Sliding mode flight control method for online neural network unmanned helicopter

Abstract

The purpose of this invention is to provide a sliding mode flight control method for unmanned helicopters based on online neural networks, specifically implemented according to the following steps: Step 1, designing dynamic nonlinear models of helicopter attitude and altitude; Step 2, designing a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on backstepping; Step 3, performing stability analysis using Lyapunov functions to ensure the stability of the helicopter system in the face of disturbances and uncertainties. This invention solves the problem of robust flight control for unmanned helicopters maintaining attitude and altitude stability under disturbances and uncertainties in existing technologies.

Description

Technical Field

[0001] This invention belongs to the field of unmanned helicopter control technology, specifically relating to an unmanned helicopter sliding mode flight control method based on online neural networks. Background Technology

[0002] Unmanned helicopters play a vital role in both military and civilian applications due to their vertical takeoff and landing, hovering, and maneuvering capabilities. However, the design of their control systems is particularly challenging due to the complexity, nonlinearity, and highly coupled dynamic characteristics of unmanned helicopter systems, coupled with the inevitable challenges of uncertainty, external disturbances, actuator failures, and input saturation in practical applications. Therefore, research on helicopter flight control has gained significant attention in academia.

[0003] Historically, flight control has been extensively studied. Traditional control methods, such as PID control, sliding mode control, LMI-based control, or observer-based control, typically rely on simplifying complex nonlinear helicopter models to linear ones or neglecting the coupling between Euler angular rates and helicopter angular velocities. While these methods simplify the control model, they also lead to decreased control accuracy and suboptimal performance. To overcome these limitations, researchers have begun combining 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, retaining the efficient handling capability of backstepping for nonlinear systems while effectively addressing system uncertainties and external disturbances. 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 uncertainties and external disturbances, it often causes significant chattering in complex environments. Neural networks, with their powerful function approximation capabilities, effectively address system uncertainties. By integrating neural networks with observers, system uncertainties can be handled more effectively, while external disturbances are handled by nonlinear disturbance observers. Combining sliding mode control with these observers not only effectively addresses system uncertainties and external disturbances, but also reduces controller chattering, enhancing system robustness and accuracy. Summary of the Invention

[0004] The purpose of this invention is to provide a sliding mode flight control method for unmanned helicopters based on online neural networks, which solves the problem of robust flight control for unmanned helicopters to maintain attitude and altitude stability under disturbance and uncertainty in the prior art.

[0005] The technical solution adopted in this invention is a sliding mode flight control method for unmanned helicopters based on online neural networks, which is implemented according to the following steps:

[0006] Step 1: Design a dynamic nonlinear model of the helicopter's attitude and altitude;

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

[0008] Step 3: Perform stability analysis using Lyapunov functions to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0009] The invention is further characterized in that,

[0010] Step 1 is implemented in the following steps:

[0011] The variables appearing in the following formulas are explained as follows: This represents the first derivative of the function f(x). Let A represent the second derivative of the function f(x). T Let A be the transpose of matrix A. -1 Let |A| denote the inverse of matrix A, and |A| denote the determinant of matrix A. Let I represent an n-dimensional vector space. n×n Represents an n-order identity matrix;

[0012] Step 1.1: Design the dynamic model of helicopter attitude and altitude:

[0013]

[0014] Where h(t) and v(t) are the altitude and climb rate of the unmanned helicopter in the inertial coordinate system, m is the mass of the unmanned helicopter, g0 is the gravitational acceleration, and Ω(t) = (φ(t) θ(t) ψ(t)). T Let W(t) represent the attitude angles of the unmanned helicopter, where φ(t), θ(t), and ψ(t) represent the roll angle, pitch angle, and yaw angle, respectively, and W(t) = (p(t) q(t) r(t)). T Let J represent 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, and J = diag{J xx J yy J zz} represents the inertial matrix of the unmanned helicopter, where J xx J yy and J zz Let H0(t) represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia, respectively, and let H0(t) be the attitude motion matrix.

