Helicopter system adaptive neural network control method with globally specified performance

Abstract

The application provides a helicopter system adaptive neural network control method with globally specified performance, comprising: establishing a nonlinear dynamics equation of a 2-DOF helicopter system according to a Lagrange mechanics model and simplifying, adopting a radial basis function neural network to approximate uncertain terms of the nonlinear dynamics equation; obtaining a tracking error of the 2-DOF helicopter system, and introducing a key function; obtaining a coordinate transformation, and introducing a dynamic surface control technology; designing a controller and an adaptive law of the 2-DOF helicopter system; establishing a Lyapunov function and analyzing to ensure the stability of the 2-DOF helicopter system; the application proposes a specified function independent of an initial value of a reference signal by adopting a time-varying scale function; and through normalization function transformation and barrier function transformation, the performance constraint is visualized as a tracking error constraint, and the original constraint error is converted into an equivalent unconstrained error, so that more accurate tracking and more stable control of the 2-DOF helicopter system are realized.

Description

TECHNICAL FIELD

[0001] The present document relates to the technical field of helicopter control, and particularly relates to a helicopter system adaptive neural network control method with global specified performance. BACKGROUND

[0002] With the rapid development of communication technology, unmanned aerial vehicles have recently made unprecedented progress. As a typical unmanned aerial vehicle, helicopters not only have low cost, strong adaptability and convenient use, but also have the functions of vertical take-off and landing, hovering and low-altitude flight in a small area. They have wide applications in both military reconnaissance fields and civilian transportation, surveying and disaster relief fields. In order to design an effective helicopter controller, people have adopted various control methods to achieve stable control of the helicopter system, including LQR control, Q-learning control and sliding mode control. However, the helicopter system is a complex multiple-input multiple-output system with uncertainty and significant inter-axis coupling. The above methods do not consider the nonlinearity and uncertainty of the system, which may cause unstable results in actual application. At the same time, in actual engineering application, considering global specified performance can eliminate the dependence of the specified function on the initial value, further reduce the complexity of controller design, reduce tracking error and improve the transient performance of the system, and ultimately achieve a global tracking control effect. Therefore, it is necessary to study an adaptive neural network control method with global specified performance to solve the nonlinearity and uncertainty of the system, achieve global error tracking and ensure the robustness of the helicopter system. SUMMARY

[0003] One or more embodiments of the present specification provide a helicopter system adaptive neural network control method with global specified performance, aiming to solve the above problems.

[0004] The helicopter system adaptive neural network control method with global specified performance provided by the embodiment of the present application comprises:

[0005] S1. According to the Lagrange mechanics model, the nonlinear dynamics equation of the 2-DOF helicopter system is established and simplified, and the uncertainty term of the nonlinear dynamics equation is determined;

[0006] S2. The uncertainty term of the nonlinear dynamics equation is approximated by a radial basis function neural network;

[0007] S3. The tracking error of the 2-DOF helicopter system is obtained and a key function is introduced;

[0008] S4. The coordinate transformation of the 2-DOF helicopter system is obtained and a dynamic surface control technology is introduced;

[0009] S5, design a controller and adaptive law for the 2-DOF helicopter system;

[0010] S6, establish a Lyapunov function;

[0011] S7, ensure the stability of the 2-DOF helicopter system by analyzing the Lyapunov function;

[0012] S8, simulate the settings of steps S1-S7 on a Matlab platform and analyze the simulation results.

[0013] By using the embodiment of the application, a specified function independent of the initial value of the reference signal is proposed by using a time-varying scale function. Then, by using a normalization function transformation and an obstacle function transformation, the performance constraint is visualized as a tracking error constraint, and the original constraint error is converted into an equivalent unconstrained error. Finally, by establishing and analyzing a Lyapunov function, it is proved that the system is globally uniformly bounded, and more accurate tracking and more stable control of the 2-DOF helicopter system are achieved. BRIEF DESCRIPTION OF DRAWINGS

[0014] In order to more clearly illustrate the technical solutions in the one or more embodiments of the present specification or the prior art, the drawings needed to be used in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments described in the present specification, and other drawings can also be obtained by those skilled in the art without creative labor.

