Aircraft fixed-time agile turning attitude control method based on quaternion

Abstract

The invention discloses an aircraft fixed-time agile turning attitude control method based on quaternion, and belongs to the field of aircraft attitude control. The invention aims to solve the problems of uncertain aerodynamic characteristics, poor anti-interference capability, difficulty in quantitative calculation of convergence time and the like in agile turning attitude control of aircrafts (vertical turning of fighters or shoulder-crossing launching of air-to-air missiles), and designs a sliding mode surface with fixed time convergence based on quaternions. According to the method, the rotation time can be adjusted, rapid convergence can be achieved, the expansion observer is designed, real-time estimation compensation can be carried out on external interference and internal uncertainty, and the controller has high robustness and adaptability. Besides, a fast and accurate convergence differentiator is further designed, all orders of derivatives of tracking signals are solved in real time, more effective information of input signals is sent to a sliding mode controller, and the stability and adaptability of the model are further improved.

Description

Technical Field

[0001] The invention is based on the research background of aircraft agile turning (vertical flip of a fighter jet or over-the-shoulder launch of an air-to-air missile) and belongs to the field of aircraft attitude control. Background Art

[0002] The difficulty of agile turning of aircraft (vertical flip of fighter jets or over-the-shoulder launch of air-to-air missiles) lies in the need to perform agile turning and capture targets after launch, and the aerodynamics of aircraft at high angles of attack present nonlinear, strongly coupled, and uncertain characteristics. In addition, the combat situation of today's air combat is complex. For different types of carrier aircraft positions and target entry angles, as well as the aircraft itself (different aerodynamic characteristics and thrust-to-weight ratio characteristics, attitude change and turning rate adaptation, angle of attack constraints, etc.), if the attitude change and time of the aircraft can be adjusted, it will be convenient to flexibly respond to different combat situations.

[0003] For controller design, the design difficulties mainly lie in three aspects: fast convergence, anti-interference ability and adjustable convergence time.

[0004] At present, the agile turning control algorithms of aircraft mainly include sliding mode control algorithm, backstepping method, dynamic surface, active disturbance rejection control and so on.

[0005] The agile attitude control algorithm designed in reference [1] is aimed at the angle of attack. However, in actual engineering, the interference of wind causes the velocity coordinate system and the airflow coordinate system to not completely coincide. At present, it is difficult to accurately measure the actual angle of attack in engineering. Reference [2] proposed a sliding mode control law based on error quaternion. Although it can guarantee finite time convergence, it cannot guarantee finite time and is difficult to quantify rapidity, which is not conducive to actual engineering analysis. Reference [3] designed a combined non-singular terminal sliding surface to improve the convergence speed, but the sliding surface is not suitable for quaternion. Because the traditional non-singular sliding surface results in a singular value matrix, it is not easy to feedback linearization. Only the constant velocity convergence law can be used, and the convergence speed and time cannot be controlled.

[0006] The scenario of the aircraft's agile turning has certain requirements and controllability for the Euler angle rate and turning time of the turn. During the entire flight control process, the missile parameters are constantly changing dynamically. Since the convergence time is adjustable, that is, missiles with different thrust-to-weight ratios, turning rates, and maximum angle of attack values, as well as different requirements during the turning process, the present invention may adapt to the parameters of the aircraft by modifying the controller parameters. Therefore, the control algorithm designed by the present invention has further improved the adjustability, flexibility, adaptability, and applicability of the design of different missile parameters.

[0007] [1] Ma Yueyue. Research on high-maneuverability flight control method of agile missile with high angle of attack[D]. Beijing Institute of Technology, 2016

[0008] [2] Zhao Qin. Space interceptor attitude control method based on quaternion[D]. Harbin Institute of Technology, 2012

[0009] [3] Zhao Xinyun, Yu Jianliang. A novel non-singular terminal sliding mode control for missile agile turning phase[J]. Journal of Astronautics, 2022, Vol. 43(4): 454-464 Summary of the invention

[0010] The purpose of the present invention is to solve the problems of uncertain aerodynamic characteristics, poor anti-interference ability, and difficulty in quantitative calculation of convergence time in the agile turning attitude control of aircraft, and to provide a fixed-time agile turning attitude control method for aircraft based on quaternions. The method designs a sliding surface with fixed-time convergence based on quaternions, which can realize adjustable rotation time and fast convergence, and designs an extended observer, which can estimate and compensate for external interference and internal uncertainty in real time, so that the controller has strong robustness and adaptability. In addition, a fast and accurate convergence differentiator is designed to solve the derivatives of each order of the tracking signal in real time, and send more effective information of the input signal to the sliding mode controller, further improving the stability and adaptability of the model.