[0015]

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

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

[0018]

[0019] T m τ(t) and τ0(t) are the thrust and control torque of the helicopter's main rotor, respectively. They are the control inputs of the unmanned helicopter's altitude and attitude system, where x = (x1, x2). T For the state of the system, x1(t) = (h(t) Ω T (t)) T Representing the state vector, x2(t) = (v(t) W T (t)) T Represents the velocity vector. and These represent the disturbance force and disturbance torque in the vertical direction, respectively. and Represents the uncertainties of the system;

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

[0021]

[0022] in, The system's control input is represented by: u1(t) = cosφ(t)cosθ(t)T m (t)-mg0, u2(t)=τ0(t); f(x1) and f(x2) represent the parameter matrices related to x1(t) and x2(t) respectively, and are expressed in the following forms: g and It is a constant matrix relating mass and moment of inertia, expressed in the following form: d(t) and Δf(x) represent the disturbances and uncertainties of the system:

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

[0024]

[0025] Where L = diag{l1,l2,l3,l4} > 0 is the gain coefficient matrix, and l1, l2, l3 and l4 are its four gain coefficients;

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

[0027] P(x) = W *T H(x)+ε * (4)

[0028] Where H(x) is the basis function of the neural network, and W * That is its optimal weight, ε * It is the optimal approximation error;

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

[0030]

[0031] in This represents the combined interference caused by external disturbances to the system and the approximation error of the neural network.

[0032] Step 2 is implemented in the following steps:

[0033] Step 2.1, Design of Nonlinear Interference Observer:

[0034] The interference observer equation is designed as follows:

[0035]

[0036] in, For interference estimates, For the optimal weight W * The estimated value, δ(t), is the constructor function;

[0037] Define the interference estimation error value as The dynamics of the disturbance estimation error are given by the following equation:

[0038]

[0039] in This refers to the weight estimation error;

[0040] Step 2.2, Design of the Neural Network Interference Observer:

[0041] The neural network interference observer is designed as follows:

[0042]

[0043] Where Π(t) is the state vector of the observer, η(t) is the constructor, and Λ=diag{λ1,λ2,λ3,λ4}>0 is the gain coefficient matrix, where λ1,λ2,λ3 and λ4 are its four gain coefficients;

[0044] Define the nominal estimation error e of the neural network observer. n If x(t) = x²(t) - Π(t), then the dynamic expression of the error is:

[0045]

[0046] Choose an adaptive rate of:

[0047]

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

[0049] Step 2.3: Design a sliding mode controller based on the backstepping method.

[0050] Step 2.3 is 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 surface;

[0054] Step 2.3.4: Design the controller.

[0055] Step 2.3.1 shall be implemented in accordance with the following steps:

[0056] Define the altitude attitude angle error e1(t):

[0057] e1(t)=x1(t)-x d (t) (3)

[0058] Where, x d (t) represents the desired tracking trajectory at high attitude;

[0059] According to formula (5), the dynamic of altitude attitude error is... Represented as:

[0060]

[0061] Define the candidate Lyapunov function V1(t) as:

[0062]

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

[0064]

[0065] Where α1(t) is the virtual control law, and e2(t) is the velocity and attitude angular velocity error term.

[0066] Since |f1(x1)|=secθ(t)≠0, f1(x1) is an invertible matrix. To ensure the negative definiteness of formula (14), α1(t) is designed as:

[0067]

[0068] 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 These are its four gain coefficients;

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

[0070]

[0071] Step 2.3.2 shall be implemented in accordance with the following steps:

[0072] Define the velocity and attitude angular velocity error term e2(t):

[0073] e2(t)=x2(t)-α1(t) (9)

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

[0075]

[0076] in

[0077] Step 2.3.3 shall be implemented in accordance with the following steps:

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

[0079] s(t)=c1e1(t)+e2(t) (11)

[0080] Where c1 > 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 V2(t) as:

[0084]

