequality relationship is obtained: in, For the helicopter attitude and altitude dynamic system described by formula (2), a neural network flight controller is designed as shown in formula (25). The controller related parameters satisfy: After the above analysis, under the action of the sliding mode flight control method of the unmanned helicopter based on online neural network, the tracking error of the helicopter can converge to the desired bounded range, realizing effective tracking of the tracking target.

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