A variable aircraft attitude control frequency domain analysis method based on active disturbance rejection control

Abstract

The application relates to a variable aircraft attitude control frequency domain analysis method based on active disturbance rejection control, which comprises the following steps: establishing a six-degree-of-freedom nonlinear model, an aerodynamic force model and an aerodynamic moment model of a variable aircraft; designing an ADRC-based variable aircraft attitude angle control law; converting the ADRC into LADRC; parameterizing the LADRC; performing a Laplace transform on the parameterized LADRC control law and the system, equivalently converting the closed-loop system into a unit negative feedback system, obtaining a disturbance transfer function and a system open-loop transfer function; analyzing the frequency domain characteristics of the disturbance transfer function, obtaining the anti-disturbance characteristics of the ADRC to internal and external disturbances of the system; and analyzing the frequency domain characteristics of the system open-loop transfer function, obtaining the robustness characteristics of the ADRC to model uncertainty. The application realizes the attitude control of the variable aircraft through the active disturbance rejection control method, and guarantees the attitude stability and accurate tracking of command signals of the variable aircraft before and after the variable and during the variable.

Description

Technical Field

[0001] The invention belongs to the field of aviation technology and relates to a frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control. Background Art

[0002] Morphing aircraft have unique advantages in improving the aerodynamic performance of aircraft, expanding the flight envelope, and increasing endurance. However, precisely because morphing aircraft can change the basic aircraft parameters and aerodynamic parameters over a large range during flight, such as wing area, wingspan, moment of inertia, center of gravity, aerodynamic focus, aerodynamic force and aerodynamic torque, general control methods are difficult to ensure its flight stability. A highly robust flight control system is needed to ensure its flight stability during the morphing process.

[0003] Active disturbance rejection control (ADRC) is an active disturbance rejection technology. Unlike the passive disturbance rejection mode of PID, its concept of observing and eliminating "total disturbances" has gradually become well-known and recognized in recent years. ADRC combines the system's internal disturbances (such as modeling errors and model uncertainties) and external disturbances (such as disturbances outside the system) into a "total disturbance," estimating and eliminating them through the extended state observer method, thereby achieving system disturbance rejection control. A morphing aircraft is a highly complex and uncertain nonlinear system. Variants can cause changes in the system model. ADRC does not rely on a precise system model, making it well-suited for flight control of morphing aircraft. Summary of the Invention

[0004] The technical problems to be solved by the present invention are:

[0005] In order to avoid the shortcomings of the existing technology, the present invention provides a frequency domain analysis method for variant aircraft attitude control based on active disturbance rejection control, which solves the problem of model uncertainty and external disturbance suppression ability of active disturbance rejection control when the variant aircraft is deformed through the frequency domain analysis method.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control is characterized by comprising:

[0008] S1. Establish a six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic moment model of the variant aircraft;

[0009] S2, designing an ADRC-based variant aircraft attitude angle control law for the six-degree-of-freedom nonlinear model, aerodynamic force, and aerodynamic moment model established in step S1;

[0010] S3, converting the ADRC control law designed in step S2 into LADRC suitable for frequency domain analysis through parameter selection;

[0011] S4, parameterizing the LADRC obtained in step S3;

[0012] S5. Performing Laplace transform on the LADRC control law and system parameterized in step S4, converting the closed-loop system into a unit negative feedback system, and obtaining a disturbance transfer function and a system open-loop transfer function;

[0013] S6. Analyze the frequency domain characteristics of the disturbance transfer function obtained in step S5 to obtain the anti-disturbance characteristics of ADRC to internal and external disturbances of the system;

[0014] S7. Analyze the frequency domain characteristics of the system open-loop transfer function obtained in step S5 to obtain the robustness of ADRC to model uncertainty.

[0015] A further technical solution of the present invention is: in step S1, a six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic moment model of the variant aircraft is established, specifically:

[0016] The six-degree-of-freedom nonlinear equation of the variant aircraft is expressed as:

[0017]

[0018]

[0019] Among them, V is the speed, α is the angle of attack, β is the sideslip angle, p, q, r are the angular velocities of the aircraft around the three axes of the aircraft system, φ, θ, ψ are the attitude angles of the aircraft, D, Y, L, T are the drag, side force, lift and engine thrust respectively, M A ,N A They are rolling moment, pitching moment and yaw moment, m is the mass of the aircraft, g is the acceleration of gravity; S x is the component of the aircraft static moment on the x-axis of the aircraft system, F Ix ,F Iy ,F Iz is the component of the inertial force caused by the variation process on the three axes of the airflow system, M Ix ,M Iy ,M Iz is the component of the inertia moment caused by the deformation process on the three axes of the machine system;

[0020] The aerodynamic force and aerodynamic torque are expressed as:

[0021] Lift:

[0022]

[0023] resistance:

[0024]

[0025] Side force:

[0026]

[0027] Rolling moment:

[0028]

[0029] Pitching moment:

[0030]

[0031] Yaw moment:

[0032]