[0085] According to equations (16), (19) and (20), the derivative of the candidate Lyapunov equation V2(t) is:

[0086]

[0087] Step 2.3.4 shall be implemented in accordance with the following steps:

[0088] Design the controller u(t):

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

[0090]

[0091] Where m1 > 0 and n1 > 0 are gain parameters, and sign(s(t)) is the sign function of s(t), which is a discontinuous switching function in sliding mode control, 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, defined as:

[0098]

[0099] According to equations (22) and (25), Rewritten as:

[0100]

[0101] Step 3 is implemented in the following steps:

[0102] Stability analysis was performed on the designed controller.

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

[0104]

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

[0106]

[0107] because:

[0108]

[0109] Where H(x) is a bounded function ||H(x)||<τ, and ε1,ε2,ε3,ε4>0 are design parameters; therefore, according to equations (29) and (30), it is assumed that And consider the following formula:

[0110]

[0111] The following inequality relationships are obtained:

[0112]

[0113] in,

[0114]

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

[0116]

[0117] Based on the above analysis, under the sliding mode flight control method for unmanned helicopters based on online neural networks, the tracking error of the helicopter can converge to the desired bounded range, thus achieving effective tracking of the target.

[0118] The beneficial effects of this invention are that, based on an online neural network-based sliding mode flight control method for unmanned helicopters, and by employing a neural network-based sliding mode flight control method combined with a nonlinear disturbance observer and a neural network estimator, the stability and robustness of the unmanned helicopter in the face of disturbances and uncertainties are significantly improved. In the design of the sliding mode controller, the introduction of a saturation function effectively eliminates control chattering, making the control input smoother and thus increasing the feasibility of the control system. Matlab / Simulink simulations demonstrate that the method of this invention can effectively control the altitude and attitude of the unmanned helicopter, enabling it to quickly and accurately track a preset trajectory, thereby improving the helicopter's tracking performance. Attached Figure Description

[0119] Figure 1This is a flowchart of the online neural network-based sliding mode flight control method for unmanned helicopters according to the present invention;

[0120] Figure 2 It is the state tracking trajectory curve of the UAV's altitude and attitude system, including altitude tracking trajectory, roll angle tracking trajectory, pitch angle tracking trajectory and yaw angle tracking trajectory;

[0121] Figure 3 It is the state tracking trajectory error curve of the UAV's 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 4 It is the speed tracking trajectory curve of the UAV's altitude 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 interference of the UAV's altitude and attitude system and its estimated curve, including the interference force curve and three interference moment curves;

[0124] Figure 6 It is the control input curve of the UAV's altitude and attitude system, including the main rotor thrust and three resultant external torques. Detailed Implementation

[0125] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0126] This invention is based on an online neural network-based sliding mode flight control method for unmanned helicopters, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

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

[0128] Step 1 is implemented in the following steps:

[0129] The variables appearing in the following formulas are explained as follows: This represents the first derivative of the function f(x). Let A represent the second derivative of the function f(x). T Let A be the transpose of matrix A. -1 Let |A| denote the inverse of matrix A, and |A| denote the determinant of matrix A. Let I represent an n-dimensional vector space. n×n Represents an n-order identity matrix;

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

[0131]

[0132] Where h(t) and v(t) are the altitude and climb rate of the unmanned helicopter in the inertial coordinate system, m is the mass of the unmanned helicopter, g0 is the gravitational acceleration, and Ω(t) = (φ(t) θ(t) ψ(t)). T Let W(t) represent the attitude angles of the unmanned helicopter, where φ(t), θ(t), and ψ(t) represent the roll angle, pitch angle, and yaw angle, respectively, and W(t) = (p(t) q(t) r(t)). T Let J represent 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, and J = diag{J xx J yy J zz} represents the inertial matrix of the unmanned helicopter, where J xx J yy and J zz Let H0(t) represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia, respectively, and let H0(t) be the attitude motion matrix.

