Helicopter system control method based on fixed-time adaptive neural network

Abstract

The embodiment of the specification provides a helicopter system control method based on a fixed-time adaptive neural network, wherein the method comprises the following steps: establishing a dynamic model of a helicopter system in actual engineering application according to a Lagrange mechanics model; defining a tracking error variable and designing an auxiliary control variable; estimating uncertain terms in the helicopter nonlinear system by using a radial basis function neural network; designing a controller and an adaptive law of the helicopter system, and proving that the system is ultimately uniformly bounded by establishing and analyzing a Lyapunov function. Not only is a faster convergence speed provided for the system, but also the tracking effect and the closed-loop stability of the helicopter system are maintained in fixed time, the system settling time is irrelevant to initial conditions of the system, and better performance is achieved.

Description

Technical Field

[0001] This document relates to the field of helicopter control technology, and in particular to a helicopter system control method based on a fixed-time adaptive neural network. Background Technology

[0002] With the rapid development of artificial intelligence technology, the performance of unmanned helicopters has gradually improved. As a typical type of unmanned aerial vehicle (UAV), helicopters have advantages such as light weight, small size, and low takeoff environmental requirements, and have been widely used in traffic monitoring, environmental detection, search and rescue, and other fields. To date, extensive research has been conducted on the control of helicopter systems, and many techniques have been proposed, such as PID control, optimal tracking control, linear quadratic regulator (LQR) control, and sliding mode control. However, the helicopter system is a nonlinear system, exhibiting model parameter uncertainties and inter-axis cross-coupling. These methods ignore the system's nonlinearity and uncertainty, potentially leading to system instability in practical applications. Meanwhile, in practical applications, fixed-time control, which derives the settling time function from the controller parameters, can be unaffected by the system's initial conditions, solving the problem of convergence time increasing infinitely with increasing initial conditions, while also providing a faster convergence speed. Therefore, it is crucial to research a fixed-time adaptive neural network control method for helicopter systems to address the system's nonlinearity and uncertainty, achieve system error tracking convergence within a fixed time, and improve the robustness of the helicopter system. Summary of the Invention

[0003] This invention provides a helicopter system control method based on a fixed-time adaptive neural network, aiming to solve the above-mentioned problems.

[0004] This invention provides a helicopter system control method based on a fixed-time adaptive neural network, comprising:

[0005] S1. Based on the Lagrange mechanical model, establish a dynamic model of the helicopter system in practical engineering applications;

[0006] S2. Define the tracking error variable and design the auxiliary control variable;

[0007] S3. Use a radial basis function neural network to estimate the uncertainties in the helicopter system;

[0008] S4. Design the controller and adaptive law for the helicopter system;

[0009] S5. Establish the Lyapunov function;

[0010] S6. Prove the stability of the helicopter system by analyzing the Lyapunov function;

[0011] S7. Perform simulation using the Matlab platform and analyze the simulation results.

[0012] This invention utilizes neural networks to estimate the unknown dynamic model of a helicopter system, designs a new controller and adaptive law, and proves that the system is eventually uniformly bounded through the establishment and analysis of the Lyapunov function. This not only provides the system with a faster convergence speed, maintaining the tracking performance and closed-loop stability of the helicopter system within a fixed time, but also achieves system settling time independent of initial conditions, resulting in better performance. Attached Figure Description

[0013] 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.

[0014] Figure 1 This is a flowchart of a helicopter system control method based on a fixed-time adaptive neural network according to an embodiment of the present invention;

[0015] Figure 2 This is a simplified schematic diagram of the 2-DOF helicopter system considered in Example 1;

[0016] Figure 3 The diagram shows the tracking response of the helicopter under different initial conditions for the actual and expected pitch angles in Example 1.

[0017] Figure 4 The graph shows the tracking response of the helicopter under different initial conditions for the actual and expected yaw angles in Example 1.

[0018] Figure 5 This is a tracking error diagram of the helicopter's actual and expected pitch angles under different initial conditions in Example 1;

[0019] Figure 6 This is a tracking error diagram of the helicopter's actual and expected yaw angles under different initial conditions in Example 1;

[0020] Figure 7 This is a diagram showing the system input voltage performance of the helicopter in Example 1. Detailed Implementation

[0021] 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.

[0022] Method Implementation Examples

[0023] This invention provides a helicopter system control method based on a fixed-time adaptive neural network. Figure 1 This is a flowchart of a helicopter system control method based on a fixed-time adaptive neural network according to an embodiment of the present invention. Figure 1 As shown, the helicopter system control method based on a fixed-time adaptive neural network according to an embodiment of the present invention specifically includes:

[0024] S1. Based on the Lagrange mechanical model, establish a dynamic model of the helicopter system for practical engineering applications; Step S1 specifically includes:

[0025] Based on the Lagrange mechanics model, a dynamic model of the helicopter system is established for practical engineering applications.