[0011] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0012] A quaternion-based fixed-time agile turning attitude control method for aircraft is as follows: first, through a fast and accurate differentiator, the derivatives of each order of the tracking signal are estimated to obtain more input information, and then a fixed-time variable structure composite sliding mode controller is used to generate control torque. In the process of dynamic control, an extended observer is used to estimate the external disturbance of the system and the uncertainty of internal modeling to compensate for it and introduce interference information into the controller. Fast and stable tracking and strong anti-interference ability of nonlinear control systems are achieved.

[0013] Furthermore, the method is specifically as follows:

[0014] The traditional method of describing attitude is Euler angles, but when rotating 90° around the second axis, this equation will have a strange situation. In addition, one degree of freedom will be lost, resulting in the phenomenon of universal lock.

[0015]

[0016] Therefore, quaternions are used to describe the attitude. The relationship between the derivative of the quaternion and the attitude angle and angular velocity is as follows:

[0017]

[0018] (1) Establishing a system dynamics model

[0019] The attitude dynamics equation for rotation around the center of mass is as follows:

[0020]

[0021] Among them, J x ,J y ,J z is the moment of inertia of the aircraft about each coordinate axis of the missile body coordinate system, ω x ,ω y ,ω z is the selected angular velocity of the aircraft body coordinate system relative to the reference inertial system, M x ,M y ,M z is the control torque;

[0022] The kinematic model uses a mathematical relationship based on quaternions, and uses quaternions to describe the aircraft attitude to avoid the singular value of the Euler angle and the universal lock phenomenon. The current attitude quaternion is q = [q0 q1 q2 q3] T ; q0 is the scalar part of the attitude quaternion, q1, q2, q3 are the vector parts of the attitude quaternion respectively;

[0023] The relationship between the derivative of the current attitude quaternion and the attitude angle and angular velocity is as follows:

[0024]

[0025] From equations (1) and (2), we can get

[0026]

[0027] in, M=[M x ,M y ,M z ] T

[0028] (2) Design of fixed-time fast non-singular sliding mode control algorithm

[0029] (2.1) Fixed-time fast non-singular sliding mode control law

[0030] The current posture quaternion is q = [q0 q1 q2 q3] T , the desired attitude quaternion is q d =[q d0 q d1 q d2 q d3 ] T ;

[0031] Define state variable x = qq d ,but

[0032]

[0033] Since the desired attitude quaternion q d The derivatives of There is no way to directly use the above relationship to find it, so a fast and accurate convergence differentiator is designed to estimate the derivative information;

[0034] Design the composite non-singular fixed-time convergent composite sliding surface as follows:

[0035]

[0036] in, p,q are odd numbers, and x is qq d , quaternion error, sliding surface parameters λ>0, m>0, n>0, the switching line of the composite sliding surface δ∈(0,1), k1>0, k2>0, p, q are odd numbers greater than 0. It can be seen from the subsequent proof that the convergence time is determined by the above parameters. By adjusting these parameters, it can be used to adjust the convergence time of the controller;

[0037] The designed sliding mode reaching law is:

[0038]

[0039] Among them, p2,q2 are positive odd numbers, It can be less than 1, v is a reaching law, and η1 and η2 are positive numbers;

[0040] The control law is obtained by feedback linearization:

[0041]

[0042] Where, E = f(q) g(J);

[0043] Since the E matrix is ​​a 4×3 column-full matrix, the inverse operation needs to be replaced by the pseudo-inverse operation, and the formula is as follows:

