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

Abstract

The invention relates to a morphing aircraft attitude control frequency domain analysis method based on active disturbance rejection control. The method comprises the following steps: establishing a six-degree-of-freedom nonlinear model and an aerodynamic force and aerodynamic moment model of a morphing aircraft; designing a variant aircraft attitude angle control law based on ADRC; the ADRC is converted into the LADRC; the LADRC is subjected to parameterization; performing Laplace transformation on the parameterized LADRC control law and system, equivalently converting a closed-loop system into a unit negative feedback system, and obtaining a disturbance transfer function and a system open-loop transfer function; analyzing the frequency domain characteristic of the disturbance transfer function to obtain the anti-interference characteristic of the ADRC to the internal and external disturbances of the system; and analyzing the frequency domain characteristic of the open-loop transfer function of the system to obtain the robust characteristic of the ADRC to the uncertainty of the model. According to the invention, attitude control of the morphing aircraft is realized through the active disturbance rejection control method, and attitude stability of the morphing aircraft before and after morphing and in the morphing process and accurate tracking of instruction signals are ensured.

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 anti-disturbance control. Background Art

[0002] Morphing aircraft have unique advantages in improving the aerodynamic performance of aircraft, expanding the flight envelope, and increasing endurance time. 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, etc., general control methods are difficult to ensure its flight stability. A flight control system with high robustness is required to ensure its flight stability during the mutation process.

[0003] Active disturbance rejection control (ADRC) technology is an active anti-disturbance technology. Different from the passive anti-disturbance mode of PID, its idea of ​​observing and eliminating "total disturbance" has gradually become known and recognized in recent years. ADRC combines the system's internal disturbance (internal disturbance of the system, such as modeling error, model uncertainty, etc.) and external disturbance (external disturbance of the system) into "total disturbance", and estimates and eliminates it through the method of extended state observer, so as to achieve the anti-disturbance control of the system. The variant aircraft is a highly complex and uncertain nonlinear system. The variant will cause the system model to change, while ADRC does not rely on the precise model of the system, which is very suitable for the flight control of variant 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 prior art, the present invention provides a frequency domain analysis method for variant aircraft attitude control based on ADRC, which solves the problem of model uncertainty and external disturbance suppression capability of ADRC when the variant aircraft is deformed through frequency domain analysis.

[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, 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, analyzing 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 characteristics of ADRC to model uncertainty.

[0015] A further technical solution of the present invention is as follows: In step S1, a six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic moment model of the variant aircraft are 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 rotating 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 deformation 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 moment are expressed as:

[0021] Lift:

[0022]

[0023] resistance:

[0024]

[0025] Side Force:

[0026]

[0027] Rolling moment:

[0028]

[0029] Pitch 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 For 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 rolling 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 rolling 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 pitch moment coefficients C m For 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 S2, the six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic moment model established in step S1 are used to design a variant aircraft attitude angle control law based on ADRC, 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 the terms in the roll angle φ loop that are not related to the aileron, f θ Contains all the terms in the pitch angle θ loop that are independent of the elevator, f ψ Contains all terms in the yaw angle ψ loop that are independent of 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 of 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 the 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 An 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 a 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 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 point 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 the differential coefficient respectively;

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

[0074] z1=y,

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

[0076]

[0077] Perform Laplace transform on it, and we 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 a second-order transfer function:

[0082]

[0083] If ξ=1, the system is in critical damping state, and the step response can track the command quickly 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 PD controller parameter k p ,k d Using a single parameter ω c To express.

[0086] A further technical solution of the present invention is: in step S5, the LADRC control law and system parameterized in step S4 are subjected to Laplace transformation, the closed-loop system is equivalently converted into a unit negative feedback system, and a disturbance transfer function and a system open-loop transfer function are obtained, 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 formula 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 parameterization 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 is 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, the disturbance transfer function is derived. The approximate transfer function of the pitch angle is:

[0108]

[0109] Among them, f θ Contains all the terms in the pitch angle loop that are not related to the elevator,

[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 disturbance transfer function of the system is G YD (s) is:

[0113]

[0114] A further technical solution of the present invention is: 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 the internal and external disturbances of the system, specifically:

[0115] The disturbance transfer function G of the system 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 of the system is G lg (s) is:

[0123]

[0124] Note 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 uncertainties.

[0125] A computer system, characterized in that it comprises: 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 auto-disturbance rejection control, which realizes attitude control of the variant aircraft through the auto-disturbance rejection control method, thereby ensuring the attitude stability of the variant aircraft before and after the transformation and during the transformation process and the accurate tracking of the command signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] The 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 components throughout the drawings.