[0015] Figure 1 A model principle diagram of the 2-DOF helicopter system considered in the embodiment of the present application;

[0016] Figure 2 A flowchart of the helicopter system adaptive neural network control method with global specified performance in the embodiment of the present application;

[0017] Figure 3 A tracking response effect diagram of the actual and expected pitch angles of the 2-DOF helicopter in the embodiment of the present application;

[0018] Figure 4 A tracking response effect diagram of the actual and expected yaw angles of the 2-DOF helicopter in the embodiment of the present application;

[0019] Figure 5 A tracking error diagram of the actual and expected angles of the 2-DOF helicopter in the embodiment of the present application;

[0020] Figure 6 A system input voltage performance diagram of the 2-DOF helicopter in the embodiment of the present application. DETAILED DESCRIPTION

[0021] In order for those skilled in the art to better understand the technical solutions in the one or more embodiments of the present specification, the technical solutions in the one or more embodiments of the present specification will be clearly and completely described in the following with reference to the drawings in the one or more embodiments of the present specification. Obviously, the described embodiments are only part of the embodiments of the present specification, rather than all the embodiments. Based on the one or more embodiments of the present specification, all other embodiments obtained by those skilled in the art without creative labor should belong to the protection scope of the present document.

[0022] Method embodiments

[0023] The embodiment of the present application provides a helicopter system adaptive neural network control method with global specified performance, Figure 2 For the flowchart of the helicopter system adaptive neural network control method with global specified performance of the embodiment of the present application, according to Figure 2 The helicopter system adaptive neural network control method with global specified performance of the embodiment of the present application includes:

[0024] S1, according to the Lagrange mechanics model, the nonlinear dynamics equation of the 2-DOF helicopter system is established and simplified, and the uncertain term of the nonlinear dynamics equation is determined; step S1 specifically includes:

[0025] According to the Lagrange mechanics model, the nonlinear dynamics equation of the 2-DOF helicopter system is as follows:

[0026]

[0027]

[0028] Wherein, J pp and J yy are the moments of inertia of the pitch motion and the yaw motion, D pp and D yy are the viscous friction coefficients, K pp is the torque thrust gain in the pitch propeller acting on the pitch axis, K py is the torque thrust gain in 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 in the yaw propeller acting on the yaw axis, θ represents the pitch angle, φ represents the yaw angle, L cm indicates the distance between the mass center and the fixed frame of the fuselage, M indicates the mass of the helicopter, g indicates the gravitational acceleration, V pp and V yyVp and Vy represent motor voltage inputs to control pitch and yaw motions, respectively.

[0029] The output vector of the system is defined as q = [q 1,2 ] T where q1 = [θ, φ] T , To simplify the design of the controller, the nonlinear dynamics of the 2-DOF helicopter system is simplified as:

[0030]

[0031]

[0032] y = q1 (5)

[0033] where ΔQ(q 1,2 ) and ΔP(q 1,2 ) are the uncertainties of the system, u = [V pp,yy ] T is the input of the controller, y is the output of the system, Q(q 1,2 ) and P(q 1,2 ) are expressed as:

[0034]

[0035]

[0036] S2, the uncertainties of the nonlinear dynamics are approximated by using a radial basis function neural network; step S2 specifically comprises:

[0037] Considering that ΔQ(q 1, q2) and ΔP(q 1, q2) are the uncertainties of the system, can be simplified again as:

[0038]

[0039] where G(q, u) = ΔQ(q1, q2) + ΔP(q1, q2)u, in practical applications, it is difficult to determine the G function, so a radial basis function neural network is used to estimate the uncertainties therein.

[0040] G(q, u) = Θ *T Ψ(X) + ε(X) (9)

[0041] where Θ * represents the ideal weight of the neural network, Ψ(X) represents the Gaussian function of the radial basis vector, X represents the input vector of the neural network, ε(X) is the approximation error of the neural network, and satisfies where is an unknown constant; define where is the weight error of neural network, is the estimated weight of neural network.