[0044] E -1 =(E T ·E) -1 ·E T

[0045] (2.2) Fast and accurate differentiator

[0046] In order to make full use of the controller input signal, that is, the information of the desired angle, and integrate it into the controller; Make an estimate; design the input variable of the differentiator to be u = q d , the output variable is The following control law is used to ensure the convergence of the differentiator

[0047]

[0048] Where sgn(x,k)=|x k *sign(x), α1, α2, α3, α4, α5 are odd numbers, k1, k2, k3, k4, k5 are positive numbers;

[0049] The fast and accurate differentiator is used to estimate the differential of the desired variable and provide information to the controller;

[0050] The input of the fast and accurate differentiator is q d =[q d0 q d1 q d2 q d3 ] T , the output is its derivatives of various orders

[0051] (2.3) Dilated Observer

[0052] As the core component of ADRC, the extended state observer can, on the one hand, track important state variables in the system to facilitate real-time understanding of the system status; on the other hand, it can estimate the uncertainty and external interference of the model through nonlinear feedback based on the total action of internal and external disturbances in the system model, and compensate the control quantity in real time; timely compensation in the form of feedback helps to improve the robustness of the system.

[0053] When considering model uncertainty and external disturbance, the modeling uncertainty and disturbance are abstracted as [δ q0 ,δ q1 ,δ q2 ,δ q3 ] T ,

[0054]

[0055] Simplify the model to

[0056]

[0057] The virtual control quantity is:

[0058]

[0059] In this method, the input state of ESO is q = [q0 q1 q2 q3] T

[0060] The input control quantity of ESO is the virtual control quantity virtual_control

[0061] The output of ESO is

[0062] Then compensate it into the control law to get the final control law

[0063]

[0064] The beneficial effects of the present invention compared to the prior art are:

[0065] 1. During over-the-shoulder launch, the aircraft's attitude turn converges within a fixed time.

[0066] 2. It can be applied to severe working conditions with uncertainty in the established mathematical model and strong external disturbances, and has strong robustness and stability.

[0067] 3. Simulation verifies that the proposed control method has faster convergence speed, stronger robustness and smaller steady-state error.

[0068] 4. The present invention uses quaternions as a mathematical model to describe the system posture and solves the singular value problem of Euler angles.

[0069] 5. The fixed-time convergence control method with strong robustness designed by the present invention, as a control algorithm framework, can solve similar posture control problems.

[0070] 6. By estimating uncertainty and interference and compensating them in real time in the control law, the interference under large angle of attack conditions can be suppressed and the stability of the control system can be maintained.

[0071] 7. Fixed time convergence is achieved. For different aircraft characteristics and combat situations, the convergence time in the attitude control process can be adjusted by modifying parameters according to its purpose.

[0072] 8. By designing a new type of composite fast non-singular fixed-time terminal sliding surface, the rapidity of convergence can be guaranteed. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is the flow chart of the overall control scheme;

[0074] Figure 2 This is a diagram of the attitude control simulation result when there is no interference in Example 1;

[0075] Figure 3 This is a diagram of the attitude control simulation result when there is interference in Example 1;

[0076] Figure 4 This is a diagram of the attitude control simulation result when there is no interference in Example 2;

[0077] Figure 5 This is a diagram of the attitude control simulation result when there is interference in Example 2;

[0078] Figure 6 This is a schematic diagram of over-the-shoulder firing operations;

[0079] Figure 7 This is a diagram showing the tracking effect of the controller on the frequency signal;

[0080] Figure 8 It is the tracking diagram of the fast and accurate differentiator (FED) to the input desired signal;

[0081] Fig. 9 Estimation of the expected first-order derivative by the fast exact differentiator (FED);

[0082] Fig.10 Estimation of the desired second-order derivative by the fast exact differentiator (FED);

[0083] Fig.11 is the estimated graph of the quaternion state by the expanded observer;

[0084] Fig.12 This is the estimation diagram of the disturbance and unknown quantity in the quaternion second-order derivative motion equation by the extended observer;

[0085] Fig.13 Figure (a) shows the Monte Carlo simulation results of controller parameter changes;

