Adaptive Width Learning Unknown Direction Control Method for 2-DOF Helicopters
By combining the adaptive width learning method and the Nussbaum function with a width learning neural network, the problem of unknown direction control for helicopters was solved, improving control accuracy and stability, and achieving bounded convergence of system state variables.
Patent Information
- Application Number
- CN202210233810.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-09
- Publication Date
- 2025-01-14
- Estimated Expiration
- 2042-03-09
AI Technical Summary
The dynamic model of a helicopter contains too many uncertain parameters and coupling effects, which increases the difficulty of controller design and makes it difficult for existing technologies to effectively solve the control problem in unknown directions.
An adaptive width learning method is adopted, which combines a width learning neural network and a Nussbaum function to design a controller to fit the system uncertainty. The system stability is then proved by using a Lyapunov function, thus achieving unknown direction control of the helicopter.
It improves helicopter control performance, enables tracking error to gradually decrease over time, ensures consistent and bounded convergence of system state variables, and enhances control accuracy and stability.
Smart Images
Figure CN114675536B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of helicopter control, and in particular to an adaptive width learning unknown direction control method for a 2-DOF helicopter. Background Art
[0002] Unmanned aerial vehicles (UAVs) have attracted widespread attention in recent years and have been rapidly developed and applied. The most common type of UAV is the helicopter, which is widely used in various fields such as material transportation, rescue operations, and detection missions. However, there are too many uncertain parameters in the dynamic model of the helicopter, and the coupling effect is strong, which makes it particularly difficult to obtain an accurate physical model of the helicopter. The inaccurate model increases the difficulty of controller design. Adaptive neural network is a recent technology that effectively approximates the uncertainty of the system. It effectively uses the powerful generalization ability of neural networks to approximate the uncertainty in the system. Among them, the most widely used is the radial basis neural network, but the selection of the number of central nodes and hidden layer nodes of the network is still a problem to be solved. Summary of the invention
[0003] The present invention provides an adaptive width learning unknown direction control method for a 2-DOF helicopter, which can overcome certain defects of the prior art.
[0004] The adaptive width learning unknown direction control method of a 2-DOF helicopter according to the present invention comprises the following steps:
[0005] (1) Establish an ideal dynamic model of the system to design the controller;
[0006] (2) combining step (1) to establish a dynamic model of the system under unknown directions in actual engineering;
[0007] (3) Design a width learning neural network to fit the uncertainty in the system;
[0008] (4) Select Nussbaum function to solve the unknown direction control problem;
[0009] (5) Define tracking error;
[0010] (6) Design the control law of the controller based on the tracking error;
[0011] (7) Design adaptability rate;
[0012] (8) Construct Lyapunov function and prove the stability of the system;
[0013] (9) Finally, numerical simulation is carried out on the Matlab platform.
[0014] Preferably, in step (1), according to the Lagrangian mechanics model, the nonlinear dynamic equation of the system is expressed as follows:
[0015]
[0016]
[0017] After simplifying the model, we get:
[0018]
[0019]
[0020] where x1 = [θ, ψ] T ,
[0021]
[0022]
[0023]
[0024]
[0025]
[0026] Among them, m represents mass, x1 is state quantity 1, x2 is state quantity 2, u is control input, θ represents pitch angle, ψ represents yaw angle, J p is the moment of inertia of pitch motion, J y is the moment of inertia of yaw motion, D p is the friction coefficient of pitching motion, D y is the friction coefficient for yaw motion, K pp is the torque thrust gain acting on the pitch axis in the pitch propeller, K py is the torque thrust gain of the yaw propeller acting on the pitch axis, K yp is the torque thrust gain in the pitch propeller acting on the yaw axis, K yy is the torque thrust gain of the yaw propeller acting on the yaw axis, l cm is the distance from the center of mass to the origin of the fixed coordinate system; g is the acceleration due to gravity, V p is the motor voltage input to control the pitch motion, V y is the motor voltage input for controlling the yaw motion, and δ1, δ2, κ1, and κ2 are the variables used to replace the function.
[0027] Preferably, in step (2), the dynamic model of the actual engineering of the system is:
[0028]
[0029]
[0030] Here, λ is an unknown positive number.