[0042] S3, obtain the tracking error of the 2-DOF helicopter system and introduce a key function; step S3 specifically includes:

[0043] Define the tracking error as e = 1 - q d , where q d = [θ d, φ d ] is the expected trajectory of the pitch angle and the yaw angle of the helicopter system. Thus

[0044] Define a time-varying scale function with the following properties:

[0045] 1) is a complex vector space;

[0046] 2) is a piecewise smooth derivable bounded function, where r = 0, 1,..., ;

[0047] When t ≥ 0, is monotonically increasing, and When t → ∞, where g c is a constant, satisfying 0 < g c < 1.

[0048] The method based on the specified performance control depends on the initial condition, which is a semi-leaf result. When the system is re-run or the reference signal changes, the specified range needs to be re-selected, making the derivation and implementation of the controller complex. In order to break the dependence of the specified function on the initial value and achieve a global result, a new specified function related to is designed here:

[0049]

[0050] where, is a function that changes over time, and θ is a normal number. According to the properties of above, it can be known that ω(t) is strictly monotonically decreasing. In addition, we also know that ω(t) = 1 and lim t→∞ ω(t) = g cThus, the initial value I(ω(0)) = ∞ can be obtained. The most remarkable feature of the proposed function I(ω) compared with other prescribed functions is that it breaks the dependence of the prescribed function on the initial value, which can be infinite, and this also promotes the development of a global result.

[0051] The derivative of I(ω) can be written as follows

[0052]

[0053] It can be seen that for any normal number When ω ∈ (-1, 1), I(ω) is strictly monotonically increasing.

[0054] In order to break the limitation of the initial value and guarantee the global transient prescribed performance of the system, the tracking error e is transformed, and the following normalized function is proposed:

[0055]

[0056] Wherein is a constant and It has the following properties:

[0057] 1) For any e, ξ(e) ∈ (-1, 1) is strictly monotonic;

[0058] 2) When e→∞, ξ(e)→1;

[0059] 3) When e→-∞, ξ(e)→-1;

[0060] 4)

[0061] According to the properties of ξ(e), if there is a constant Satisfying It is not difficult to obtain Is bounded.

[0062] In order to visualize the performance characteristics as tracking error constraints and realize the evolution of tracking error within the specified boundary, the following transformation is adopted:

[0063]

[0064] According to And the properties of ξ(e(t)), when t = 0, the following can be obtained:

[0065]

[0066] For any initial condition, including any initial trajectory error e(0), |Ψ(0)|<1.

[0067] Consider the following barrier function:

[0068]

[0069] where η→∞ if and only if Ψ(t)→-1 or Ψ(t)→1.

[0070] Based on the above analysis, the following assumptions are made:

[0071] If η is guaranteed to be bounded for t≥0, then |Ψ(t)|<1 and |Ψ(0)|<1 can be further guaranteed. At the same time, there exists a μ>0 that satisfies the following inequality:

[0072]

[0073] Combining and we can get:

[0074]

[0075] According to the properties of I(ω), we can deduce:

[0076] I(-ω)<I(ξ)<I(ω) (18)

[0077] Further, we get:

[0078]

[0079] Therefore, from the above derivation of the conjecture, it can be concluded that proving the evolution of the tracking error within the specified boundary translates to proving that η(t) is bounded for t≥0.

[0080] S4, obtain the coordinate transformation of the 2-DOF helicopter system and introduce dynamic surface control technology; step S4 specifically includes:

[0081] Taking the derivative of η(t) gives:

[0082]

[0083] Taking the derivative of Ψ gives:

[0084]

[0085] where the derivative of ξ is:

[0086]

[0087] Thus can be re-expressed as:

[0088]

[0089] where Define the following coordinate transformation:

[0090] z1= η (24)

[0091] z2= q2- a (25)

[0092] where a is an auxiliary control variable defined as

[0093]

[0094] where k1 is a positive design parameter, is the derivative of the desired trajectory with respect to time.

[0095] It can be shown that a is a function of x1, q d , In the following steps, it is very complicated to repeatedly differentiate a. Therefore, we use a dynamic surface control technique to overcome this difficulty. Introduce the following first-order filter τ, and let a pass through it:

[0096]

[0097] where β is the time constant of the filter.