[0086] Fig.14 Figure (ii) shows the Monte Carlo simulation results of controller parameter changes;

[0087] Fig.15 Figure (iii) shows the Monte Carlo simulation results of controller parameter changes;

[0088] Fig.16 The angle of attack and ballistic inclination diagram calculated by Gaussian pseudospectral method;

[0089] Fig.17 Pitch command diagram designed for Gaussian pseudospectral method;

[0090] Fig.18 It is the pitch angle command diagram fitted by the 4th order polynomial;

[0091] Fig.19 Ideal ballistics diagram for over-the-shoulder firing. DETAILED DESCRIPTION

[0092] The technical solutions in the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0093] Over the shoulder launch: An air-to-air missile is launched forward and then turns 180 degrees to attack backward.

[0094] The present invention designs a non-singular fixed-time convergence control method for a second-order nonlinear system, which can be applied to severe working conditions with uncertainty in the established mathematical model and strong external disturbances. It has strong robustness and stability and is a controller algorithm framework, which mainly includes the following contents:

[0095] 1. A fast and accurate convergence differentiator that fully utilizes the information of the controller input signal (desired angle) and integrates it into the controller.

[0096] 2. A sliding mode controller with a composite non-singular terminal sliding surface with strong robustness and fixed-time convergence. A composite new non-singular terminal sliding surface is designed to ensure rapid convergence and fixed-time convergence. The control law is designed based on the feedback linearization method. Fixed-time convergence and time adjustability are achieved by modifying the controller parameters.

[0097] 3. And improve the extended observer to estimate the uncertainties and external unknown disturbances in the modeling process in real time and compensate for them in the controller.

[0098] This novel sliding mode control method, based on Lyapunov stability theory, constructs a fixed-time convergence and proves that the control error converges to an arbitrary small closed sphere within a fixed time. The simulation of attitude control of a quadrotor aircraft verifies that the proposed method has faster convergence speed, stronger robustness and smaller steady-state error.

[0099] The original idea of ​​the present invention comes from the over-the-shoulder launch scenario of air-to-air missiles. The agile turning attitude control algorithm designed by the present invention can be used in the control system of the initial program turning section of the vertical flip of fighter jets, large off-axis launch, and over-the-shoulder launch of fourth-generation air-to-air missiles. From the simulation effect, the controller has very good rapidity, stability, and anti-interference ability.

[0100] A method for controlling the fixed-time agile turning attitude of an aircraft based on quaternions is as follows:

[0101] The traditional method of describing attitude is Euler angles, but when rotating 90° around the second axis, this equation will have a strange situation. In addition, one degree of freedom will be lost, resulting in the phenomenon of universal lock.

[0102]

[0103] Therefore, quaternions are used to describe the attitude. The relationship between the derivative of the quaternion and the attitude angle and angular velocity is as follows:

[0104]

[0105] (1) Establishing a system dynamics model

[0106] The attitude dynamics equation for rotation around the center of mass is as follows:

[0107]

[0108] Among them, J x ,J y ,J z is the moment of inertia of the aircraft about each coordinate axis of the missile body coordinate system, ω x ,ω y ,ω z is the selected angular velocity of the aircraft body coordinate system relative to the reference inertial system, M x ,M y ,M z is the control torque;

[0109] The kinematic model uses a mathematical relationship based on quaternions, and uses quaternions to describe the aircraft attitude to avoid the singular value of the Euler angle and the universal lock phenomenon. The current attitude quaternion is q = [q0 q1 q2 q3] T ; q0 is the scalar part of the attitude quaternion, q1, q2, q3 are the vector parts of the attitude quaternion respectively;

[0110] The relationship between the derivative of the current attitude quaternion and the attitude angle and angular velocity is as follows:

[0111]

[0112] From equations (1) and (2), we can get

[0113]

[0114] in, M=[M x ,M y ,M z ] T

[0115] (2) Design of fixed-time fast non-singular sliding mode control algorithm

[0116] (2.1) Fixed-time fast non-singular sliding mode control law

[0117] The current posture quaternion is q = [q0 q1 q2 q3] T , the desired attitude quaternion is q d =[q d0 q d1 q d2 q d3 ] T ;

