Adaptive Neural Network Control Method for Helicopter System Based on Specified Performance Constraints

Abstract

The present invention relates to the technical field of helicopter system control, and to a helicopter system adaptive neural network control method based on specified performance constraints, comprising the following steps: step 1: establishing a nonlinear model of a 2-DOF helicopter system; step 2: introducing a performance function to help evaluate the specified performance of the system; step 3: designing a controller; step 4: constructing an adaptive law based on the controller; step 5: constructing a Lyapunov equation and verifying the stability of the 2-DOF helicopter system; step 6: performing simulation, and viewing and analyzing the simulation effect. The present invention can better control the helicopter system.

Description

Technical Field

[0001] The present invention relates to the technical field of helicopter system control, and in particular to an adaptive neural network control method for a helicopter system based on specified performance constraints. Background Art

[0002] In recent years, unmanned aerial vehicles have been widely used in aerial photography, agriculture, plant protection, express delivery, disaster relief, manufacturing and other fields. Unmanned helicopters have attracted the attention of many people due to their good advantages. In practical applications, the helicopter control system is a complex nonlinear system with multiple inputs and multiple outputs, which puts higher requirements on the controller design of the helicopter; at the same time, the helicopter system itself also has constraints due to mechanical design and safety limitations. If the system constraints are ignored in the control process, the system performance may be reduced, and even serious consequences may occur. In addition, with the improvement of mission accuracy, more requirements are put forward for the transient performance indicators of the helicopter. In fact, transient performance plays an important role in improving the performance of the helicopter control system. For example, a large overshoot may cause the actuator to exceed the physical limit, resulting in instability of the closed-loop system. The study of transient performance such as overshoot and convergence speed needs further consideration. Therefore, it is necessary to study the tracking control problem of the helicopter system under the conditions of meeting the specified performance constraints. Summary of the invention

[0003] The present invention provides an adaptive neural network control method for a helicopter system based on specified performance constraints, which can overcome certain or some defects of the prior art.

[0004] The helicopter system adaptive neural network control method based on specified performance constraints according to the present invention comprises the following steps:

[0005] Step 1: Establish a nonlinear model of the 2-DOF helicopter system;

[0006] Step 2: Introduce performance functions to help evaluate the specified performance of the system;

[0007] Step 3: Design the controller;

[0008] Step 4: Construct an adaptive law based on the controller;

[0009] Step 5: Construct Lyapunov equations and verify the stability of the 2-DOF helicopter system;

[0010] Step 6: Perform simulation and analyze the simulation results.

[0011] Preferably, in step 1, according to the Lagrangian mechanics model, the nonlinear dynamic equation of the system is as follows:

[0012]

[0013] Among them, J b and J d Expressed as the moment of inertia around the pitch axis and the yaw axis, V c is the voltage applied to the pitch rotor motor, V d is the voltage applied to the yaw rotor motor; M d represents the mass of the helicopter, l c represents the distance from the center of mass of the fuselage fixed frame origin, θ represents the pitch angle, φ represents the yaw angle, K cpp represents the torque thrust gain acting on the pitch axis in the pitch propeller, K cpy represents the torque thrust gain of the yaw propeller acting on the pitch axis, K cyy represents the torque thrust gain of the yaw propeller acting on the yaw axis, K cyp represents the torque thrust gain of the pitch propeller acting on the yaw axis, D a and D b represents the viscous friction coefficient, g represents the acceleration due to gravity;

[0014] By converting equation (1) and equation (2) into a simple form, we can get:

[0015]

[0016]

[0017]

[0018]

[0019] a1, a2, b1, and b2 are variables used to replace functions;

[0020] (1) Based on the nonlinear dynamic equation of the 2-DOF helicopter system, the nonlinear system is expressed as:

[0021]

[0022]

[0023]

[0024]

[0025] Where x1 = [θ, φ] T ,u=[V c ,V d ] T represents the control input, and y represents the control output;

[0026] (2) Define the error variable Z1 = x1-x 1d , Z2=x2-x 2d , combining equation (7) and equation (8), the dynamic error equation of the helicopter system is derived as follows:

[0027]

[0028]

[0029] At the same time, the radial basis function neural network is used to estimate the unknown term f(x) in the system and express it as:

[0030]

[0031] Among them, S(Ψ) represents the activation function, Ψ represents the input vector of the neural network, It is a satisfying The approximation error of the neural network is defined as W * represents the ideal weights of the neural network, are the weights estimated by the radial basis neural network.