[0031] Preferably, in step (3), the width learning neural network is:
[0032] The width learning neural network is composed of incremental nodes and enhanced nodes;
[0033] Incremental node c new It is expressed as:
[0034] c new =c avg +γ(Z)-c avg ) (11)
[0035]
[0036] Among them, γ is an adjustable parameter, Z is the current input vector, and c avg are the n nodes with the smallest two-norm distance to the current input vector μ={μ1,μ2,…,μ n}average;
[0037] The enhanced node E(t) is expressed as:
[0038] E(t)=[E1,…,E i ],i=1,…,j (13)
[0039] E i =[cos(s i (Z)),sin(s i (Z))] (14)
[0040] Among them, j refers to the current number of strengthening nodes, s i (Z) is the Gaussian function, S(Z) is the Gaussian function s i (Z) a collection;
[0041]
[0042] Among them, Y(Φ) is the output of the width learning neural network, H is the hidden layer node of the width learning neural network, is the weight of the width learning neural network, and T represents the transposed matrix.
[0043] Preferably, in step (4), the Nussbaum function is:
[0044] The Nussbaum function satisfies the following conditions:
[0045]
[0046]
[0047] The Nussbaum function selected is: N(k)=k 2 cosk, N(k) is the Nussbaum function, and k is the independent variable of the function.
[0048] Preferably, in step (5), the tracking error is:
[0049] e1=x1-x d (18)
[0050] e2=x2-α (19)
[0051]
[0052] Among them, x1 is the pitch angle and yaw angle position state quantity of the helicopter system, x2 is the pitch angle and yaw angle angular velocity state quantity of the helicopter system; x d are the pitch and yaw angles of the helicopter system and the desired tracking trajectory, is its derivative with respect to time; α is a defined auxiliary variable; e1 and e2 are the errors of x1 and x2 with respect to the expected value respectively; c1 is an adjustable positive number.
[0053] Preferably, in step (6), the control law is:
[0054]
[0055] in, c2 is an adjustable positive number, is the time derivative of the auxiliary variable α, is the neural network weight error.
[0056] Preferably, in step (7), the adaptive rate is:
[0057]
[0058] Among them, Γ>0 is the weight update gain coefficient, and σ is a very small positive number.
[0059] Preferably, in step (8), the Lyapunov function is:
[0060]
[0061] Taking its derivative we get:
[0062]
[0063] in, is the neural network weight error, λ is a constant, is the optimal weight of the neural network, are the neural network approximation weights, and
[0064] Further we can get:
[0065]
[0066] Therefore, according to the lemma, all state quantities in the system converge uniformly and boundedly.
[0067] The present invention introduces the Nussbaum function to solve the unknown control direction problem of the 2-DOF helicopter. The present invention introduces width learning to improve the radial basis network to improve the control performance of the 2-DOF helicopter, and realizes that the tracking error is gradually reduced over time. BRIEF DESCRIPTION OF THE DRAWINGS
[0068] Figure 1 A flowchart of an adaptive width learning unknown direction control method for a 2-DOF helicopter in Example 1;
[0069] Figure 2 This is a simplified structural diagram of the 2-DOF helicopter in Example 1. DETAILED DESCRIPTION
[0070] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.
[0071] Example 1
[0072] like Figure 1 As shown, this embodiment provides an adaptive width learning unknown direction control method for a 2-DOF helicopter, which includes the following steps:
[0073] (1) Establish an ideal dynamic model of the system to design the controller;
[0074] According to the Lagrangian mechanics model, the nonlinear dynamic equation of the system is expressed as follows:
[0075]
[0076]
[0077] After simplifying the model, we get:
[0078]
[0079]
[0080] where x1 = [θ, ψ] T ,
[0081]
[0082]
[0083]
[0084]
[0085]
[0086] Among them, m represents mass, x1 is state quantity 1, x2 is state quantity 2, u is control input, θ represents pitch angle, ψ represents yaw angle, J p is the moment of inertia of pitch motion, J y is the moment of inertia of yaw motion, D p is the friction coefficient of pitching motion, D y is the friction coefficient for yaw motion, K pp is the torque thrust gain acting on the pitch axis in the pitch propeller, K py is the torque thrust gain of the yaw propeller acting on the pitch axis, K yp is the torque thrust gain in the pitch propeller acting on the yaw axis, K yy is the torque thrust gain of the yaw propeller acting on the yaw axis, l cm is the distance from the center of mass to the origin of the fixed coordinate system; g is the acceleration due to gravity, V p is the motor voltage input to control the pitch motion, V y is the motor voltage input for controlling the yaw motion, and δ1, δ2, κ1, and κ2 are the variables used to replace the function.