[0033] Where Q = ρV 2 / 2 is the dynamic pressure, ρ is the air density, S w is the wing area; C L0 is the lift coefficient at zero angle of attack, C Lα 、 They are lift coefficient versus angle of attack α and elevator deflection angle δ respectively e The derivative of C D0 is the drag coefficient at zero angle of attack, C Dα 、 The resistance coefficient C D Angle of attack α, elevator deflection angle δ e The derivative of C Yβ 、 C Yp 、C Yr They are the lateral force coefficients C Y Side slip angle β, aileron deflection angle δ a , rudder deflection angle δ r , the derivative of the roll angular velocity p, the yaw angular velocity r; C lβ 、 C lp 、C lr They are rolling moment coefficients C l Side slip angle β, aileron deflection angle δ a , rudder deflection angle δ r , the derivative of the roll angular velocity p, the yaw angular velocity r; C m0 is the pitching moment coefficient at zero angle of attack, C mα 、 C mqThey are the pitching moment coefficients C m Angle of attack α, elevator deflection angle δ e , the derivative of the pitch angular velocity q; C nβ 、 C np 、C nr They are the yaw moment coefficients C n Side slip angle β, aileron deflection angle δ a , rudder deflection angle δ r , the derivative of the roll angular velocity p, and the yaw angular velocity r.

[0034] A further technical solution of the present invention is: in step S2, a variant aircraft attitude angle control law based on ADRC is designed for the six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic torque model established in step S1, specifically:

[0035] The nonlinear motion equation of the attitude angle loop is:

[0036]

[0037] Differentiating the above formula yields:

[0038]

[0039] Combining the angular velocity, attitude angle, and torque equations and simplifying them, we get:

[0040]

[0041] Among them, f φ Contains all aileron-independent terms in the roll angle φ loop, f θ Contains all elevator-independent terms in the pitch angle θ loop, f ψ Contains all terms in the yaw angle ψ loop that are not related to the rudder; b φ ,b θ ,b ψ are the attitude angle loop control input δ a ,δ e ,δ r The coefficient of

[0042] The specific form of the tracking differentiator TD is:

[0043]

[0044] Where i = φ, θ, ψ, v cmd,i is the input command signal, v 1,i v cmd,i The tracking signal can also be regarded as a continuous and smoothed command signal, v 2,i v1,i The differential signal of can be approximately regarded as v cmd,i The differential signal of , h is the sampling step; let v 3,i =dv 2,i / dt, that is, v 3,i v 1,i The second-order differential signal can be approximately regarded as v cmd,i The second-order differential signal of

[0045] The specific form of the third-order extended state observer ESO is:

[0046]

[0047] Among them, β 01,i ,β 02,i ,β 03,i ,δ i is a parameter that needs to be adjusted, b 0,i is parameter b i The nominal value of can be calculated from the balancing value, h is the sampling step; z 1,i is the system output state y i The estimated value of z 2,i yes The estimated value of z 3,i is the total disturbance f i estimated value of;

[0048] The control law of the i-th channel is:

[0049]

[0050] A further technical solution of the present invention is as follows: in step S3, the ADRC control law designed in step S2 is converted into LADRC suitable for frequency domain analysis by parameter selection, specifically:

[0051] For the fal(x,a,δ) function in ADRC, Taking parameter a = 1, then fal(x, a, δ) = x, and removing TD at the same time, ADRC is converted to LADRC. The complete algorithm of LADRC after conversion is expressed as follows:

[0052]

[0053] A further technical solution of the present invention is: in step S4, the LADRC obtained in step S3 is parameterized, specifically:

[0054] (1) Parameterization of LESO

[0055] Rewriting LESO into a state space expression, we have:

[0056]

[0057] Expand to

[0058]

[0059] in,

[0060] Its characteristic polynomial is:

[0061]

[0062] By using the pole placement method, all the poles of LESO are placed at -ω o ,Right now

[0063]

[0064] Comparing the parameters on both sides of the equation, we get

[0065] β1=3ω o ,

[0066] Therefore, LESO is converted into the following single-parameter LESO through parameterization:

[0067]

[0068] Where z1, z2, z3 are the states of LESO, u is the system input, y is the system output, b0 is the nominal value of the system input coefficient b, -ω o It is the extreme of LESO;

[0069] (2) Parameterize the PD controller

[0070] For the system Substituting into the PD controller of LESO, the closed-loop system expression is:

[0071]

[0072] Where r is the given instruction, y is the system output, k p ,k d are the proportional coefficient and differential coefficient respectively;

[0073] If the LESO parameters are properly selected and accurately estimated, then we can approximate:

[0074] z1=y,

[0075] The closed-loop system expression is approximately:

[0076]

[0077] Perform Laplace transform on it and get:

[0078] s 2 Y(s)=k p (R(s)-Y(s))-k d sY(s)

[0079] The closed-loop system transfer function is:

[0080]

[0081] Let k d =2ξω c , Then the closed-loop system is in the standard form of the second-order transfer function:

[0082]

[0083] If ξ=1, the system is in critical damping state, and the step response can track the instruction quickly and without overshoot. d =2ω c , The characteristic equation of the system is:

[0084]

[0085] Its closed-loop poles are all located at -ω c At this point, the parameter k of the PD controller is p ,k d Using a single parameter ω c To express.