[0032] Preferably, in step 2, in order to mathematically represent the constraint conditions, a performance function is introduced to help evaluate the specified performance of the system. The performance function is in the form of:

[0033]

[0034] where ρ i0 >ρ i∞ >0 and is a predefined parameter; where η is a constant;

[0035] The tracking error that meets the specified performance constraints is:

[0036] -η i ρ i (t) <e i (t)<ρ i (t)if e i (0)≥0

[0037] -ρ i (t) <e i (t)<η i ρ i (t)if e i (0)≤0 (15)

[0038] By choosing appropriate parameters To design performance functions;

[0039] To convert the inequality constraint (15) into an equality constraint, a transformation function is needed:

[0040] e i (t) = p i (t)T i (ψ i )

[0041] Among them, T i (ψ i ) is the transfer function, and is a smooth and strictly increasing function;

[0042] T i (ψ i ) is designed as follows:

[0043]

[0044]

[0045] Based on formula (15), the unconstrained transformation error is derived:

[0046]

[0047]

[0048] Preferably, in step 3, the controller is for the converted unconstrained error ψ i The designed derivative of the unconstrained error is:

[0049]

[0050] Among them, Θ i The expression is:

[0051]

[0052]

[0053] Define the unconstrained error vector Ξ=[ψ1,ψ2,…,ψ n ], the derivative of the error vector is:

[0054]

[0055] in,

[0056] Π=diag{Θ1,Θ2} (21)

[0057]

[0058] diag represents a diagonal matrix;

[0059] The filtering error is:

[0060]

[0061] Among them s =[ψ s1 ,ψ s2 ,…,ψ sn ] T , ζ is a positive definite diagonal constant matrix;

[0062] Ξ s The derivative of is:

[0063]

[0064] in,

[0065]

[0066] is the second-order derivative of the predetermined trajectory;

[0067] According to the above steps, the controller expression of the designed system is:

[0068]

[0069] Preferably, in step 4, the adaptive law is:

[0070]

[0071] where the diagonal matrix Λ and the constant All are greater than 0.

[0072] Preferably, in step 5, the Lyapunov equation is constructed as:

[0073]

[0074] Taking the first-order derivative of V with respect to time, we can obtain:

[0075]

[0076] According to Young's inequality, we can get:

[0077]

[0078]

[0079]

[0080]

[0081] Substituting the above inequality into the equation we get:

[0082]

[0083] in

[0084] Combining with the Lyapunov equation we get:

[0085]

[0086]

[0087]

[0088] It is thus obtained that all signals in the closed-loop system are bounded, the tracking error converges to a small neighborhood of zero, and satisfies the specified performance constraints.

[0089] Preferably, in step 6, the two-degree-of-freedom helicopter system is simulated by MATLAB simulation software, and the simulation effect is checked and analyzed.

[0090] The present invention provides an adaptive neural network control of a nonlinear two-degree-of-freedom unmanned helicopter system with specified performance, which is characterized in that a specified performance function is introduced to represent the constraints of the system, and a constrained tracking control problem is converted into an equivalent unconstrained stability problem through error transformation. The neural network controller is intended to ensure that the tracking error converges to a small zero neighborhood and satisfies the specified performance constraints. In addition, the stability and error convergence of the system are analyzed using the Lyapunov direct method, and more stable and accurate tracking and control of the two-degree-of-freedom helicopter is achieved. The present invention is applicable to the field of automatic control technology.

[0091] The present invention considers the specified performance constraints in the two-DOF helicopter system and improves the robustness based on the adaptive neural network technology developed based on system uncertainty. It can effectively improve the transient performance of the helicopter system, thereby achieving more stable and accurate tracking and control of the 2-DOF helicopter; at the same time, the system requires fewer sensors and controls, has low cost, and has broad prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 is a flow chart of an adaptive neural network control method for a helicopter system based on specified performance constraints in Example 1;

[0093] Figure 2 This is a simplified model diagram of a 2-DOF helicopter. DETAILED DESCRIPTION

[0094] 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.