[0130] Figure 1 A framework diagram is designed 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 It 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 purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain 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 can 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 specification 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 can be 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 that are 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 anti-interference characteristics of ADRC cannot be clearly observed from the system response curve in the time domain, some characteristics can only be intuitively obtained in the frequency domain, such as the cutoff frequency and stability margin of the system. The cutoff frequency reflects the bandwidth of the system. If the cutoff frequency is low, the system stability is good, but the transient response is poor, and the tracking speed of the input command is slow; if the cutoff frequency is high, the system transient response is good, the tracking speed is fast, but the stability is poor. The stability margin reflects the limit of the gain change and phase lag that the system can withstand, which are important parameter indicators that need to be considered in the frequency domain analysis design. Therefore, the present invention will study the anti-interference characteristics and anti-interference ability of the variant aircraft attitude control based on self-disturbance rejection control from the perspective of the frequency domain.

[0141] Since ADRC has a good effect in suppressing internal and external disturbances and model uncertainties of 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, and the suppression characteristics of the control law parameters on 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 variant aircraft, taking into account the changes in aerodynamic force and aerodynamic moment caused by the variant;

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

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

[0151] This embodiment takes a variable-sweep wing aircraft as the object, and designs the attitude angle control law of the variant aircraft through the self-disturbance rejection control for the attitude control of the variant aircraft. 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 to reduce the parameters that need to be adjusted in the control law 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 of six degrees of freedom for 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 a 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 rotating 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 deformation 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 moment can be expressed as:

[0158] Lift:

[0159]

[0160] resistance:

[0161]

[0162] Side Force:

[0163]

[0164] Rolling moment:

[0165]

[0166] Pitch 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 For 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 rolling 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 rolling 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 pitch moment coefficients C m For 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 pitch 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 the attitude angle, the present invention uses 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 deflection of the aileron, elevator, and rudder, 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 decoupled control between different attitudes, we assume that the roll angle φ is only affected by the aileron δ a The deflection of 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 angular acceleration Yaw acceleration To reflect.

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

[0180]

[0181] In the formula, f φ Contains all the terms in the roll angle φ loop that are not related to the aileron, f θ Contains all the terms in the pitch angle θ loop that are independent of the elevator, f ψ Contains all terms in the yaw angle ψ loop that are independent of 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 of 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 the 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 The estimated value of .

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

[0189]

[0190] (d) Convert ADRC to LADRC

[0191] Compared with traditional ADRC, LADRC does not have TD to arrange the transition process of the command signal and obtain the differential signal, and 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 state space expression, we have:

[0197]

[0198] Expand to

[0199]

[0200] in,

[0201] Its characteristic polynomial is:

[0202]

[0203] For simplicity, all the poles of LESO are placed at -ω by 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 PD controller of LESO, 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 the differential coefficient respectively.

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

[0215] z1=y,

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

[0217]

[0218] Perform Laplace transform on it, and we 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 a second-order transfer function:

[0223]

[0224] If ξ=1, the system is in critical damping state, and the step response can track the command quickly 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 get:

[0229]

[0230] Simplified:

[0231]

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

[0233]

[0234] Substitute Z1(s) into the above formula 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, G p (s) is the transfer function of the controlled object.

[0241] So we have:

[0242]

[0243] The parameterization 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 is 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, the disturbance transfer function is derived. The approximate transfer function of the pitch angle is:

[0249]

[0250] Among them, f θ Contains all the terms in the pitch angle loop that are not related to the elevator,

[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 disturbance transfer function of the system is G YD (s) is:

[0254]

[0255] It can be seen from the above formula 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 disturbance transfer function G of the system 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 of the system is G lg (s) is:

[0265]

[0266] Note 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 uncertainties.

[0267] The designed variant aircraft deceleration maneuver decision algorithm based on reinforcement learning is simulated and verified as follows:

[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 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 that when the balancing 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) It is known that the system has no open-loop poles in the right half s plane, so 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 curve of the pitch angle when a takes the corresponding value is shown. It can be seen from the figure that when a takes a value greater than or equal to -52, the system response overshoots, and the larger the value, the greater the overshoot; when a takes a value less than -52, the system response curve is almost the same. Therefore, when the value of a is between the interval [-0.1, -200], the system is always stable, which is the same as the conclusion drawn from the previous logarithmic stability criterion analysis.