[0086] A further technical solution of the present invention is: in step S5, Laplace transform is performed on the LADRC control law and system parameterized in step S4, and the closed-loop system is equivalently converted into a unit negative feedback system to obtain the disturbance transfer function and the system open-loop transfer function, which are specifically:

[0087] First, find the transfer function of the third-order LESO and take the Laplace transform of the third-order LESO to get:

[0088]

[0089] Simplified:

[0090]

[0091] Continue to simplify to get Z1(s):

[0092]

[0093] Substitute Z1(s) into the above equation to find Z2(s) and Z3(s):

[0094]

[0095]

[0096] Taking Laplace transform of the PD controller of LADRC, we get:

[0097]

[0098] Substituting Z1(s), Z2(s), and Z3(s) into the above formula and simplifying it to the unit negative feedback form, we get:

[0099]

[0100] So we have:

[0101]

[0102] The parameterized result β1=3ω o , k d =2ω c , Substituting into the above formula, we get

[0103]

[0104] Therefore, the open-loop transfer function of the system G lg (s) and the closed-loop transfer function G cl 9s) are:

[0105] G lg (s)=G c (s)G p (s)

[0106]

[0107] Taking the pitch angle as an example to derive the disturbance transfer function, the approximate transfer function of the pitch angle is:

[0108]

[0109] Among them, f θ Contains all elevator-independent terms in the pitch angle loop.

[0110] Let θ(s) = Y(s), b θ =b0, substitute U(s) into the above formula and simplify it to get:

[0111]

[0112] Therefore, the system's disturbance transfer function G YD (s) is:

[0113]

[0114] A further technical solution of the present invention is as follows: in step S6, the frequency domain characteristics of the disturbance transfer function obtained in step S5 are analyzed to obtain the anti-disturbance characteristics of ADRC to internal and external disturbances of the system, specifically:

[0115] The system's disturbance transfer function G YD (s) is:

[0116]

[0117] Choose different ω o and ω c , draw its Bode diagram, and analyze the ADRC's ability to suppress disturbances through the amplitude in the Bode diagram.

[0118] A further technical solution of the present invention is: in step S7, the frequency domain characteristics of the system open-loop transfer function obtained in step S5 are analyzed to obtain the robustness characteristics of ADRC to model uncertainty, specifically:

[0119] The approximate transfer function of the pitch angle after ignoring the disturbance term is:

[0120]

[0121] in,

[0122] The open-loop transfer function G of the system lg (s) is:

[0123]

[0124] Note λ θ =b θ / b0, when considering the uncertainty of the model, that is, considering the change of a, let λ p =1 fixed, change the value of a, and observe the open-loop transfer function G lg The amplitude margin and phase margin of (s) are used to analyze the robustness of ADRC to model uncertainty.

[0125] A computer system, characterized in that it includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method.

[0126] A computer-readable storage medium is characterized by storing computer-executable instructions, which are used to implement the above method when executed.

[0127] The beneficial effects of the present invention are:

[0128] The present invention provides a frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control, which realizes attitude control of the variant aircraft through the active disturbance rejection control method, ensuring the attitude stability of the variant aircraft before, during and after the transformation and the accurate tracking of the command signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0130] Figure 1 Design a framework diagram for the frequency domain analysis method of variant aircraft attitude control based on active disturbance rejection control.

[0131] Figure 2 This is a diagram of a variant aircraft object.

[0132] Figure 3 This is the overall control structure diagram for level flight deceleration maneuvers.

[0133] Figure 4 This is the block diagram of the equivalent unit negative feedback system.

[0134] Figure 5 The frequency domain characteristic curve of the disturbance transfer function (ω c change).

[0135] Figure 6 The frequency domain characteristic curve of the disturbance transfer function (ω o change).

[0136] Figure 7 G is the system open-loop transfer function lg (s) Bode plot when a=[-0.1,-1,-10,-52,-100,-200].

[0137] Figure 8 This is the pitch angle square wave response curve when a=[-0.1,-1,-10,-52,-100,-200]. DETAILED DESCRIPTION

[0138] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0139] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way are interchangeable where appropriate so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0140] Since the system response curve in the time domain cannot clearly observe the anti-interference characteristics of ADRC, some characteristics can only be intuitively obtained in the frequency domain, such as the system's cutoff frequency and stability margin. The cutoff frequency reflects the bandwidth of the system. A low cutoff frequency means good system stability, but poor transient response and slow tracking speed for input commands; a high cutoff frequency means good system transient response and fast tracking speed, but poor stability. The stability margin reflects the limit of gain variation and phase lag that the system can withstand. They are important parameter indicators that need to be considered in frequency domain analysis and design. Therefore, the present invention will study the anti-interference characteristics and anti-interference capability of variant aircraft attitude control based on ADRC from the perspective of frequency domain.