[0118] Define state variable x = qq d ,but

[0119]

[0120] Since the desired attitude quaternion q d The derivatives of There is no way to directly use the above relationship to find it, so a fast and accurate convergence differentiator is designed to estimate the derivative information;

[0121] Design the composite non-singular fixed-time convergent composite sliding surface as follows:

[0122]

[0123] in, p,q are odd numbers, and x is qq d , quaternion error, sliding surface parameters λ>0, m>0, n>0, the switching line of the composite sliding surface δ∈(0,1), k1>0, k2>0, p, q are odd numbers greater than 0. It can be seen from the subsequent proof that the convergence time is determined by the above parameters. By adjusting these parameters, it can be used to adjust the convergence time of the controller;

[0124] The designed sliding mode reaching law is:

[0125]

[0126] Among them, p2,q2 are positive odd numbers, It can be less than 1, v is a reaching law, and η1 and η2 are positive numbers;

[0127] The control law is obtained by feedback linearization:

[0128]

[0129] Where, E = f(q) g(J);

[0130] Since the E matrix is ​​a 4×3 column-full matrix, the inverse operation needs to be replaced by the pseudo-inverse operation, and the formula is as follows:

[0131] E -1 =(E T E) -1·E T

[0132] (2.2) Fast and accurate differentiator

[0133] In order to make full use of the controller input signal, that is, the information of the desired angle, and integrate it into the controller; Make an estimate; design the input variable of the differentiator to be u = q d , the output variable is The following control law is used to ensure the convergence of the differentiator

[0134]

[0135] Where sgn(x,k)=|x k *sign(x), α1, α2, α3, α4, α5, α6 are odd numbers, k1, k2, k3, k4, k5, k6 are positive numbers;

[0136] The fast and accurate differentiator is used to estimate the differential of the desired variable and provide information to the controller;

[0137] The input of the fast and accurate differentiator is q d =[q d0 q d1 q d2 q d3 ] T , the output is its derivatives of various orders

[0138] (2.3) Dilated Observer

[0139] As the core component of ADRC, the extended state observer can, on the one hand, track important state variables in the system to facilitate real-time understanding of the system status; on the other hand, it can estimate the uncertainty and external interference of the model through nonlinear feedback based on the total action of internal and external disturbances in the system model, and compensate the control quantity in real time; timely compensation in the form of feedback helps to improve the robustness of the system.

[0140] When considering model uncertainty and external disturbance, the modeling uncertainty and disturbance are abstracted as [δ q0 ,δ q1 ,δ q2 ,δ q3 ] T ,

[0141]

[0142] Simplify the model to

[0143]

[0144] The virtual control quantity is:

[0145]

[0146] In this method, the input state of ESO is q = [q0 q1 q2 q3] T

[0147] The input control quantity of ESO is the virtual control quantity virtual_control

[0148] The output of ESO is

[0149] Then compensate it into the control law to get the final control law

[0150]

[0151] (3) Proof of fixed time convergence and stability (3.1) Proof of controller stability

[0152] Analyze the designed composite sliding surface separately:

[0153]

[0154] A. Stability of Approaching Modes

[0155] For S1, consider choosing the following Lyapunov function The designed composite sliding surface, when the control law is

[0156] Then the following equation is satisfied under the approaching mode:

[0157]

[0158] For S2, consider choosing the following Lyapunov function The designed composite sliding surface, when the control law is Then the following equation is satisfied under the approaching mode:

[0159]

[0160] And there will be no singular phenomena, so the approach process is stable;

[0161] B. Stability of sliding modes

[0162] The designed composite sliding surface is analyzed separately

[0163] When the sliding surface is reached:

[0164]

[0165] Consider choosing the following Lyapunov function Derivative of V

[0166]

[0167] When reaching sliding surface 2:

[0168]

[0169] Also choose the following Lyapunov function Derivative of V

[0170]

[0171] (3.2) Proof of fixed-time convergence of controller

[0172] A. Convergence of Approaching Modes

[0173]

[0174] Let y = ln|s|, then s = e y

[0175]