[0026]

[0027]

[0028]

[0029] Among them, J f and J d These are the moments of inertia of pitch and yaw motions, respectively, D f and D d 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 This refers to the torque thrust gain acting on the yaw shaft in a yaw propeller, where α represents the pitch angle, β represents the yaw angle, and l v The distance in meters (m) represents the distance from the center of mass of a point furthest from the fixed frame of the fuselage. a V represents the mass of the helicopter, g represents the acceleration due to gravity, and V represents the acceleration due to gravity. f and V dThese represent the motor voltage inputs that control pitch and yaw motions, respectively.

[0030] Define the system's output vector as p = [p1, p2] T where p1 = [α, β] T , To simplify the controller design, the 2-DOF helicopter system model is simplified as follows:

[0031]

[0032]

[0033] y = p1 (5)

[0034] Where ΔG(p1,p2) and ΔH(p1,p2) are the uncertainties of the system, U=[V f V d ] T y is the input to the controller, and y is the output of the system. Q(p1,p2) and P(p1,p2) are represented as follows:

[0035]

[0036]

[0037] S2. Define the tracking error variable and design the auxiliary control variable; Step S2 specifically includes:

[0038] Define tracking errors e1 and e2:

[0039] e1 = p1 - p d (8)

[0040] e2=p2-γ (9)

[0041] Where p d The expected trajectory of the helicopter system's pitch and yaw angles, where γ is an auxiliary control variable defined as:

[0042]

[0043] Where k 11 and k 12 It is a positive design parameter. It is the derivative of the expected trajectory with respect to time.

[0044] S3. Estimate the uncertainties in the helicopter system using a radial basis function neural network; Step S3 specifically includes:

[0045] Considering that ΔG(p1,p2) and ΔH(p1,p2) are uncertainties of the system, This can be simplified again to:

[0046]

[0047] in In practical applications, the R function is difficult to determine, so radial basis function neural networks are used to estimate the uncertain terms.

[0048] R(p,U)=Φ *T Ξ(Z)+ξ(Z) (12)

[0049] Where, Φ * Let ξ(Z) represent the ideal weights of the neural network, Ξ(Z) represent the Gaussian function of the radial basis vectors, Z represent the input vector of the neural network, and ξ(Z) be the approximation error of the neural network, satisfying the following condition: in It is an unknown positive constant; defined in It is the weight error of the neural network. These are the weights estimated by the neural network.

[0050] S4. Design the controller and adaptive law for the helicopter system. Step S4 specifically includes:

[0051] Design the system's controller:

[0052]

[0053] Where k 21 and k 22 It is a positive design parameter.

[0054] The design adaptive law is:

[0055]

[0056] Where Γ Φ >0, σ Φ1 and σ Φ2 It is a positive constant in the design.

[0057] S5. Establish the Lyapunov function. Step S5 specifically includes:

[0058] Establish the Lyapunov function:

[0059]

[0060]

[0061]

[0062] S6. Prove the stability of the helicopter system by analyzing the Lyapunov function. Step S6 specifically includes:

[0063] First, take the derivative with respect to e1:

[0064]

[0065] The derivative of V1 is obtained:

[0066]

[0067] Substituting α, we get:

[0068]

[0069] Then, taking the derivative with respect to e², we get:

[0070]

[0071] Differentiate V2:

[0072]

[0073] Substituting U into the equation yields:

[0074]

[0075] Differentiate V3:

[0076]

[0077] Consider the following inequality:

[0078]

[0079] Furthermore, we can deduce that:

[0080]

[0081] in

[0082]

[0083]

[0084]

[0085] σ Φ3 These are positive constants in the design. To ensure that ρ1, ρ2 > 0 and k > 0, the choice of these values ​​should satisfy the following:

[0086]

[0087] Therefore, it can be proven that all signals in the system are uniformly eventually bounded, e1, e2, At a fixed time T f Converging to a compact concentration, where T f Represented as:

[0088]

[0089] Where 0 < θ < 1 is a constant, and ρ1 and ρ2 are positive constants.

[0090] S7. Perform simulation using the Matlab platform and analyze the simulation results.

[0091] like Figure 2 The diagram shown is a simplified schematic of a 2-DOF helicopter model according to an embodiment of the present invention. X, Y, and Z represent the X-axis, Y-axis, and Z-axis, respectively. This model has two identical propellers. The horizontally positioned propeller is driven by a front motor 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. y A 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 and yaw angles.