[0141] Since ADRC has a good effect in suppressing internal and external disturbances and model uncertainties in the system, an attitude angle control law based on ADRC is designed for the variant aircraft. Then, ADRC is converted into LADRC for frequency domain analysis. LADRC is parameterized to reduce the number of adjustable parameters of the control law. Then, the disturbance transfer function and open-loop transfer function of the system are calculated. The suppression characteristics of the control law parameters to disturbances and the robustness of the control law to model uncertainties are analyzed respectively. Finally, a simulation experiment of the attitude angle control law of the variant aircraft based on active disturbance rejection control is carried out by combining time domain and frequency domain.

[0142] like Figure 1 As shown, the present invention provides a frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control, comprising the following steps:

[0143] (1) Establish a six-degree-of-freedom nonlinear model, aerodynamic force, and aerodynamic moment model for the morphing aircraft, taking into account the changes in aerodynamic force and aerodynamic moment caused by the morphing;

[0144] (2) Design the attitude angle control law of the morphing aircraft based on ADRC based on the morphing aircraft's six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic moment model;

[0145] (3) Set the parameter a=1 for the fal(x,a,δ) function, remove TD from the control system, and convert ADRC into LADRC;

[0146] (4) Parameterize LADRC to further reduce adjustable parameters;

[0147] (5) Perform Laplace transform on the parameterized LADRC control law and system, convert the closed-loop system into a unit negative feedback system, and obtain the disturbance transfer function and the system open-loop transfer function;

[0148] (6) Analyze the frequency domain characteristics of the disturbance transfer function to obtain the anti-disturbance characteristics of ADRC to internal and external disturbances of the system;

[0149] (7) The frequency domain characteristics of the system open-loop transfer function are analyzed to obtain the robustness of ADRC to model uncertainties.

[0150] Example 1:

[0151] This embodiment takes a variable-sweep wing aircraft as the object, and designs a variant aircraft attitude angle control law for the attitude control of the variant aircraft through the self-disturbance rejection control. However, the designed control law cannot clearly observe its ability to suppress disturbances and its robustness to model uncertainty only in the time domain. Therefore, through the selection of parameters, the self-disturbance rejection control law is converted into a linear self-disturbance rejection control (LADRC) suitable for frequency domain analysis. As a special case of ADRC, LADRC does not change its characteristics to disturbances and model uncertainty. Subsequently, LADRC is parameterized, and the parameters that need to be adjusted in the control law are reduced to only 2. The analysis of the frequency domain is inseparable from the transfer function, so the open-loop transfer function and disturbance transfer function of the system are obtained, and their frequency domain characteristics are analyzed to obtain the final ADRC's ability to suppress disturbances and robustness to model uncertainty. The following steps are included:

[0152] (a) Nonlinear equations for the six degrees of freedom of a variant aircraft

[0153] The variant aircraft object in this embodiment is Figure 2 The variable-sweep wing aircraft shown in the figure has a sweep angle that can vary within the range of 20° to 68°, and its six-degree-of-freedom nonlinear equation can be expressed as:

[0154]

[0155] Among them, V is the speed, α is the angle of attack, β is the sideslip angle, p, q, r are the angular velocities of the aircraft around the three axes of the aircraft system, φ, θ, ψ are the attitude angles of the aircraft, D, Y, L, T are the drag, side force, lift and engine thrust respectively, M A ,N AThey are rolling moment, pitching moment and yaw moment, m is the mass of the aircraft, g is the acceleration of gravity; S x is the component of the aircraft static moment on the x-axis of the aircraft system, F Ix ,F Iy ,F Iz is the component of the inertial force caused by the variation process on the three axes of the airflow system, M Ix ,M Iy ,M Iz is the component of the inertia moment caused by the deformation process on the three axes of the machine system;

[0156] (b) Establishment of the aerodynamic force and aerodynamic moment model of the variant aircraft

[0157] The aerodynamic force and aerodynamic torque can be expressed as:

[0158] Lift:

[0159]

[0160] resistance:

[0161]

[0162] Side force:

[0163]

[0164] Rolling moment:

[0165]

[0166] Pitching moment:

[0167]

[0168] Yaw moment:

[0169]

[0170] Where Q = ρV 2 / 2 is the dynamic pressure, ρ is the air density, S w is the wing area; C L0 is the lift coefficient at zero angle of attack, C Lα 、 They are lift coefficient versus angle of attack α and elevator deflection angle δ respectively e The derivative of C D0 is the drag coefficient at zero angle of attack, C Dα 、 The resistance coefficient C D Angle of attack α, elevator deflection angle δ e The derivative of CYβ 、 C Yp 、C Yr They are the lateral force coefficients C Y Side slip angle β, aileron deflection angle δ a , rudder deflection angle δ r , the derivative of the roll angular velocity p, the yaw angular velocity r; C lβ 、 C lp 、C lr They are rolling moment coefficients C l Side slip angle β, aileron deflection angle δ a , rudder deflection angle δ r , the derivative of the roll angular velocity p, the yaw angular velocity r; C m0 is the pitching moment coefficient at zero angle of attack, C mα 、 C mq They are the pitching moment coefficients C m Angle of attack α, elevator deflection angle δ e , the derivative of the pitch angular velocity q; C nβ 、 C np 、C nr They are the yaw moment coefficients C n Side slip angle β, aileron deflection angle δ a , rudder deflection angle δ r , the derivative of the roll angular velocity p, and the yaw angular velocity r.

