Helicopter system adaptive neural network control method with input saturation constraint

Abstract

The embodiment of the specification provides a helicopter system adaptive neural network control method with input saturation constraint, wherein the method comprises the following steps: establishing a nonlinear dynamics model of a 2-DOF helicopter system according to a Lagrange mechanics model; approximating input saturation constraint as a smooth function, adopting a radial basis function neural network to approximate the system, and constructing a helicopter system equation; defining a tracking error variable, designing a controller and an adaptive law according to the tracking error variable; constructing a Lyapunov equation; proving the stability of the 2-DOF helicopter system according to the Lyapunov equation, the controller and the adaptive law; and analyzing simulation results through a Matlab platform. The method can avoid the problem of input saturation of the system and improve the stability of the system.

Description

Technical Field

[0001] This document relates to the field of helicopter system control technology, and in particular to an adaptive neural network control method for helicopter systems with input saturation constraints. Background Technology

[0002] With the rapid development of science and technology, unmanned aerial vehicle (UAV) technology has gradually matured and attracted widespread attention. Helicopters, as a typical type of UAV, are not only low-cost, small in size, and highly survivable, but also simple in structure and easy to use. They have been widely applied in military reconnaissance aircraft and unmanned aerial vehicles, as well as in civil aviation photography, express delivery, disaster relief, and other fields. To achieve stable control of helicopter systems, researchers have designed many control strategies, including LQR control, Q-learning control, and sliding mode control. However, since the helicopter system is a nonlinear system with uncertainties in model parameters and cross-coupling between axes, the above methods ignore the nonlinearity and uncertainty of the system, which may lead to instability in practical applications. Furthermore, in practical engineering applications, input saturation constraints often occur. If the system input exceeds a certain limit, it may cause unnecessary vibrations and reduce the system's stability. These characteristics pose significant challenges to controller design. Therefore, it is essential to research an effective control method to overcome these challenges and ensure the robustness of the helicopter system. Summary of the Invention

[0003] This specification provides one or more embodiments of an adaptive neural network control method for a helicopter system with input saturation constraints, including:

[0004] S1. Based on the Lagrange mechanical model, establish a nonlinear dynamic model of the 2-DOF helicopter system;

[0005] S2. Approximate the input saturation constraint as a smooth function, and use a radial basis function neural network to approximate the system, thus constructing the helicopter system equations;

[0006] S3. Define the tracking error variable, and design the controller and adaptive law based on the tracking error variable;

[0007] S4. Construct the Lyapunov equations;

[0008] S5. Prove the stability of the 2-DOF helicopter system based on the Lyapunov equations, controller, and adaptive law.

[0009] S6. Perform simulation using the Matlab platform and analyze the simulation results.

[0010] This specification provides one or more embodiments of an electronic device, including:

[0011] Processor; and,

[0012] A memory is configured to store computer-executable instructions, which, when executed, cause the processor to implement the steps of the aforementioned adaptive neural network control method for a helicopter system with input saturation constraints.

[0013] This specification provides one or more embodiments of a storage medium for storing computer-executable instructions that, when executed, implement the steps of the above-described adaptive neural network control method for a helicopter system with input saturation constraints.

[0014] The beneficial effects of this invention are as follows:

[0015] This invention addresses the input saturation constraint problem frequently encountered in practical engineering applications. It designs an adaptive neural network control method for helicopter systems with input saturation constraints. The method utilizes a neural network to estimate the unknown dynamic model of the helicopter and employs a smooth non-affine function to approximate and handle nonlinear constraint functions, effectively reducing damage to the system when the input exceeds certain limits. Finally, through the establishment and analysis of the Lyapunov function, it is proven that the system is ultimately uniformly bounded, achieving more accurate tracking and more stable control of the 2-DOF helicopter system.