[0133]

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

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

[0136]

[0137] T m τ(t) and τ0(t) are the thrust and control torque of the helicopter's main rotor, respectively. They are the control inputs of the unmanned helicopter's altitude and attitude system, where x = (x1, x2). T For the state of the system, x1(t) = (h(t) Ω T (t)) T Representing the state vector, x2(t) = (v(t) W T (t)) T Represents the velocity vector. and These represent the disturbance force and disturbance torque in the vertical direction, respectively. and Represents the uncertainties of the system;

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

[0139]

[0140] in, The system's control input is represented by: u1(t) = cosφ(t)cosθ(t)T m (t)-mg0, u2(t)=τ0(t); f(x1) and f(x2) represent the parameter matrices related to x1(t) and x2(t) respectively, and are expressed in the following forms: g and It is a constant matrix relating mass and moment of inertia, expressed in the following form: d(t) and Δf(x) represent the disturbances and uncertainties of the system:

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

[0142]

[0143] Where L = diag{l1,l2,l3,l4} > 0 is the gain coefficient matrix, and l1, l2, l3 and l4 are its four gain coefficients;

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

[0145] P(x) = W *T H(x)+ε * (4)

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

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

[0148]

[0149] in This represents the combined interference caused by external disturbances to the system and the approximation error of the neural network.

[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 implemented in the following steps:

[0152] Step 2.1, Design of Nonlinear Interference Observer:

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

[0154]

[0155] in, For interference estimates, For the optimal weight W * The estimated value, δ(t), is the constructor function;

[0156] Define the interference estimation error value as The dynamics of the disturbance estimation error are given by the following equation:

[0157]

[0158] in This refers to the weight estimation error;

[0159] Step 2.2, Design of the Neural Network Interference Observer:

[0160] The neural network interference observer is designed as follows:

[0161]

[0162] Where Π(t) is the state vector of the observer, η(t) is the constructor, and Λ=diag{λ1,λ2,λ3,λ4}>0 is the gain coefficient matrix, where λ1,λ2,λ3 and λ4 are its four gain coefficients;

[0163] Define the nominal estimation error e of the neural network observer. n If x(t) = x²(t) - Π(t), then the dynamic expression of the error is:

[0164]

[0165] Choose an adaptive rate of:

[0166]

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

[0168] Step 2.3: Design a sliding mode controller based on the backstepping method.

[0169] Step 2.3 is 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 shall be implemented in accordance with the following steps:

[0175] Define the altitude attitude angle error e1(t):

[0176] e1(t)=x1(t)-x d (t) (27)

[0177] Where, x d (t) represents the desired tracking trajectory at high attitude;

[0178] According to formula (5), the dynamic of altitude attitude error is... Represented as:

[0179]

[0180] Define the candidate Lyapunov function V1(t) as:

[0181]

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

[0183]

[0184] Where α1(t) is the virtual control law, and e2(t) is the velocity and attitude angular velocity error term.

[0185] Since |f1(x1)|=secθ(t)≠0, f1(x1) is an invertible matrix. To ensure the negative definiteness of formula (14), α1(t) is designed as:

[0186]

[0187] 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 These are its four gain coefficients;

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

[0189]

[0190] Step 2.3.2 shall be implemented in accordance with the following steps:

[0191] Define the velocity and attitude angular velocity error term e2(t):

[0192] e2(t)=x2(t)-α1(t) (33)

[0193] According to formula (5), the dynamic expression of altitude attitude error, velocity, and attitude angular velocity error is as follows:

[0194]

[0195] in

[0196] Step 2.3.3 shall be implemented in accordance with the following steps:

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

[0198] s(t)=c1e1(t)+e2(t) (35)

[0199] Where c1 > 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 V2(t) as:

[0203]

[0204] According to equations (16), (19) and (20), the derivative of the candidate Lyapunov equation V2(t) is:

[0205]

[0206] Step 2.3.4 shall be implemented in accordance with the following steps:

[0207] Design the controller u(t):

[0208] Similar to step 2.3.1, g is obviously an invertible matrix. In order to ensure the negative definiteness of equation (22), the controller u(t) is designed as follows:

[0209]

[0210] Where m1 > 0 and n1 > 0 are gain parameters, and sign(s(t)) is the sign function of s(t), which is a discontinuous switching function in sliding mode control, 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, defined as:

[0217]

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

[0219]

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

[0221] Step 3 is implemented in the following steps:

[0222] Stability analysis was performed on the designed controller.