[0171] The variant aircraft used in the present invention is a conventional layout aircraft having three control surfaces, namely, elevator, aileron and rudder. e is the elevator deflection angle, positive deflection produces a negative pitching moment M A ; δ a is the aileron deflection angle, the left and right ailerons are differentially deflected, and positive deflection produces a negative rolling moment δ r is the rudder deflection angle, positive deflection produces a negative yaw moment N A .

[0172] (c) Design of attitude angle control law for variant aircraft based on ADRC

[0173] The control structure of the attitude angle loop is as follows: Figure 3 In order to realize the decoupling control of attitude angle, the present invention adopts a disturbance decoupling control method, assuming that the three channels φ, θ, and ψ are only controlled by δ a ,δ e ,δ rThe three inputs are controlled separately, i.e., the roll angle, pitch angle, and yaw angle are controlled only by the aileron, elevator, and rudder deflections, respectively, and the influence of the rudder on the roll and the influence of the aileron on the yaw are regarded as disturbances.

[0174] The nonlinear motion equation of the attitude angle loop is:

[0175]

[0176] Differentiating the above formula yields:

[0177]

[0178] In order to achieve decoupling control between different attitudes, we consider that the roll angle φ is only affected by the aileron δ a The deflection of the elevator is affected by the pitch angle θ, which is only affected by the elevator δ e The yaw angle ψ is only affected by the rudder δ r The deflection effect of the aileron δ a 、Elevator δ e 、Rudder δ r The attitude is controlled by rolling angular acceleration Pitch acceleration Yaw acceleration To reflect.

[0179] Therefore, combining the angular velocity, attitude angle, and torque equations and simplifying them, we get:

[0180]

[0181] Where, f φ Contains all aileron-independent terms in the roll angle φ loop, f θ Contains all elevator-independent terms in the pitch angle θ loop, f ψ Contains all terms in the yaw angle ψ loop that are not related to the rudder. φ ,b θ ,b ψ are the attitude angle loop control input δ a ,δ e ,δ r The coefficient of .

[0182] The specific form of TD is:

[0183]

[0184] Where i = φ, θ, ψ, v cmd,i is the input command signal, v 1,i v cmd,i The tracking signal can also be regarded as a continuous and smoothed command signal, v2,i v 1,i The differential signal of can be approximately regarded as v cmd,i The differential signal of , h is the sampling step. Let v 3,i =dv 2,i / dt, that is, v 3,i v 1,i The second-order differential signal can be approximately regarded as v cmd,i The second-order differential signal of .

[0185] The specific form of the third-order ESO is:

[0186]

[0187] Among them, β 01,i ,β 02,i ,β 03,i ,δ i is a parameter that needs to be adjusted, b 0,i is parameter b i The nominal value of can be calculated from the trim value, and h is the sampling step size. 1,i is the system output state y i The estimated value of z 2,i yes The estimated value of z 3,i is the total disturbance f i estimated value.

[0188] The control law of the i-th channel is:

[0189]

[0190] (d) Convert ADRC to LADRC

[0191] Compared to traditional ADRC, LADRC lacks the TD to arrange the transition process for the command signal and to obtain the differential signal. The nonlinear fal(x, a, δ) function is also replaced by a linear link. In fact, when a = 1, fal(x, a, δ) = x, so LADRC is actually a linear special case of ADRC.

[0192] The complete algorithm of LADRC after conversion is expressed as follows:

[0193]

[0194] (e) Parameterizing LADRC

[0195] First, LESO is parameterized.

[0196] Rewriting LESO into a state space expression, we have:

[0197]

[0198] Expand to

[0199]

[0200] in,

[0201] Its characteristic polynomial is:

[0202]

[0203] For the sake of simplicity, all the poles of LESO are placed at -ω by the pole placement method. o ,Right now

[0204]

[0205] Comparing the parameters on both sides of the equation, we get

[0206] β1=3ω o ,

[0207] Therefore, LESO is converted into the following single-parameter LESO through parameterization:

[0208]

[0209] Where z1, z2, z3 are the states of the LESO, u is the system input, y is the system output, and b0 is the nominal value of the system input coefficient b. o It is the extreme point of LESO, also known as the "bandwidth" of LESO. It should be noted that the "bandwidth" here only represents the tracking speed of LESO. The larger the "bandwidth", the faster the tracking speed. It is not the concept of 3dB bandwidth in the frequency domain, and the two should not be confused.