[0098] Define γ = τ - a, then we have

[0099]

[0100] where M is a continuous function vector with respect to Considering the continuity property, the set Ω(·) is compact for given initial conditions. On the set Ω(·), there exists a maximum value satisfying

[0101] Therefore, we have

[0102]

[0103] S5, design the controller and adaptive law of the 2-DOF helicopter system; step S5 specifically includes:

[0104] Design the controller of the system:

[0105]

[0106] where k2 is a positive design parameter.

[0107] Design the adaptive law as:

[0108]

[0109] where Λ Θ >0, σ Θ is a design constant.

[0110] S6, establishing a Lyapunov function; step S6 specifically includes:

[0111]

[0112]

[0113]

[0114] S7, ensuring stability of the 2-DOF helicopter system by analyzing the Lyapunov function; step S7 specifically includes:

[0115] First, derive z1:

[0116]

[0117] Get the derivative of V1:

[0118]

[0119] Substitute α to get:

[0120]

[0121] Then, derive z2 to get:

[0122]

[0123] Derive V2:

[0124]

[0125] Substitute u to get:

[0126] Derive V3:

[0127] Use the following Young's inequality:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] Further deduced:

[0134]

[0135] Wherein,

[0136]

[0137]

[0138] In order to ensure The selection of k1, k2 should satisfy:

[0139]

[0140] Therefore, it can be proved that all signals in the system are uniformly ultimately bounded, and the system is asymptotically stable.

[0141] S8, the settings of steps S1-S7 are simulated through the Matlab platform, and the simulation results are analyzed.

[0142] Figure 3 And Figure 4 Respectively represent the tracking response of the actual pitch angle and the yaw angle of the system to the expected trajectory, it can be seen that the expected trajectory is realized in a short time, and good tracking performance is presented; from Figure 5 The tracking error diagram of the actual angle and the expected angle can be seen, the error quickly converges to an arbitrarily small residual set, and always remains within the preset performance range, and good tracking performance is presented. Figure 6 The input voltage performance diagram of the system is represented, it can be seen that the motor input voltage quickly tends to be stable, and good input voltage performance is presented.

[0143] In actual engineering application, the global specified performance constraint of the system cannot be ignored, through the global specified performance, the dependence on the initial condition in the design process is eliminated, the tracking error converges to an arbitrarily small residual set, the convergence speed is guaranteed to be not less than a pre-specified value, and a maximum overshoot is less than a pre-specified constant. At the same time, the specified performance characteristics are visualized as tracking error constraints, through error conversion, the “constrained” system is converted into an equivalent “unconstrained” system. Through strict verification, it is proved that the application can effectively reduce the tracking error and improve the transient performance of the system, and the robustness of the system is improved.

[0144] By adopting the embodiment of the application, the following beneficial effects are achieved:

[0145] The embodiment of the application designs a helicopter system adaptive neural network control method with globally specified performance, which is characterized by using a neural network to estimate the unknown dynamic model of a helicopter. A time-varying scaling function is used to propose a specified function independent of the initial value of the reference signal. Then, through normalization function transformation and barrier function transformation, the performance constraint is visualized as a tracking error constraint, and the original constraint error is converted into an equivalent unconstrained error. Finally, through the establishment and analysis of the Lyapunov function, it is proved that the system is globally uniformly bounded, and more accurate tracking and more stable control of the 2-DOF helicopter system are achieved.

[0146] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application, and not to limit them; although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the application.