[0087] (2) combining step (1) to establish a dynamic model of the system under unknown directions in actual engineering;
[0088] Dynamic model in practical engineering of the system:
[0089]
[0090]
[0091] Here, λ is an unknown positive number.
[0092] (3) Design a width learning neural network to fit the uncertainty in the system;
[0093] The width learning neural network is:
[0094] The width learning neural network is composed of incremental nodes and enhanced nodes;
[0095] Incremental node c new It is expressed as:
[0096] c new =c avg +γ(Zc avg ) (11)
[0097]
[0098] Among them, γ is an adjustable parameter, Z is the current input vector, and c avg are the n nodes with the smallest two-norm distance to the current input vector μ={μ1,μ2,…,μ n}average;
[0099] The enhanced node E(t) is expressed as:
[0100] E(t)=[E1,…,E i ],i=1,…,j (13)
[0101] E i =[cos(s i (Z)),sin(s i (Z))] (14)
[0102] Among them, j refers to the current number of strengthening nodes, s i (Z) is the Gaussian function, S(Z) is the Gaussian function s i (Z) a collection;
[0103]
[0104] Among them, Y(Φ) is the output of the width learning neural network, H is the hidden layer node of the width learning neural network, is the weight of the width learning neural network, and T represents the transposed matrix.
[0105] (4) Select Nussbaum function to solve the unknown direction control problem;
[0106] The Nussbaum function is:
[0107] The Nussbaum function satisfies the following conditions:
[0108]
[0109]
[0110] The Nussbaum function selected is: N(k)=k 2 cos k, N(k) is the Nussbaum function, and k is the independent variable of the function.
[0111] (5) Define tracking error;
[0112] The tracking error is:
[0113] e1=x1-x d (18)
[0114] e2=x2-α (19)
[0115]
[0116] Among them, x1 is the pitch angle and yaw angle position state quantity of the helicopter system, x2 is the pitch angle and yaw angle angular velocity state quantity of the helicopter system; x d are the pitch and yaw angles of the helicopter system and the desired tracking trajectory, is its derivative with respect to time; α is a defined auxiliary variable; e1 and e2 are the errors of x1 and x2 with respect to the expected value respectively; c1 is an adjustable positive number.
[0117] (6) Design the control law of the controller based on the tracking error;
[0118] The control law is:
[0119]
[0120] in, c2 is an adjustable positive number, is the time derivative of the auxiliary variable α, is the neural network weight error.
[0121] (7) Design adaptability rate;
[0122] The adaptive rate is:
[0123]
[0124] Among them, Γ>0 is the weight update gain coefficient, and σ is a very small positive number.
[0125] (8) Construct Lyapunov function and prove the stability of the system;
[0126] The Lyapunov function is:
[0127]
[0128] Taking its derivative we get:
[0129]
[0130] in, is the neural network weight error, λ is a constant, is the optimal weight of the neural network, are the neural network approximation weights, and
[0131] Further we can get:
[0132]
[0133] Therefore, according to the lemma, all state quantities in the system converge uniformly and boundedly.
[0134] (9) Finally, numerical simulation is carried out on the Matlab platform.
[0135] Width learning is a strategy to improve the generalization ability of neural networks by adding nodes. Integrating width learning into neural networks can effectively improve the approximation ability of neural networks.
[0136] Figure 2 This is a simplified diagram of the structure of a 2-DOF helicopter, where Yaw is the pitch angle, Pitch is the yaw angle, X, Y, Z are the X-axis, Y-axis and Z-axis respectively, and F p is the thrust generated by the front motor, F y is the thrust generated by the rear motor. FRONT and BACK represent the front motor and rear motor respectively.
[0137] In actual engineering, helicopter systems often have control coefficients that are not 1. In order to solve the problem of parameterized strict feedback systems with unknown constant control coefficients and virtual control coefficients, it is proposed to use the Nussbaum function to solve it. After rigorous theoretical derivation, the effectiveness of this method is proved.
[0138] The present invention and its embodiments are described schematically above, and the description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it and designs a structural method and an embodiment similar to the technical solution without creativity without departing from the purpose of the invention, they shall all fall within the protection scope of the present invention.