[0092] Figure 3 and Figure 4 The figures represent the tracking response of the system's actual pitch and yaw angles to the desired trajectory, respectively. It can be seen that regardless of the initial values ​​of 0.1, 0.2, and 0.3, both the actual pitch and yaw angles can track the desired angular trajectory within a fixed time. Figure 5 and Figure 6 The tracking error graphs of the actual angle and the expected angle also show that, regardless of the initial values ​​of 0.1, 0.2 and 0.3, the error can quickly approach zero, demonstrating good tracking performance. Figure 7 The graph shows the system input voltage performance. Regardless of the initial values ​​of 0.1, 0.2, and 0.3, the system voltage eventually tends to be bounded and stable, exhibiting good performance.

[0093] In practical engineering applications, a fixed-time control method is considered, ensuring that the upper bound of the convergence time is independent of the initial conditions and depends only on the system design parameters. Rigorous verification has proven that this invention effectively eliminates the dependence of the convergence time on the initial state, resulting in faster convergence speed and higher control accuracy, significantly guaranteeing system performance and improving system robustness.

[0094] By employing the embodiments of the present invention, the following beneficial effects are achieved:

[0095] This invention presents a fixed-time adaptive neural network control method for helicopter systems. Its key feature is the use of a neural network to estimate the unknown dynamic model of the helicopter system, the design of a novel controller and adaptive law, and the proof that the system is ultimately uniformly bounded through the establishment and analysis of the Lyapunov function. This method not only provides faster convergence speed and maintains the tracking performance and closed-loop stability of the 2-DOF helicopter system within a fixed time, but also achieves system settling time independent of initial conditions, resulting in better performance.

[0096] 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. A helicopter system control method based on a fixed-time adaptive neural network, characterized in that, Includes the following steps: S1. Based on the Lagrange mechanical model, establish a dynamic model of the helicopter system in practical engineering applications; S2. Define the tracking error variable and design the auxiliary control variable; S3. Use a radial basis function neural network to estimate the uncertainties in the helicopter system; S4. Design the controller and adaptive law for the helicopter system; S5. Establish the Lyapunov function; S6. Prove the stability of the helicopter system by analyzing the Lyapunov function; S7. Perform simulations using the Matlab platform and analyze the simulation results; Step S1 specifically includes: Based on the Lagrange mechanical model, a dynamic model of the helicopter system is established for practical engineering applications. Official 1; Official 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 represents the distance from the center of mass of a 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 output vector of the helicopter system as ,in , The dynamic model of the elevator system is simplified as follows: Official 3; Official 4; Official 5; in, and It is an uncertain term in the system. It is the controller input. It is the system output. and Represented as: Official 6; Official 7; Step S2 specifically includes: Define the tracking error of the helicopter system. and : Official 8; Official 9; in It is the desired trajectory of the helicopter system's pitch and yaw angles. It is an auxiliary control variable, defined as: Official 10; in and It is a positive design parameter. It is the derivative of the expected trajectory with respect to time; Step S3 specifically includes: and This is an uncertainty term of the helicopter system. Simplify again to: Official 11; in, , A radial basis function neural network is used to estimate the uncertainties. Official 12; in, Represents the ideal weights of the 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 ,in It is the weight error of the neural network. These are the weights estimated by the neural network; The controller for designing the helicopter system in step S4 specifically includes: Design the controller for the helicopter system using Formula 13: Official 13; in and It is a positive design parameter.

2. The method according to claim 1, characterized in that, The adaptive rate involved in step S4 specifically includes: The adaptive law is designed using Equation 14 as follows: Official 14; in >0, and It is a positive constant in the design.

3. The method according to claim 1, characterized in that, Step S5 specifically includes: Lyapunov functions are established using formulas 15-17: Official 15; Official 16; Official 17.

4. The method according to claim 3, characterized in that, Step S6 specifically includes: Analyze the Lyapunov function and prove the stability of the 2-DOF helicopter system; First of all Differentiate: Official 18; get The derivative: ( ( Official 19; Will Substituting, we get: Official 20; Then to Taking the derivative, we get: Official 21; right Differentiate: Official 22; Substituting U, we get: Official 23; right Differentiate: Official 24; Consider the following inequality: Official 25; Furthermore, we can deduce that: Official 26; in Official 27; Official 28; Official 29; These are positive constants in the design, to ensure , The choice should satisfy: Official 30; This proves that all signals in the system are uniformly eventually bounded. At a fixed time Converging to a compact concentration, where Represented as: Official 31; in It is a constant. and It is a normal number.

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