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

[0224]

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

[0226]

[0227] because:

[0228]

[0229] Where H(x) is a bounded function ||H(x)||<τ, and ε1,ε2,ε3,ε4>0 are design parameters;

[0230] Therefore, according to equations (29) and (30), we assume And consider the following formula:

[0231]

[0232] The following inequality relationships are obtained:

[0233]

[0234] in,

[0235]

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

[0237]

[0238] Based on the above analysis, under the sliding mode flight control method for unmanned helicopters based on online neural networks, the tracking error of the helicopter can converge to the desired bounded range, thus achieving effective tracking of the target.

[0239] Through the above stability analysis, we can obtain that, for helicopter systems with uncertainties and disturbances, formula (2), designing controller (25) and observers (6) and (8), if there exists a given gain coefficient matrix that satisfies and the gain coefficient satisfy The unmanned helicopter error tracking system, according to 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] This invention is based on an online neural network-based sliding mode flight control method for unmanned helicopters, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

[0242] Step 1: Design a dynamic nonlinear model of the helicopter's 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 using Lyapunov functions to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0245] Example 2

[0246] This invention is based on an online neural network-based sliding mode flight control method for unmanned helicopters, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

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

[0248] Step 1 is implemented in the following steps:

[0249] The variables appearing in the following formulas are explained as follows: This represents the first derivative of the function f(x). Let A represent the second derivative of the function f(x). T Let A be the transpose of matrix A. -1 Let |A| denote the inverse of matrix A, and |A| denote the determinant of matrix A. Let I represent an n-dimensional vector space. n×n Represents an n-order identity matrix;

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

[0251]

[0252] Where h(t) and v(t) are the altitude and climb rate of the unmanned helicopter in the inertial coordinate system, m is the mass of the unmanned helicopter, g0 is the gravitational acceleration, and Ω(t) = (φ(t) θ(t) ψ(t)). T Let W(t) represent the attitude angles of the unmanned helicopter, where φ(t), θ(t), and ψ(t) represent the roll angle, pitch angle, and yaw angle, respectively, and W(t) = (p(t) q(t) r(t)). T Let J represent 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, and J = diag{J xx J yy J zz} represents the inertial matrix of the unmanned helicopter, where J xx J yy and J zz Let H0(t) represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia, respectively, and let H0(t) be the attitude motion matrix.

[0253]

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

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

[0256]

[0257] T m τ(t) and τ0(t) are the thrust and control torque of the helicopter's main rotor, respectively. They are the control inputs of the unmanned helicopter's altitude and attitude system, where x = (x1, x2). T For the state of the system, x1(t) = (h(t) Ω T (t))T Representing the state vector, x2(t) = (v(t) W T (t)) T Represents the velocity vector. and These represent the disturbance force and disturbance torque in the vertical direction, respectively. and Represents the uncertainties of the system;

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

[0259]

[0260] in, The system's control input is represented by: u1(t) = cosφ(t)cosθ(t)T m (t)-mg0, u2(t)=τ0(t); f(x1) and f(x2) represent the parameter matrices related to x1(t) and x2(t) respectively, and are expressed in the following forms: g and It is a constant matrix relating mass and moment of inertia, expressed in the following form: d(t) and Δf(x) represent the disturbances and uncertainties of the system:

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

[0262]

[0263] Where L = diag{l1,l2,l3,l4} > 0 is the gain coefficient matrix, and l1, l2, l3 and l4 are its four gain coefficients;

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

[0265] P(x) = W *T H(x)+ε * (4)

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

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

[0268]

[0269] in This represents the combined interference caused by external disturbances to the system and the approximation error of the neural network.