[0016] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A simplified schematic diagram of a 2-DOF helicopter model;

[0019] Figure 2 A flowchart illustrating an adaptive neural network control method for a helicopter system with input saturation constraints, provided for one or more embodiments of this specification;

[0020] Figure 3A schematic diagram illustrating the tracking response of the actual and desired pitch angles of a 2-DOF helicopter provided in one or more embodiments of this specification;

[0021] Figure 4 A schematic diagram illustrating the tracking response of the actual and desired yaw angles of a 2-DOF helicopter provided in one or more embodiments of this specification;

[0022] Figure 5 A schematic diagram illustrating the tracking error of the actual and desired angles of a 2-DOF helicopter provided for one or more embodiments of this specification;

[0023] Figure 6 A schematic diagram of the system input voltage performance of a 2-DOF helicopter provided for one or more embodiments of this specification;

[0024] Figure 7 A schematic diagram of the system input saturation voltage performance of a 2-DOF helicopter provided for one or more embodiments of this specification;

[0025] Figure 8 This is a schematic diagram of the structure of an electronic device provided for one or more embodiments of this specification. Detailed Implementation

[0026] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0027] Method Implementation Examples

[0028] This invention provides an adaptive neural network control method for a helicopter system with input saturation constraints, applied to a 2-DOF helicopter system. Figure 1 A simplified schematic diagram of a 2-DOF helicopter model, as shown below. Figure 1 As shown, the 2-DOF helicopter model has two identical propellers. The horizontally positioned propeller is driven by a front motor, located at a distance r from the center of mass. p A thrust Fp and a torque about the Y-axis are generated at a point to achieve pitch motion. Another vertically positioned propeller, driven by a rear motor (BACK), is located at a distance r from the center of mass. yA thrust Fy is generated at the point of origin, and a torque is generated about the Z-axis to achieve yaw motion. The helicopter is a multi-input multi-output nonlinear system. The system input is the voltage of the electric motor that controls the propeller, and the output is the system's pitch angle and yaw angle.

[0029] Figure 2 A flowchart illustrating an adaptive neural network control method for a helicopter system with input saturation constraints, provided for one or more embodiments of this specification, is shown below. Figure 2 As shown, the adaptive neural network control method for a helicopter system with input saturation constraints according to an embodiment of the present invention specifically includes:

[0030] S1. Based on the Lagrange mechanical model, establish a nonlinear dynamic model of the 2-DOF helicopter system.

[0031] The nonlinear dynamic model of the 2-DOF helicopter system is established as follows:

[0032]

[0033]

[0034] Among them, J pr and J yr These are the moments of inertia of pitch and yaw motions, respectively, D pr and D yr It is the coefficient of viscous friction, K. pp K is the torque thrust gain acting on the pitch shaft of a pitch propeller. py K is the torque thrust gain acting on the pitch axis in a yaw propeller. yp K is the torque thrust gain acting on the yaw shaft in a pitch propeller. yy It is the torque thrust gain acting on the yaw shaft in a yaw propeller, where θ represents the pitch angle, ψ represents the yaw angle, and l m M represents the distance from the center of mass of the helicopter to the point furthest from the fixed frame of the fuselage, g represents the acceleration due to gravity, and V represents the mass of the helicopter. pr and V yr These represent the motor voltage inputs that control pitch and yaw motion, respectively.

[0035] Define the system's output vector as x = [x1, x2] T , where x1=[θ,ψ] T , To simplify the controller design, the 2-DOF helicopter system model is simplified as follows:

[0036]

[0037]

[0038] y = x1 (5)

[0039] Where x1 and x2 are the output angle and angular velocity variables, respectively, and ΔQ(x1,x2) and ΔP(x1,x2) are the uncertainties of the system. Let represent the derivatives of the angle variable and the angular velocity variable, respectively. Q(x1,x2) and P(x1,x2) are the system gain matrices, expressed as follows:

[0040]

[0041]

[0042] Meanwhile, v is the input to the controller, U(v) = [V pr V yr ] T The saturated input and saturated nonlinear output of the system are represented as follows:

[0043]

[0044] Where u max It is a known boundary of U(v).

[0045] S2. Approximate the input saturation constraint as a smooth function, and use a radial basis function neural network to approximate the system, thus constructing the helicopter system equations.