[0095] Example 1

[0096] like Figure 1 As shown, this embodiment provides a helicopter system adaptive neural network control method based on specified performance constraints, which includes the following steps:

[0097] Step 1: Establish a nonlinear model of the 2-DOF helicopter system;

[0098] In step 1, according to the Lagrangian mechanics model, the nonlinear dynamic equation of the system is as follows:

[0099]

[0100] Among them, J b and J d Expressed as the moment of inertia around the pitch axis and the yaw axis, V c is the voltage applied to the pitch rotor motor, V d is the voltage applied to the yaw rotor motor; M d represents the mass of the helicopter, l c represents the distance from the center of mass of the fuselage fixed frame origin, θ represents the pitch angle, φ represents the yaw angle, K cpp represents the torque thrust gain acting on the pitch axis in the pitch propeller, K cpy represents the torque thrust gain of the yaw propeller acting on the pitch axis, K cyy represents the torque thrust gain of the yaw propeller acting on the yaw axis, K cyp represents the torque thrust gain of the pitch propeller acting on the yaw axis, D a and D b represents the viscous friction coefficient, g represents the acceleration due to gravity;

[0101] By converting equation (1) and equation (2) into a simple form, we can get:

[0102]

[0103]

[0104]

[0105]

[0106] a1, a2, b1, and b2 are variables used to replace functions;

[0107] (1) Based on the nonlinear dynamic equation of the 2-DOF helicopter system, the nonlinear system is expressed as:

[0108]

[0109]

[0110]

[0111]

[0112] Where x1 = [θ, φ] T ,u=[V c ,V d ] T represents the control input, and y represents the control output;

[0113] (2) Define the error variable Z1 = x1-x 1d , Z2=x2-x 2d , combining equation (7) and equation (8), the dynamic error equation of the helicopter system is derived as follows:

[0114]

[0115]

[0116] At the same time, the radial basis function neural network is used to estimate the unknown term f(x) in the system and express it as:

[0117]

[0118] Among them, S(Ψ) represents the activation function, Ψ represents the input vector of the neural network, It is a satisfying The approximation error of the neural network is defined as W * represents the ideal weights of the neural network, are the weights estimated by the radial basis neural network.

[0119] Step 2: Introduce performance functions to help evaluate the specified performance of the system;

[0120] In step 2, in order to mathematically represent the constraints, a performance function is introduced to help evaluate the specified performance of the system. The form of the performance function is:

[0121]

[0122] where ρ i0 >ρ i∞ >0 and are predefined parameters;

[0123] The tracking error that meets the specified performance constraints is:

[0124] -η i ρ i (t) <e i (t)<ρ i (t)if e i (0)≥0

[0125] -ρ i (t) <e i (t)<η i ρ i (t)if e i (0)≤0 (15)

[0126] By choosing appropriate parameters To design the performance function; where η is a constant;

[0127] Formula (15) is an inequality, which is not conducive to the direct design of the controller. Therefore, to convert the inequality constraint (15) into an equality constraint, a transformation function is needed:

[0128] e i (t) = p i (t)T i (ψ i )

[0129] Among them, T i (ψ i ) is the transfer function, and is a smooth and strictly increasing function;

[0130] T i (ψ i ) is designed as follows:

[0131]

[0132]

[0133] Based on formula (15), the unconstrained transformation error is derived:

[0134]

[0135]

[0136] Step 3: Design the controller;

[0137] In step 3, the controller is the unconstrained error ψ after transformation i The designed derivative of the unconstrained error is:

[0138]

[0139] Among them, Θ i The expression is:

[0140]

[0141]

[0142] Define the unconstrained error vector Ξ=[ψ1,ψ2,…,ψ n ], the derivative of the error vector is:

[0143]

[0144] in,

[0145] Π=diag{Θ1,Θ2} (21)

[0146]

[0147] diag represents a diagonal matrix;

[0148] The filtering error is:

[0149]

[0150] Among them s =[ψ s1 ,ψ s2 ,…,ψ sn ] T , ζ is a positive definite diagonal constant matrix;

[0151] Ξ s The derivative of is:

[0152]

[0153] in,

[0154]

[0155] is the second-order derivative of the predetermined trajectory;

[0156] According to the above steps, the controller expression of the designed system is:

[0157]

[0158] Step 4: Construct an adaptive law based on the controller;

[0159] The adaptive law is:

[0160]

[0161] where the diagonal matrix Λ and the constant All are greater than 0.

[0162] Step 5: Construct Lyapunov equations and verify the stability of the 2-DOF helicopter system;

[0163] In step 5, the Lyapunov equation is constructed as:

[0164]

[0165] Taking the first-order derivative of V with respect to time, we can obtain:

[0166]

[0167] According to Young's inequality, we can get:

[0168]

[0169]

[0170]

[0171]

[0172] Substituting the above inequality into the equation we get:

[0173]

[0174] in

[0175] Combining with the Lyapunov equation we get:

[0176]

[0177]

[0178]

[0179] It is thus obtained that all signals in the closed-loop system are bounded, the tracking error converges to a small neighborhood of zero, and satisfies the specified performance constraints.