[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: Perform stability analysis using Lyapunov functions to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0272] Example 3

[0273] This invention is based on an online neural network-based sliding mode flight control method for unmanned helicopters, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

[0274] Step 1: Design a dynamic nonlinear model of the helicopter's 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 implemented in the following steps:

[0277] Step 2.1, Design of Nonlinear Interference Observer:

[0278] The interference observer equation is designed as follows:

[0279]

[0280] in, For interference estimates, For the optimal weight W * The estimated value, δ(t), is the constructor function;

[0281] Define the interference estimation error value as The dynamics of the disturbance estimation error are given by the following equation:

[0282]

[0283] in This refers to the weight estimation error;

[0284] Step 2.2, Design of the Neural Network Interference Observer:

[0285] The neural network interference observer is designed as follows:

[0286]

[0287] Where Π(t) is the state vector of the observer, η(t) is the constructor, and Λ=diag{λ1,λ2,λ3,λ4}>0 is the gain coefficient matrix, where λ1,λ2,λ3 and λ4 are its four gain coefficients;

[0288] Define the nominal estimation error e of the neural network observer. n If x(t) = x²(t) - Π(t), then the dynamic expression of the error is:

[0289]

[0290] Choose an adaptive rate of:

[0291]

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

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

[0294] Step 3: Perform stability analysis using Lyapunov functions to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0295] Example 4

[0296] This invention is based on an online neural network-based sliding mode flight control method for unmanned helicopters, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

[0297] Step 1: Design a dynamic nonlinear model of the helicopter's 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: Perform stability analysis using Lyapunov functions to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0300] Step 3 is implemented in the following steps:

[0301] Step 3 is implemented in the following steps:

[0302] Stability analysis was performed on the designed controller.

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

[0304]

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

[0306]

[0307] because:

[0308]

[0309] Where H(x) is a bounded function ||H(x)||<τ, and ε1,ε2,ε3,ε4>0 are design parameters;

[0310] Therefore, according to equations (29) and (30), we assume And consider the following formula:

[0311]

[0312] The following inequality relationships are obtained:

[0313]

[0314] in,

[0315]

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

[0317]

[0318] Based on the above analysis, under the sliding mode flight control method for unmanned helicopters based on online neural networks, the tracking error of the helicopter can converge to the desired bounded range, thus achieving effective tracking of the target.

[0319] Example 5

[0320] This invention is based on an online neural network-based sliding mode flight control method for unmanned helicopters, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

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

[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 implemented in the following steps:

[0324] Step 2.1, Design of Nonlinear Interference Observer:

[0325] The interference observer equation is designed as follows:

[0326]

[0327] in, For interference estimates, For the optimal weight W * The estimated value, δ(t), is the constructor function;

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

[0329]

[0330] in This refers to the weight estimation error;

[0331] Step 2.2, Design of the Neural Network Interference Observer:

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

[0333]

[0334] Where Π(t) is the state vector of the observer, η(t) is the constructor, and Λ=diag{λ1,λ2,λ3,λ4}>0 is the gain coefficient matrix, where λ1,λ2,λ3 and λ4 are its four gain coefficients;

[0335] Define the nominal estimation error e of the neural network observer. n If x(t) = x²(t) - Π(t), then the dynamic expression of the error is:

[0336]

[0337] Choose an adaptive rate of:

[0338]

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

[0340] Step 2.3: Design a sliding mode controller based on the backstepping method.

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

[0342] Step 2.3.1: Define the altitude 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 surface;

[0345] Step 2.3.4: Design the controller.

[0346] Step 3: Perform stability analysis using Lyapunov functions to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

[0347] Example 6

[0348] The invention will now be further described with reference to the accompanying drawings and a specific example.