[0176] Among them, s is the sliding surface variable, t0 is the initial time, t s It is the time taken for the initial state to converge to the sliding surface, that is, the time from s0 to s = 0;

[0177] B. Convergence of Sliding Mode

[0178] Sliding surface moment:

[0179] When the state vector converges to the sliding surface, the state vector satisfies the following relationship

[0180]

[0181] Among them, x0 is the state when reaching the sliding mode, x f1 is the end state of the first surface of the composite sliding surface, x f1 ∈[0,x0], which can be adjusted. It is essentially the intersection point of two sliding surfaces. You can choose a smooth intersection point as much as possible. s is the time taken for the above approach process, t f1 is the time to reach the first sliding surface and then slide to the first end state.

[0182] Sliding surface 2:

[0183]

[0184] The proof method is the same as the proof of the above-mentioned convergence law.

[0185] Let z = ln|x|, then x = e y

[0186]

[0187] x f2 It is the final state point of the entire sliding process, generally the origin, that is, it converges to the equilibrium point.

[0188] (3.3) Controller convergence time

[0189] From the above proof, we can see that when the initial state s0 is outside the switch line of the composite sliding surface, |s0|>δ, the state first approaches s1=0, and the convergence time of the approach process is t s It means that the state x0 is reached, and then the sliding mode s1 is reached along the sliding surface, and the state converges from x0 to x f1 , the convergence time is t f1 , at this time switch the sliding mode of s2 from x f1 Converges to the origin, the convergence time is t f2 .

[0190] When the initial state s0 is within the switching line of the composite sliding surface, |s0|≤δ, the state directly approaches s2=0, and the convergence time of the approach process is t s Indicates that reaching state x f1 Then, along the sliding mode of the sliding surface s2, from x f1 Converges to the origin, the convergence time is t f2 .

[0191] The total time to converge from any initial state to the set terminal state is

[0192]

[0193] The moment of inertia of the aircraft is selected as the AIM-9x body parameter J=diag([0.45,65,65]).

[0194] Controller parameter selection

[0195] k1=diag([5,5,5,5]),k2=diag([3,3,3,3]),λ=diag([5,5,5,5])

[0196] eta1=diag([5,5,5,5]), eta2=diag([10,10,10,10]), eta3=diag([5,5,5,5])

[0197] p=7,q=5,p2=3,q2=5

[0198] The effectiveness of the algorithm is verified based on the above specific parameters.

[0199] Example 1: STT control

[0200] For an axisymmetric aircraft, the control of over-the-shoulder launch only needs to control the pitch angle to 180°, that is, the controller test effect when the Euler angle is [180, 0, 0].

[0201] 1.1 In the absence of interference, the test results are as follows Figure 2 shown.

[0202] 1.2 When there is random disturbance torque, the test results are as shown in the attached Figure 3 shown.

[0203] The 180° and -180° jumps in the figure are essentially oscillations that are disturbed near the same angle.

[0204] Example 2: BTT Control

[0205] For a plane-symmetric aircraft, it is necessary to first control the pitch to rotate 180° and then roll 180°. In this case, it is ultimately equivalent to a yaw of 180°. That is, the expected Euler angle is first [180, 0, 0], and then [180, 0, 180] (ultimately equivalent to [0, 180, 0]) after the pitch rotates 180°. The controller test effect.

[0206] 2.1 In the absence of interference, the test results are as follows Figure 4 shown.

[0207] 2.2 When there is random disturbance torque, the test results are as shown in the attached Figure 5 shown.

[0208] The 180° and -180° jumps in the figure are essentially oscillations that are disturbed near the same angle.

[0209] This control algorithm framework and control design can also be used in the following scenarios: vertical flip of a fighter jet, programmed turning process of the initial vertical launch of a missile; the initial agile turning process of an aircraft or the over-the-shoulder launch process; terminal guidance and rapid maneuvering penetration of an offensive missile; and rapid attitude adjustment during the terminal interception process of an interceptor missile.

[0210] Example 3: Dynamic performance analysis, tracking frequency signals

[0211] Measure the frequency response of the controller to verify the rapidity of the controller's dynamic characteristics, and track the sinusoidal signal y(t) = π·sin(2t). The test results are shown in the attached figure. Figure 7 shown.