Claims

1. An adaptive neural network control method for a helicopter system with globally specified performance, characterized in that, include: S1. Based on the Lagrange mechanical model, establish and simplify the nonlinear dynamic equations of the 2-DOF helicopter system, and determine the uncertain terms of the nonlinear dynamic equations; S2. The uncertainty term of the nonlinear dynamic equation is approximated by a radial basis function neural network; S3. Obtain the tracking error of the 2-DOF helicopter system and introduce a key function; S4. Obtain the coordinate transformation of the 2-DOF helicopter system and introduce dynamic surface control technology; S5. Design the controller and adaptive law for the 2-DOF helicopter system; S6. Establish the Lyapunov function; S7. By analyzing the Lyapunov function, ensure the stability of the 2-DOF helicopter system; S8. Simulate the settings in steps S1-S7 using the Matlab platform and analyze the simulation results; The specific steps in step S3 of obtaining the tracking error of the 2-DOF helicopter system include: The tracking error is defined as ,in It is the desired trajectory of the helicopter system's pitch and yaw angles; The key function introduced in step S3 specifically includes: The introduction of time-varying scaling functions, specified performance functions, error transformation functions, and barrier functions specifically includes: Define the time-varying scaling function as The time-varying scaling function satisfy: It is a complex vector space; It is a piecewise smooth, differentiable, and bounded function, where ;when When ≥0, It is monotonically increasing, and when hour, ,in It is a constant that satisfies ; The specified performance function is defined by formula 10. : (Official 10); in, It is a function that changes over time. It is a positive constant. Strictly monotonically decreasing, , The initial value is ; Obtained through formula 11 The derivative: (Official 11); For any positive constant ,when When ∈ (-1,1), Strictly monotonically increasing; The error transformation function is obtained through formula 12. : (Official 12); in, It is a constant and , Satisfy: For any , ∈ (-1, 1) is strictly monotonic; when hour, ;when hour, ; ; Obtain the obstacle function using formula 13. : (Official 13); in, .

2. The method according to claim 1, characterized in that, The step S1, which involves establishing and simplifying the nonlinear dynamic equations of the 2-DOF helicopter system, specifically includes: The nonlinear dynamic equations of the 2-DOF helicopter system are established using Equations 1 and 2: (Official 1); (Official 2); Define the output vector of the 2-DOF helicopter system as: ,in, , The nonlinear dynamic equations of the 2-DOF helicopter system are simplified using Equations 3-5: (Official 3); (Official 4); (Formula 5); 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 motions, respectively. It is the controller input. It is the system output.

3. The method according to claim 2, characterized in that, The determination of the uncertainty term in the nonlinear dynamic equation in step S1 specifically includes: The uncertainty terms of the nonlinear dynamic equations are determined using Equations 6 and 7. and : (Official 6); (Official 7).

4. The method according to claim 3, characterized in that, Step S2 specifically includes: Using Formula 8 Simplify again: (Official 8) Share in, The uncertainties are estimated using a radial basis function neural network according to Equation 9. (Official 9) 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.

5. The method according to claim 4, characterized in that, Step S4 specifically includes: The barrier function is described by formula 14. Differentiate: (Official 14); Through formula 15 Differentiate: (Official 15); Obtained through formula 16 The derivative: (Official 16); Reexpressed using Formula 17 : (Official 17); in, , ; Coordinate transformations are defined using formulas 18 and 19: (Official 18); (Official 19); in, It is a defined auxiliary control variable; The auxiliary control variable is obtained using formula 20: (Official 20); in, It is a positive design parameter. It is the derivative of the expected trajectory with respect to time; Is with , , , , The relevant functions are implemented using dynamic surface control technology. The iterative differentiation specifically includes: (Official 21); in, It is the time constant of the filter. It is a first-order filter; definition Then we can get: (Official 22); in, It is about A continuous function vector, considering the continuity property, set For a given initial condition, it is compact in the set. There exists a maximum value above. satisfy ; Therefore, we get: (Official 23).

6. The method according to claim 5, characterized in that, Step S5 specifically includes: The controller for the 2-DOF helicopter system is designed using Formula 24: (Official 24); in, It is a positive design parameter; The adaptive law for the 2-DOF helicopter system is designed using Equation 25: (Official 25); in, >0, It is a positive constant in the design.

7. The method according to claim 6, characterized in that, Step S6 specifically includes: The Lyapunov function is established using formulas 26-28: (Official 26); (Official 27); (Official 28).

8. The method according to claim 7, characterized in that, Step S7 specifically includes: Through formula 29 Differentiate: (Official 29); Through formula 30 pairs Differentiate: ( (Official 30); Will Substituting, we get: (Official 31); Then to Taking the derivative, we get: (Official 32); right Differentiate: (Official 33); Will Substituting, we get: (Official 34); right Differentiate: (Official 35); The following Young's inequalities are adopted: (Official 36); (Official 37); (Official 38); (Official 39); (Official 40); Furthermore, we can deduce that: (Official 41); in, (Official 42); (Official 43); To ensure , , The choice satisfies: (Official 44).

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