[0349] The simulation of the unmanned helicopter system is verified in the Matlab / Simulink environment by referencing 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 =0.35kg·m 2 J zz =0.29 kg·m 2

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

[0353] k 11 =6,k 12 =6,k 13 =6,k 14 =6,l1=20,l2=10,l3=10,l4=10,

[0354] λ1=20, λ2=10, λ3=10, λ4=10, c1=3, m1=3, n1=3, γ=0.1, σ=1, Φ=0.3

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

[0356]

[0357] The uncertainty term of the unmanned helicopter system is given by the following formula:

[0358]

[0359] The initial state of the unmanned helicopter is (50.10.10.1), and the tracking trajectory x is set. d (t) is:

[0360]

[0361] The simulation curve of the unmanned helicopter's state variable x1(t) tracking is as follows: Figure 2 As shown, the trajectory tracking error simulation curve is as follows: Figure 3 As shown in the figure, simulation results demonstrate that the unmanned helicopter can rapidly track the preset desired trajectory in terms of altitude and attitude. The proposed control strategy effectively reduces jitter, achieves smooth control actions, and maintains performance under various operating conditions. This indicates that the system has good robustness and its potential for practical applications.

[0362] The simulation curve of the unmanned helicopter's state variable x2(t) is shown below. Figure 4 As shown in the figure, the climb rate, roll rate, pitch rate, and yaw rate of the unmanned helicopter can quickly track the preset tracking trajectory.

[0363] like Figure 5 As shown, the nonlinear disturbance observer accurately estimates the disturbances present in the system. The control inputs of the unmanned helicopter system are as follows: Figure 6 As shown in the figure, using a saturation function when designing a sliding mode controller can effectively eliminate chattering and make the control curve smoother.

Claims

1. An online neural network based unmanned helicopter sliding mode flight control method, characterized in that, The specific steps are as follows: Step 1: Design a dynamic nonlinear model of the helicopter's attitude and altitude; Step 2: Design a nonlinear disturbance observer, a neural network estimator, and a sliding mode robust controller based on the backstepping method; Step 2 is implemented in the following steps: Step 2.1, Design of Nonlinear Interference Observer: The interference observer equations are designed as follows: （6） wherein is an estimate of the interference, is an optimal weight is an estimate of the interference, is a constructor; The interference estimation error value is defined as The dynamics of the interference estimation error are then given by （7） wherein is the weight estimation error; Step 2.2, Design of the Neural Network Interference Observer: The neural network interference observer is designed as follows: （8） in, Let be the state vector of the observer. For constructor, This is the gain coefficient matrix. and These are its four gain coefficients; Define the nominal estimation error of a neural network observer. Then the dynamic expression of the error is: （9） Choose an adaptive rate of: （10） in, and This is the gain coefficient. This is for the sliding surface that will be designed later; Step 2.3: Design a sliding mode controller based on the backstepping method; Step 2.3 is implemented in the following steps: Step 2.3.1: Define the altitude attitude angle error; Step 2.3.1 is implemented in the following steps: Defining a high attitude angle error : （11） wherein is a highly desired tracking trajectory; According to equation (5), the dynamics of the height attitude error is is expressed as: （12） Defining a candidate Lyapunov function is: （13） According to equations (11) and (12), the derivative of equation (13) is: （14） wherein is the virtual control rate, is the velocity and attitude angular velocity error term, because ,so For an invertible matrix, to ensure the negative definiteness of (14), design... for: （15） in This is the gain coefficient matrix. and These are its four gain coefficients; According to equations (14) and (15), Rewritten as: （16）； Step 2.3.2: Define the velocity and attitude angular velocity error terms; Step 2.3.2 is implemented in accordance with the following steps: Defining velocity and attitude angular velocity error terms : （17） According to formula (5), the dynamic expression of altitude attitude error, velocity, and attitude angular velocity error is as follows: （18） wherein ; Step 2.3.3: Define the sliding surface; Step 2.3.3 is implemented in the following steps: Defining a sliding surface : （19） wherein G is a gain coefficient; Combine equations (12), (15), (17), (18), and (19). The derivative is: （20） Defining a candidate Lyapunov function is: （21） According to equations (16), (19) and (20), the derivative of the candidate Lyapunov equation is: （22）； Steps 2.3.4: Design the controller; Step 2.3.4 is implemented in accordance with the following steps: Designing a controller : Similarly to step 2.3.1, it is obvious Given an invertible matrix, to ensure the negative definiteness of (22), a controller is designed. as follows: （23） in, and For gain parameters, for The sign function, a discontinuous switching function in sliding mode control, is defined as: （24） The boundary layer formula is as follows: in Given the boundary layer thickness, the feedback control law becomes: （25） wherein is a saturation function defined as: （26） According to (22) and (25), Rewritten as: （27）； Step 3: Perform stability analysis using Lyapunov functions to ensure the stability of the helicopter system in the face of disturbances and uncertainties.