[0210] The PD controller is then parameterized.

[0211] For the system Substituting into the LESO PD controller, the closed-loop system expression is:

[0212]

[0213] Among them, r is the given instruction, y is the system output, k p ,k d are the proportional coefficient and differential coefficient respectively.

[0214] If the LESO parameters are properly selected and accurately estimated, then we can approximate:

[0215] z1=y,

[0216] The closed-loop system expression is approximately:

[0217]

[0218] Perform Laplace transform on it and get:

[0219] s 2 Y(s)=k p (R(s)-Y(s))-k d sY(s)

[0220] The closed-loop system transfer function is:

[0221]

[0222] Let k d =2ξω c , Then the closed-loop system is in the standard form of the second-order transfer function:

[0223]

[0224] If ξ=1, the system is in critical damping state, and the step response can track the instruction quickly and without overshoot. d =2ω c , The characteristic equation of the system is:

[0225]

[0226] Its closed-loop poles are all located at -ω c Therefore, the parameter k of the PD controller is p ,k d Using a single parameter ω c To express.

[0227] (f) Convert the closed-loop system into a unit negative feedback system to obtain the disturbance transfer function and the system open-loop transfer function

[0228] First, find the transfer function of the third-order LESO. Take the Laplace transform of the third-order LESO and we get:

[0229]

[0230] Simplified:

[0231]

[0232] Continue to simplify to get Z1(s):

[0233]

[0234] Substitute Z1(s) into the above equation to find Z2(s) and Z3(s):

[0235]

[0236] Taking Laplace transform of the PD controller of LADRC, we get:

[0237]

[0238] Substituting Z1(s), Z2(s), and Z3(s) into the above formula and simplifying it to the unit negative feedback form, we get:

[0239]

[0240] The equivalent simplified unit negative feedback system is as follows Figure 4 As shown, where G p (s) is the transfer function of the controlled object.

[0241] So we have:

[0242]

[0243] The parameterized result β1=3ω o , k d =2ω c , Substituting into the above formula, we get

[0244]

[0245] Therefore, the open-loop transfer function of the system G lg (s) and the closed-loop transfer function G cl (s) are:

[0246] G lg (s)=G c (s)G p (s)

[0247]

[0248] Taking the pitch angle as an example to derive the disturbance transfer function, the approximate transfer function of the pitch angle is:

[0249]

[0250] Among them, f θ Contains all elevator-independent terms in the pitch angle loop.

[0251] Let θ(s) = Y(s), b θ =b0, substitute U(s) into the above formula and simplify it to get:

[0252]

[0253] Therefore, the system's disturbance transfer function G YD (s) is:

[0254]

[0255] From the above formula, we can see that the influence of disturbance is related to the LADRC controller parameter ω o and ω c related.

[0256] (g) Analysis of the anti-disturbance characteristics of ADRC through the frequency domain characteristics of the disturbance transfer function and the system open-loop transfer function First, consider the impact of the disturbance on the system.

[0257] The system's disturbance transfer function G YD (s) is:

[0258]

[0259] Choose different ω o and ω c , draw its Bode diagram, and analyze the ADRC's ability to suppress disturbances through the amplitude in the Bode diagram.

[0260] Subsequently, the impact of model uncertainty on the system is considered.

[0261] The approximate transfer function of the pitch angle after ignoring the disturbance term is:

[0262]

[0263] in,

[0264] The open-loop transfer function G of the system lg (s) is:

[0265]

[0266] Note λ θ =b θ / b0, when considering the uncertainty of the model, that is, considering the change of a, let λ p =1 fixed, change the value of a, and observe the open-loop transfer function G lg The amplitude margin and phase margin of (s) are used to analyze the robustness of ADRC to model uncertainty.

[0267] The following simulation verifies the designed variant aircraft deceleration maneuver decision algorithm based on reinforcement learning:

[0268] The initial condition of the aircraft is steady level flight, with an altitude of 1000m, a speed of 40m / s, an angle of attack and pitch of 4.23°, and a sweep angle of 20°.

[0269] First, the disturbance transfer function G YD (s) for frequency domain analysis. Select ω o =10,ω c =10,20,…,50, draw its Bode diagram as Figure 5 As shown; select ω c =10,ω o =10,20,…,50, draw its Bode diagram as Figure 6 As shown. Figure 5 and Figure 6 It can be seen that the disturbance transfer function G YD (s) The amplitude of the logarithmic amplitude-frequency characteristic curve is always negative, indicating that the system has the ability to suppress disturbances; increasing ω o and ω c Both can further reduce the amplitude of the logarithmic amplitude-frequency characteristic curve in the low frequency band, enhance the anti-interference ability of the system, and increase ω o The disturbance suppression effect of increasing ω is better than c More obvious.

[0270] Then, the system open-loop transfer function G lg (s) Perform frequency domain analysis.

[0271] Since c9 in a is unmeasurable, the value of a cannot be accurately known, but it can be calculated from the balancing condition. The value of a is approximated by the value of , so some possible value ranges of a are given below for verification.