Claims
1. Adaptive width learning unknown direction control method for 2-DOF helicopter, characterized by: The following steps are involved: (1) Establish an ideal dynamic model of the system to design the controller; (2) combining step (1) to establish a dynamic model of the system under unknown directions in actual engineering; (3) Design a width learning neural network to fit the uncertainty in the system; (4) Select Nussbaum function to solve the unknown direction control problem; (5) Define tracking error; (6) Design the control law of the controller based on the tracking error; (7) Design adaptability rate; (8) Construct Lyapunov function and prove the stability of the system; (9) Finally, numerical simulation is carried out on the Matlab platform; In step (1), according to the Lagrangian mechanics model, the nonlinear dynamic equation of the system is expressed as follows: After simplifying the model, we get: Where, x1=[θ,ψ] T , u=[V p ,V y ] T ; Among them, m represents mass, x1 is state quantity 1, x2 is state quantity 2, u is control input, θ represents pitch angle, ψ represents yaw angle, J p is the moment of inertia of pitch motion, J y is the moment of inertia of yaw motion, D p is the friction coefficient of pitching motion, D y is the friction coefficient for yaw motion, K pp is the torque thrust gain acting on the pitch axis in the pitch propeller, K py is the torque thrust gain of the yaw propeller acting on the pitch axis, K yp is the torque thrust gain in the pitch propeller acting on the yaw axis, K yy is the torque thrust gain of the yaw propeller acting on the yaw axis, l cm is the distance from the center of mass to the origin of the fixed coordinate system; g is the acceleration due to gravity, V p is the motor voltage input to control the pitch motion, V y is the motor voltage input to control the yaw motion, δ1, δ2, κ1, and κ2 are the variables used to replace the function; Among them, in step (2), the dynamic model of the system in actual engineering is: Among them, λ is an unknown positive number; Among them, in step (3), the width learning neural network is: The width learning neural network is composed of incremental nodes and enhanced nodes; Incremental node c new It is expressed as: c new =c avg +γ(Z-c avg )(11) Among them, γ is an adjustable parameter, Z is the current input vector, and c avg are the n nodes with the smallest two-norm distance to the current input vector μ={μ1,μ2,…,μ n }average; The enhanced node E(t) is expressed as: E(t)=[E1,…,E i ],i=1,…,j (13) E i =[cos(s i (Z)),sin(s i (Z))] (14) Among them, j refers to the current number of strengthening nodes, s i (Z) is the Gaussian function, S(Z) is the Gaussian function s i (Z) a collection; Among them, Y(Φ) is the output of the width learning neural network, H is the hidden layer node of the width learning neural network, is the weight of the width learning neural network; Among them, in step (4), the Nussbaum function is: The Nussbaum function satisfies the following conditions: The Nussbaum function selected is: N(k)=k 2 cost, N(k) is the Nussbaum function, k is the independent variable of the function; Among them, in step (8), the Lyapunov function is: Taking its derivative we get: in, is the neural network weight error, λ is an unknown positive number, is the optimal weight of the neural network, are the neural network approximation weights, and Further we can get: Therefore, according to the lemma, all state quantities in the system converge uniformly and boundedly.
2. The adaptive width learning unknown direction control method of a 2-DOF helicopter according to claim 1, characterized in that: In step (5), the tracking error is: e1=x1-x d (18)e2=x2-α(19) Among them, x1 is the pitch angle and yaw angle position state quantity of the helicopter system, x2 is the pitch angle and yaw angle angular velocity state quantity of the helicopter system; x d are the pitch and yaw angles of the helicopter system and the desired tracking trajectory, is its derivative with respect to time; α is a defined auxiliary variable; e1 and e2 are the errors of x1 and x2 with respect to the expected value respectively; c1 is an adjustable positive number.
3. The adaptive width learning unknown direction control method of a 2-DOF helicopter according to claim 2, characterized in that: In step (6), the control law is: in, c2 is an adjustable positive number, is the time derivative of the auxiliary variable α, is the neural network weight error.
4. The adaptive width learning unknown direction control method of a 2-DOF helicopter according to claim 3, characterized in that: In step (7), the adaptation rate is: Among them, Γ>0 is the weight update gain coefficient, and σ is a very small positive number.