2. The online neural network based unmanned helicopter sliding mode flight control method according to claim 1, wherein, Step 1 is implemented in the following steps: The variables appearing in the following formulas are explained as follows: Representation function The first derivative, Representation function The second derivative, Representation matrix The transpose of the matrix, Representation matrix The inverse matrix, Representation matrix The determinant, express 3D vector space, express An identity matrix of order 1; Step 1.1: Design the dynamic model of helicopter attitude and altitude: （1） in, and It represents the altitude position and climb rate of the unmanned helicopter in an inertial coordinate system. It's the quality of the unmanned helicopter. It is gravitational acceleration. The attitude angle of the unmanned helicopter is represented by the angle of inclination. and These represent the roll angle, pitch angle, and yaw angle, respectively. Denotes the angular velocity vector, where and These represent the roll rate, pitch rate, and yaw rate, respectively. The inertial matrix of the unmanned helicopter is represented by, where, and These represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia, respectively. It is the attitude motion matrix: in, and These represent the sine, cosine, tangent, and cosecant functions in trigonometric functions, respectively. Representing the cross product operator matrix: and These are the thrust and control torque of the helicopter's main rotor, which are the control inputs to the altitude and attitude system of the unmanned helicopter. For the state of the system, Represents the state vector. Represents the velocity vector. and These represent the disturbance force and disturbance torque in the vertical direction, respectively. and Represents the uncertainties of the system; Step 1.2: Based on the above helicopter attitude and altitude model, rewrite the system: （2） in, Indicates the system's control input: , ; and They represent the relevant and The parameter matrix is ​​represented in the following form: , ; and It is a constant matrix relating mass and moment of inertia, expressed in the following form: , ; and This indicates the disturbances and uncertainties in the system: , ; To handle the uncertainty of the system, a continuous function is defined （3） in, It is the gain coefficient matrix. and These are its four gain coefficients; Approximation of continuous functions using radial basis function neural networks is of the form （4） in, These are the basis functions of the neural network. That is its optimal weight. It is the optimal approximation error; According to formulas (3) and (4), we have Therefore, formula (2) is rewritten as: （5） wherein represents the compound disturbance composed of the system external disturbance and the neural network approximation error.

3. The online neural network based unmanned helicopter sliding mode flight control method of claim 2, wherein, Step 3 is implemented in the following steps: Stability analysis was performed on the designed controller. To ensure stability of the helicopter system, consider the Lyapunov function is: （28） Combining equations (27) and (7), the derivative of the function （29） because: （30） wherein is a bounded function , is a design parameter; Thus, according to equations (29), (30), assuming and considering the following equation: （31） The following inequality relationships are obtained: （32） in, For the helicopter attitude and altitude dynamic system described by formula (2), a neural network flight controller of the form of formula (25) is designed, and the relevant parameters of the controller satisfy: , ; Based on the above analysis, under the sliding mode flight control method for unmanned helicopters based on online neural networks, the tracking error of the helicopter can converge to the desired bounded range, thus achieving effective tracking of the target.

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