[0272] When the initial trim value is H = 1000m, V = 40m / s, sweep = 20°, a ≈ -52;

[0273] When the initial trim value is H = 1000m, V = 40m / s, sweep = 50°, a ≈ -33;

[0274] When the initial trim value is H = 1000m, V = 40m / s, sweep = 68°, a ≈ -16;

[0275] It can be seen from this that when the trim speed remains unchanged, the value of a basically varies in the range of [-16, -52]. Given the speed variation range V∈[20, 80], the variation range of a is expanded to [-8, -104]. Then -8 is relaxed to -0.1, and -104 is relaxed to -200. Therefore, the value of a selected for verification is a=[-0.1, -1, -10, -52, -100, -200].

[0276] Select ω o =200,ω c =5, the control effect is better at this time, a=[-0.1,-1,-10,-52,-100,-200], draw the Bode diagram of the system open-loop transfer function as shown Figure 7 The stability margin of each curve is shown in Table 1. Figure 7 The results show that when a=-0.1, -1, the system open-loop phase-frequency characteristic curve crosses the -180° line once in the frequency range of L(ω)>0 (N + =1), negatively crosses the -180° line once (N - =1), by the open-loop transfer function G lg (s) Knowing that the system has no open-loop poles in the right half s-plane, P = 0, N = N + -N - = 0, according to the logarithmic stability criterion, P-2N = 0, the closed-loop system is stable. Similarly, when a = -10, -52, -100, -200, N = N + -N - =1 / 2-1 / 2=0, P=0, according to the logarithmic stability criterion, P-2N=0, the closed-loop system is stable.

[0277] Table 1 System open-loop transfer function G lg (s) Amplitude margin and phase margin when a=[-0.1,-1,-10,-52,-100,-200]

[0278]

[0279] Figure 8 The square wave response curves for the pitch angle are shown for various values ​​of a. As can be seen, when a is greater than or equal to -52, the system response overshoots, with larger values ​​increasing the overshoot. However, when a is less than -52, the system response curve remains virtually unchanged. Therefore, when a is within the range [-0.1, -200], the system is consistently stable, which aligns with the conclusion drawn from the logarithmic stability criterion analysis above.

[0280] In fact, when the flight speed remains constant at V = 40 m / s, as the sweep angle changes from 20° to 68°, the range of a remains essentially constant between [-16, -52]. This range is within the interval [-0.1, -200], with a margin on both sides. In other words, the disturbance rejection capability of the pitch angle loop ADRC control law fully meets the requirements of a variable-sweep wing. Therefore, when the sweep angle varies between [20°, 68°], that is, when a varies between [-16, -52], the pitch angle response curve can be considered virtually unchanged.

[0281] Based on the above simulation results, the effectiveness of the frequency domain analysis method of variant aircraft attitude control based on ADRC in the present invention is demonstrated. It can clearly observe and analyze the anti-disturbance capability of ADRC for the variant aircraft attitude angle loop and its robustness to model uncertainties in the frequency domain.

[0282] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present invention, and these modifications or replacements should all be included in the scope of protection of the present invention.

Claims

1. A frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control, characterized in that: include: S1. Establish a six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic moment model of the variant aircraft; S2, designing an ADRC-based variant aircraft attitude angle control law for the six-degree-of-freedom nonlinear model, aerodynamic force, and aerodynamic moment model established in step S1; S3. Convert the ADRC control law designed in step S2 into LADRC suitable for frequency domain analysis through parameter selection; specifically: For ADRC function, , take the parameters ,but , and remove TD at the same time, converting ADRC into LADRC. The complete algorithm of LADRC after conversion is expressed as follows: in, is the system input coefficient The nominal value of S4, parameterize the LADRC obtained in step S3; specifically: (1) Parameterization of LESO Rewriting LESO into a state space expression, we have: Expand to in, , , , ; Its characteristic polynomial is: By using the pole configuration method, all the poles of LESO are placed at ,Right now Comparing the parameters on both sides of the equation, we get Therefore, LESO is converted into the following single-parameter LESO through parameterization: in, It is the state of LESO, is the system input, is the system output, It is the extreme of LESO; (2) Parameterize the PD controller For the system , substituting into the LESO PD controller, the closed-loop system expression is: in For a given instruction, is the system output, are the proportional coefficient and differential coefficient respectively; If the LESO parameters are properly selected and accurately estimated, then we can approximate: The closed-loop system expression is approximately: Perform Laplace transform on it and get: The closed-loop system transfer function is: make , then the closed-loop system is the standard form of the second-order transfer function: Pick , the system is in a critical damping state, and the step response can track the instruction quickly and without overshoot. , the characteristic equation of the system is: Its closed-loop poles are located at At this point, the parameters of the PD controller are Using a single parameter To express; S5. Perform Laplace transform on the LADRC control law and system parameterized in step S4, convert the closed-loop system into a unit negative feedback system, and obtain the disturbance transfer function and the system open-loop transfer function; specifically: First, find the transfer function of the third-order LESO and take the Laplace transform of the third-order LESO to get: Simplified: Continuing to simplify, we get : Will Substituting into the above formula, we can get and : Taking Laplace transform of the PD controller of LADRC, we get: Will 、 、 Substituting into the above formula and simplifying it to the unit negative feedback form, we get: So we have: The parameterized result Substituting into the above formula, we get Therefore, the open-loop transfer function of the system is and the closed-loop transfer function They are: Taking the pitch angle as an example to derive the disturbance transfer function, the approximate transfer function of the pitch angle is: in, Contains all elevator-independent terms in the pitch angle loop. ; remember , ,Will Substituting into the above formula, simplifying it, we get: Therefore, the disturbance transfer function of the system is for: S6. Analyze the frequency domain characteristics of the disturbance transfer function obtained in step S5 to obtain the anti-disturbance characteristics of ADRC to internal and external disturbances of the system; specifically: The disturbance transfer function of the system for: Choose different and , draw its Bode diagram, and analyze the ability of ADRC to suppress disturbances through the amplitude in the Bode diagram; S7. Analyze the frequency domain characteristics of the system open-loop transfer function obtained in step S5 to obtain the robustness of ADRC to model uncertainty; specifically: The approximate transfer function of the pitch angle after ignoring the disturbance term is: in, , ; The open-loop transfer function of the system for: remember , when considering model uncertainty, that is, considering The changes in Fixed, changed , observe the open-loop transfer function The amplitude margin and phase margin of the ADRC are used to analyze the robustness of the ADRC to model uncertainties.