[0046] A smooth nonlinear function is used to approximate the saturation constraint function, and the function is transformed into an affine form according to the mean value theorem. From (8), it can be seen that when v = u max When there is an acute angle, it is not differentiable. To avoid this situation, the input saturation constraint can be approximated as a smooth function, defined as:

[0047]

[0048] Clearly, there exists a deviation d(v) between U(v) and h(v). Due to the boundedness of the sat and tanh functions, we know that the deviation d(v) is a bounded function, and its bound can be derived as follows:

[0049]

[0050] Applying the Mean Value Theorem, there exists a constant δ, 0 < δ < 1, such that:

[0051]

[0052] in

[0053]

[0054]

[0055] Choosing v0 = 0, we get the following again:

[0056]

[0057] And thus regain

[0058]

[0059] Where L(x,v)=ΔQ(x1,x2)+ΔP(x1,x2)(h vm Since ΔQ(x1,x2) and ΔP(x1,x2) are uncertainties in the helicopter system, L(x,v) is an unknown equation of the system. Simultaneously, Ξ=P(x1,x2)d(v), and P(x1,x2) is bounded, satisfying... in and It is an unknown positive constant; from (11), we know that d(v) is bounded, so Ξ is bounded, satisfying in It is an unknown positive constant, defined as in It is to compensate for errors. It is an estimate of the compensation amount.

[0060] The uncertainty term L(x,v) in a nonlinear system is approximated using a radial basis function neural network:

[0061] L(x,v)=W *T S(Z)+ε(Z) (16)

[0062] Among them, W * Let S(Z) represent the ideal weights of the neural network, S(Z) represent the Gaussian function of the radial basis vectors, Z represent the input vector of the neural network, and ε(Z) be the approximation error of the neural network, satisfying the following condition: in It is an unknown positive constant; defined as in It is the weight error of the neural network. These are the weights estimated by the neural network.

[0063] S3. Define the tracking error variable, and design the controller and adaptive law based on the tracking error variable.

[0064] Define the tracking errors z1 and z2 as follows:

[0065] z1 = x1 - x d(17)

[0066] z² = x² - α (18)

[0067] Where, x d The expected trajectory of the helicopter system's pitch and yaw angles, where α is an auxiliary control variable, defined as follows:

[0068]

[0069] Where k1 is a positive design parameter. It is the derivative of the expected trajectory with respect to time;

[0070] Design the system controller as follows:

[0071]

[0072] Where k2 is a positive design parameter, and ∈ is a positive constant. The derivative of the auxiliary control variable;

[0073] The adaptive law is designed as follows:

[0074]

[0075]

[0076] Among them, Γ w For positive parameters of the design, Let Γ be the update rate of the neural network based on the hyperbolic tangent function. w >0, σ w and It is a positive constant in the design.

[0077] S4. Construct the Lyapunov equations.

[0078] Specifically, the following are included:

[0079]

[0080]

[0081]

[0082] Here, V1, V2, and V3 all represent the constructed Lyapunov equations.

[0083] S5. Based on the Lyapunov equations, controller, and adaptive law, prove the stability of the 2-DOF helicopter system.

[0084] Specifically,

[0085] First, take the derivative with respect to z1:

[0086]

[0087] The derivative of V1 is obtained:

[0088]

[0089] Substituting α into (27) yields:

[0090]

[0091] Then, taking the derivative with respect to z2, we get:

[0092]

[0093] Differentiate V2:

[0094]

[0095] Will Substituting, we get:

[0096]

[0097] Taking the derivative of V3, the details are as follows:

[0098] Based on the following inequality:

[0099]

[0100]

[0101] Based on the existence of any And θ>0, such that Established, resulting in:

[0102]

[0103] Therefore, we get:

[0104]

[0105] By adopting the following Young's inequality:

[0106]

[0107]

[0108]

[0109] Therefore, we get:

[0110]

[0111] in,

[0112]

[0113]

[0114] in, is the update rate of the radial basis function neural network.

[0115] To ensure The choice of k1 and k2 must satisfy:

[0116]

[0117] When the above inequality is satisfied, it proves that all signals in the system are uniformly eventually bounded, and the system is asymptotically stable.

[0118] S6. Perform simulation using the Matlab platform and analyze the simulation results.