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

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

[0282] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should be included in the protection scope 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, converting the ADRC control law designed in step S2 into LADRC suitable for frequency domain analysis through parameter selection; S4, parameterizing the LADRC obtained in step S3; 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; S6, analyzing 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; S7. Analyze the frequency domain characteristics of the system open-loop transfer function obtained in step S5 to obtain the robustness characteristics of ADRC to model uncertainty.

2. The frequency domain analysis method for attitude control of a variant aircraft 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: 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 rotating 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, 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 deformation 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; The aerodynamic force and aerodynamic moment are expressed as: Lift: resistance: Side Force: Rolling moment: Pitch moment: Yaw moment: 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 drag coefficient C D For 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 rolling angular velocity p, the yaw angular velocity r; C lβ , C lp , C lr They are rolling moment coefficient C l Side slip angle β, aileron deflection angle δ a 、Rudder deflection angle δ r , the derivative of the rolling 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 pitch moment coefficients C m For 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.

3. The frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control according to claim 2 is characterized in that: In S2, the six-degree-of-freedom nonlinear model, aerodynamic force and aerodynamic moment 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: Among them, f φ Contains all the terms in the roll angle φ loop that are not related to the aileron, f θ Contains all the terms in the pitch angle θ loop that are independent of the elevator, f ψ Contains all terms in the yaw angle ψ loop that are independent of the rudder; b φ ,b θ ,b ψ are the attitude angle loop control input δ a ,δ e ,δ r The coefficient of The specific form of the tracking differentiator TD is: 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 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 of can be approximately regarded as v cmd,i The second-order differential signal of The specific form of the third-order extended state observer ESO is: Among them, β 01,i ,β 02,i ,β 03,i ,δ i is the 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 An estimated value of The control law of the i-th channel is:

4. The frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control according to claim 3 is characterized in that: In step S3, the ADRC control law designed in step S2 is converted into LADRC suitable for frequency domain analysis through parameter selection, specifically: 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:

5. The frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control according to claim 4, It is characterized in that In step S4, the LADRC obtained in step S3 is parameterized, specifically: (1) Parameterization of LESO Rewriting LESO into state space expression, we have: Expand to in, Its characteristic polynomial is: By using the pole placement method, all the poles of LESO are placed at -ω o ,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: 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 point of LESO; (2) Parameterize the PD controller For the system Substituting into the PD controller of LESO, the closed-loop system expression is: Where r is the given instruction, y is the system output, k p ,k d are the proportional coefficient and the differential coefficient respectively; If the LESO parameters are selected appropriately and estimated accurately, then we can get: The closed-loop system expression is approximately changed to: Perform Laplace transform on it, and we get: s 2 Y(s)=k p (R(s)-Y(s))-k d sY(s) The closed-loop system transfer function is: Let k d =2ξω c , Then the closed-loop system is in the standard form of a second-order transfer function: If ξ=1, the system is in critical damping state, and the step response can track the command quickly without overshoot. d =2ω c , The characteristic equation of the system is: Its closed-loop poles are all located at -ω c At this point, the PD controller parameter k p ,k d Using a single parameter ω c To express.

6. The frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control according to claim 5 is characterized in that: 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: First, find the transfer function of the third-order LESO and take the Laplace transform of the third-order LESO to get: Simplified: Continue to simplify to get Z1(s): Substitute Z1(s) into the above formula to find Z2(s) and Z3(s): Taking Laplace transform of the PD controller of LADRC, we get: Substituting Z1(s), Z2(s), and Z3(s) into the above formula and simplifying it to the unit negative feedback form, we get: So we have: The parameterization result β1=3ω o , k d =2ω c , Substituting into the above formula, we get Therefore, the open-loop transfer function of the system is G lg (s) and the closed-loop transfer function G cl (s) are: Taking the pitch angle as an example, the disturbance transfer function is derived. The approximate transfer function of the pitch angle is: Among them, f θ Contains all the terms in the pitch angle loop that are not related to the elevator, Let θ(s) = Y(s), b θ =b0, substitute U(s) into the above formula and simplify it to get: Therefore, the disturbance transfer function of the system is G YD (s) is:

7. The frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control according to claim 6 is characterized in that: 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 the internal and external disturbances of the system, specifically: The disturbance transfer function G of the system YD (s) is: 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.

8. The frequency domain analysis method for attitude control of a variant aircraft based on active disturbance rejection control according to claim 7 is characterized in that: 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: The approximate transfer function of the pitch angle after ignoring the disturbance term is: in, The open-loop transfer function of the system is G lg (s) is: Note 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 uncertainties.

9. 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.

10. 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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