2. The frequency domain analysis method for variant aircraft attitude control based on active disturbance rejection control according to claim 1 is characterized in that: In step S1, a six-degree-of-freedom nonlinear model, aerodynamic force, and aerodynamic moment model of the variant aircraft are established, specifically: The six-degree-of-freedom nonlinear equation of the variant aircraft is expressed as: in, It's speed, is the angle of attack, is the sideslip angle, is the angular velocity of the aircraft rotating around the three axes of the aircraft system, is the aircraft's attitude angle, They are drag, side force, lift and engine thrust. They are rolling moment, pitching moment and yaw moment, The mass of the aircraft. is the acceleration due to gravity; The static moment of the aircraft in the aircraft system The component on the axis, is the component of the inertial force caused by the variation process on the three axes of the airflow system, is the component of the inertia moment caused by the deformation process on the three axes of the machine system; , , , , , , , , , , , , , , ; The aerodynamic force and aerodynamic torque are expressed as: Lift: resistance: Lateral force: Rolling moment: Pitching moment: Yaw moment: in, is the dynamic pressure, is the air density, is the wing area; is the lift coefficient at zero angle of attack, 、 Lift coefficient versus angle of attack , elevator deflection angle The derivative of is the drag coefficient at zero angle of attack, 、 The drag coefficient Angle of attack , elevator deflection angle The derivative of 、 、 、 、 The lateral force coefficients Side slip angle , aileron deflection angle , rudder deflection angle , roll angular velocity , yaw angular velocity The derivative of 、 、 、 、 Rolling moment coefficients Side slip angle , aileron deflection angle , rudder deflection angle , roll angular velocity , yaw angular velocity The derivative of is the pitching moment coefficient at zero angle of attack, 、 、 Pitching moment coefficients Angle of attack , elevator deflection angle , pitch angular velocity The derivative of 、 、 、 、 are the yaw moment coefficients Side slip angle , aileron deflection angle , rudder deflection angle , roll angular velocity , yaw angular velocity The derivative of .

3. The frequency domain analysis method for variant aircraft attitude control based on active disturbance rejection control according to claim 2 is characterized in that: In step S2, the six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic torque model established in step S1 are used to design a variant aircraft attitude angle control law based on ADRC, specifically: The nonlinear motion equation of the attitude angle loop is: Differentiating the above formula yields: Combining the angular velocity, attitude angle, and torque equations and simplifying them, we get: in, Included in the roll angle In the loop, all terms that are not related to the aileron, Includes pitch angle In the loop, all terms not related to the elevator, Included in the yaw angle In the loop, all terms not related to the rudder; They are attitude angle loop control inputs The coefficient of The specific form of the tracking differentiator TD is: in, , is the input command signal, for The tracking signal can also be regarded as a continuous and smoothed command signal. for The differential signal of The differential signal of is the sampling step length; let ,Right now for The second-order differential signal of The second-order differential signal of The specific form of the third-order extended state observer ESO is: in, is a parameter that needs to be adjusted. is a parameter The nominal value of can be calculated from the balancing value, is the sampling step size; Is the system output status The estimated value of yes The estimated value of is the total disturbance estimated value of; No. The control law of the channel is: 。 4. A computer system, characterized in that include: One or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method of claim 1.

5. A computer-readable storage medium, characterized in that Computer-executable instructions are stored, and when the instructions are executed, they are used to implement the method of claim 1.

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