[0119] Figure 3 and Figure 4 The figures represent the system's actual pitch and yaw angles in response to the desired trajectory, respectively. It can be seen that the system tracked the desired trajectory in a short time. Figure 5 The tracking error graphs of the actual angle and the expected angle also show that the error quickly approaches zero, demonstrating good tracking performance. Figure 6 This represents the system input voltage performance graph, which initially shows the input voltage exceeding a certain value, and then tends to stabilize. Figure 7 The diagram shows the system's input saturation voltage performance. It can be seen that the initial values ​​were subject to input saturation constraints, ensuring that the voltage remained between [24V, -24V] and then tended to stabilize.

[0120] The beneficial effects of this invention are as follows:

[0121] This invention addresses the input saturation constraint problem that frequently occurs in practical engineering applications. To solve this problem, a neural network is used to estimate the unknown dynamic model of the helicopter. A smooth non-affine function is used to approximate and handle the nonlinear constraint function, effectively reducing the damage to the system when the input exceeds a certain limit. Finally, through the establishment and analysis of the Lyapunov function, it is proved that the system is eventually uniformly bounded. After rigorous verification, it is demonstrated that this invention can effectively handle the phenomenon of input exceeding a certain limit value, greatly protecting the system, improving the system's robustness, and achieving more accurate tracking and more stable control of the 2-DOF helicopter system.

[0122] Device Example 1

[0123] This invention provides an electronic device, such as... Figure 8 As shown, it includes: a memory 80, a processor 82, and a computer program stored in the memory 80 and executable on the processor 82. When the computer program is executed by the processor 82, it performs the following method steps:

[0124] S1. Based on the Lagrange mechanical model, establish a nonlinear dynamic model of the 2-DOF helicopter system;

[0125] S2. Approximate the input saturation constraint as a smooth function, and use a radial basis function neural network to approximate the system, thus constructing the helicopter system equations;

[0126] S3. Define the tracking error variable, and design the controller and adaptive law based on the tracking error variable;

[0127] S4. Construct the Lyapunov equations;

[0128] S5. Prove the stability of the 2-DOF helicopter system based on the Lyapunov equations, controller, and adaptive law.

[0129] S6. Perform simulation using the Matlab platform and analyze the simulation results.

[0130] Device Example 2

[0131] This invention provides a storage medium on which a program for information transmission is stored. When executed by a processor 82, the program performs the following method steps:

[0132] S1. Based on the Lagrange mechanical model, establish a nonlinear dynamic model of the 2-DOF helicopter system;

[0133] S2. Approximate the input saturation constraint as a smooth function, and use a radial basis function neural network to approximate the system, thus constructing the helicopter system equations;

[0134] S3. Define the tracking error variable, and design the controller and adaptive law based on the tracking error variable;

[0135] S4. Construct the Lyapunov equations;

[0136] S5. Prove the stability of the 2-DOF helicopter system based on the Lyapunov equations, controller, and adaptive law.

[0137] S6. Perform simulation using the Matlab platform and analyze the simulation results.

[0138] The computer-readable storage media described in this embodiment include, but are not limited to, ROM, RAM, disk, or optical disk.