[0180] Step 6: Perform simulation and analyze the simulation results.

[0181] In step 6, the two-degree-of-freedom helicopter system is simulated by MATLAB simulation software, and the simulation effect is checked and analyzed.

[0182] Figure 2This is a simplified model diagram 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.

[0183] 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. An adaptive neural network control method for a helicopter system based on specified performance constraints, characterized in that: The following steps are involved: Step 1: Establish a nonlinear model of the 2-DOF helicopter system; According to the Lagrangian mechanics model, the nonlinear dynamic equation of the system is as follows: Among them, J b and J d Expressed as the moment of inertia around the pitch axis and the yaw axis, V c is the voltage applied to the pitch rotor motor, V d is the voltage applied to the yaw rotor motor; M d represents the mass of the helicopter, l c represents the distance from the center of mass of the fuselage fixed frame origin, θ represents the pitch angle, φ represents the yaw angle, K cpp represents the torque thrust gain acting on the pitch axis in the pitch propeller, K cpy represents the torque thrust gain of the yaw propeller acting on the pitch axis, K cyy represents the torque thrust gain of the yaw propeller acting on the yaw axis, K cyp represents the torque thrust gain of the pitch propeller acting on the yaw axis, D a and D b represents the viscous friction coefficient, G represents the acceleration due to gravity; By converting equation (1) and equation (2) into a simple form, we can get: a1, a2, b1, and b2 are variables used to replace functions; (1) Based on the nonlinear dynamic equation of the 2-DOF helicopter system, the nonlinear dynamic equation is expressed as: Where x1 = [θ, φ] T ,u=[V c ,V d ] T represents control input; (2) Define the error variable Z1 = x1-x 1d , Z2=x2-x 2d , combining equation (7) and equation (8), the dynamic error equation of the helicopter system is derived as follows: At the same time, the radial basis function neural network is used to estimate the unknown term f(x) in the system and express it as: Among them, S(Ψ) represents the activation function, Ψ represents the input vector of the neural network, It is a satisfying The approximation error of the neural network is defined as W * represents the ideal weights of the neural network, are the weights estimated by the radial basis neural network; Step 2: Introduce performance functions to help evaluate the specified performance of the system; In order to express the constraints mathematically, a performance function is introduced to help evaluate the specified performance of the system. The form of the performance function is: where ρ i0 >ρ i∞ >0 and are predefined parameters; The tracking error that meets the specified performance constraints is: -er i (t) <e i (t)<ρ i (t)if e i (0)>0 -ρ i (t) <e i (t)<ηρ i (t)if e i (0)≤0(15) by choosing appropriate parameters To design the performance function, where η is a constant; To convert the inequality constraint (15) into an equality constraint, a transformation function is needed: e i (t)=ρ i (t)T i (ψ i ) Among them, T i (ψ i ) is the transfer function, and is a smooth and strictly increasing function; T i (ψ i ) is designed as follows: Based on formula (15), the unconstrained transformation error is derived: Step 3: Design the controller; The controller is the unconstrained error ψ after transformation i The designed derivative of the unconstrained error is: Among them, Θ i The expression is: Define the unconstrained error vector Ξ=[ψ1,ψ2,…,ψ n ], the derivative of the error vector is: in, Π=diag{Θ1,Θ2}(21) diag represents a diagonal matrix; The filtering error is: Among them s =[ψ s1 ,ψ s2 ,…,ψ sn ] T , ζ is a positive definite diagonal constant matrix; Ξ s The derivative of is: in, is the second-order derivative of the predetermined trajectory; According to the above steps, the controller expression of the designed system is: Step 4: Construct an adaptive law based on the controller; The adaptive law is: where the diagonal matrix Λ and the constant All are greater than 0; Step 5: Construct the Lyapunov equation and verify the stability of the 2-DOF helicopter system; construct the Lyapunov equation as: Taking the first-order derivative of V with respect to time, we can obtain: According to Young's inequality, we can get: Substituting the above inequality into the equation, we get: in Combining with the Lyapunov equation we get: Therefore, we can conclude that: all signals in the closed-loop system are bounded, the tracking error converges to a small zero neighborhood, and satisfies the specified performance constraints; Step 6: Perform simulation and analyze the simulation results.

2. The helicopter system adaptive neural network control method based on specified performance constraints according to claim 1, characterized in that: In step 6, the two-degree-of-freedom helicopter system is simulated by MATLAB simulation software, and the simulation effect is checked and analyzed.

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