[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive neural network control method for a helicopter system with input saturation constraints, characterized in that, include: S1. Based on the Lagrange mechanical model, establish a nonlinear dynamic model of the 2-DOF helicopter system; In step S1, the nonlinear dynamic model of the 2-DOF helicopter system is established based on the Lagrange mechanical model. The specific nonlinear dynamic model of the 2-DOF helicopter system is as follows: （1） （2） in, and These are the moments of inertia for pitch and yaw motions, respectively. and It is the coefficient of viscous friction. It is the torque thrust gain acting on the pitch shaft in a pitch propeller. It is the torque thrust gain acting on the pitch axis in a yaw propeller. It is the torque thrust gain acting on the yaw axis in a pitch propeller. It is the torque thrust gain acting on the yaw shaft in a yaw propeller. The representative is the pitch angle. This represents the yaw angle. This indicates the distance of the center of mass from the point furthest from the fixed frame of the fuselage. Indicates the mass of the helicopter. Represents gravitational acceleration. and These represent the motor voltage inputs that control pitch and yaw motion, respectively. Define the system's output vector as ,in , To simplify the controller design, the 2-DOF helicopter system model is simplified as follows: （3） （4） （5） in To output the angle and angular velocity variables, and It is an uncertain term in the system. , Let represent the derivatives of the angle variable and the angular velocity variable, respectively. and Here are the system gain matrices, expressed as follows: （6） （7） at the same time, It is the controller input. The saturated input of the system is represented as: （8） in yes A known boundary; S2. Approximate the input saturation constraint as a smooth function, and use a radial basis function neural network to approximate the system, thus constructing the helicopter system equations; Step S2, which approximates the input saturation constraint as a smooth function, specifically means that the smooth function is defined as: （9） Obviously, in and There are deviations ,because functions and The boundedness of a function allows us to determine the deviation. It is a bounded function, and its bound can be derived as: （10） Applying the mean value theorem, there exists a constant. ,0< <1, such that: （11） in （12） （13） choose , regain: （14） And thus regain : （15） in ,because and This is an uncertainty in the helicopter system, therefore It is an unknown equation of the system; at the same time, ,and It is bounded, satisfying ,in and It is an unknown positive constant; as can be seen from equation (11), It is bounded, therefore It is bounded, satisfying < ,in It is an unknown positive constant, defined as ,in It is to compensate for errors. It is an estimate of the compensation amount; S3. Define the tracking error variable, and design the controller and adaptive law based on the tracking error variable; S4. Construct the Lyapunov equations; S5. Prove the stability of the 2-DOF helicopter system based on the Lyapunov equations, controller, and adaptive law. S6. Perform simulation using the Matlab platform and analyze the simulation results.

2. The method according to claim 1, characterized in that, Step S2 describes the use of a radial basis function neural network to approximate the system, constructing the helicopter system equations as follows: Radial basis function neural networks are used to approximate the uncertainties in nonlinear systems. : （16） in, Represents the ideal weights of a neural network. The Gaussian function representing the radial basis vectors, This represents the input vector of the neural network. It is the approximation error of the neural network, satisfying ,in It is an unknown positive constant; defined as ,in It is the weight error of the neural network. These are the weights estimated by the neural network.

3. The method according to claim 2, characterized in that, Step S3, which defines the tracking error variable and designs the controller and adaptive law based on the tracking error variable, specifically involves: Define tracking error and ,as follows: （17） （18） in, It is the desired trajectory of the helicopter system's pitch and yaw angles. It is an auxiliary control variable. Defined as: （19） in, It is a positive design parameter. It is the derivative of the expected trajectory with respect to time; Design the system controller as follows: （20） in, It is a positive design parameter. It is a positive constant. The derivative of the auxiliary control variable; The adaptive law is designed as follows: （21） （22） in, For positive parameters of the design, The update rate of the neural network based on the hyperbolic tangent function. >0, >0, and It is a positive constant in the design.

4. The method according to claim 3, characterized in that, Step S4, which involves constructing the Lyapunov equations, specifically includes the following: （23） （24） （25） in, , , Both represent the Lyapunov equations constructed.

5. The method according to claim 4, characterized in that, The specific method for proving the stability of the 2-DOF helicopter system based on the Lyapunov equations, controller, and adaptive law, as described in step S5, is as follows: right The derivative is determined as follows: （32） Based on the following inequality: （33） （34） Based on the existence of any and >0 , making 0.2785 Established, resulting in: （35） Therefore, we get: （36） By using the following Young's inequality: （37） （38） （39） Therefore, we get: （40） in, （41） （42） in, is the update rate of the radial basis function neural network.

6. The method according to claim 5, characterized in that, To ensure , , The choice satisfies: （43） When the above inequality is satisfied, it proves that all signals in the system are uniformly eventually bounded, and the system is asymptotically stable.

7. An electronic device, characterized in that, include: processor; as well as, A memory is configured to store computer-executable instructions, which, when executed, cause the processor to implement an adaptive neural network control method for a helicopter system with input saturation constraints as described in any one of claims 1-6.

8. A storage medium, characterized in that, Used to store computer-executable instructions, which, when executed, implement an adaptive neural network control method for a helicopter system with input saturation constraints as described in any one of claims 1-6.

Images