[0212] Fast exact differentiator test results are as follows Figure 8 , 9 As shown in Figure 10, it can be seen that the fast and accurate differentiator can quickly track the input signal and estimate its first-order derivative quickly. Since the second-order derivative itself has little effect on the controller, a slight lag in the second-order derivative estimation is also acceptable.

[0213] The extended observer estimates the quaternion state as Fig.11 As shown,

[0214] The extended observer estimates the disturbance and unknown quantities in the quaternion second-order derivative motion equation as follows: Fig.12 Shown

[0215] Monte Carlo simulation of the effect of changing controller parameters on convergence

[0216] The controller parameters are selected as follows, some variables are modified, and other parameters remain unchanged. Monte Carlo simulation is used to test the sensitivity of the controller to the parameters and the influence of the parameters on the convergence effect of the controller, such as Figures 13-15 shown.

[0217] η1=diag([5,5,5,5]), eta2=diag([10,10,10,10]), k1=diag([5,5,5,5]),

[0218] k2=diag([3,3,3,3]),λ=diag([5,5,5,5])

[0219] Example 4: Taking the over-the-shoulder launch of an AIM-9X missile in a vertical plane as an example, this case aims to demonstrate how to perform program angle design and the instantiation verification of the attitude control turning algorithm of this patent.

[0220] Program angle design and attitude control of AIM-9X missile over-the-shoulder launch in the vertical plane.

[0221] Simulation conditions: Altitude: 8km; initial speed: 0.8Mach; maximum angle of attack: 60°; initial ballistic inclination: 0°; initial attitude angle: (0°, 0°, 0°).

[0222] Firstly, the trajectory is designed based on the Gaussian pseudospectral method, with the angle of attack derivative as the control variable and the terminal constraint of the trajectory inclination angle of 180°. The desired pitch angle is optimized as the instruction.

[0223] Then, a command curve of pitch angle changing with time is obtained through fourth-order polynomial fitting.

[0224] Fitting results:

[0225] Finally, in the six-degree-of-freedom model, giving instructions to the controller to track can achieve over-the-shoulder launch.

[0226] The angle of attack and trajectory inclination calculated by Gaussian pseudospectral method are as follows: Fig.16 The pitch angle command designed by Gaussian pseudo-spectral method is shown as Fig.17 The pitch angle command of the 4th order polynomial fitting is as follows: Fig.18 The ideal trajectory of over-the-shoulder firing is as follows. Fig.19 shown.

Claims

1. A quaternion-based fixed-time agile turning attitude control method for an aircraft, characterized by: The method is as follows: first, the derivatives of each order of the tracking signal are estimated through a fast and accurate differentiator to obtain more input information, and then a fixed-time variable structure composite sliding mode controller is used to generate the control torque. In the process of dynamic control, an extended observer is used to estimate the external disturbance of the system and the uncertainty of internal modeling to compensate for it in the controller, thereby introducing interference information into the controller.

2. The quaternion-based fixed-time agile turning attitude control method for an aircraft according to claim 1, characterized in that: The method is specifically as follows: (1) Establishing a system dynamics model The attitude dynamics equation for rotation around the center of mass is as follows: Among them, J x ,J y ,J z is the moment of inertia of the aircraft about each coordinate axis of the missile body coordinate system, ω x ,ω y ,ω z is the selected angular velocity of the aircraft body coordinate system relative to the reference inertial system, M x ,M y ,M z is the control torque; The kinematic model uses a mathematical relationship based on quaternions, and the current posture quaternion is q = [q0 q1 q2 q3] T ; q0 is the scalar part of the attitude quaternion, q1, q2, q3 are the vector parts of the attitude quaternion respectively; Among them, the relationship between the derivative of the current attitude quaternion and the attitude angle angular velocity is as follows: From equations (1) and (2), we can get in, M=[M x ,M y ,M z ] T (2) Design of fixed-time fast non-singular sliding mode control algorithm (2.1) Fixed-time fast non-singular sliding mode control law The current posture quaternion is q = [q0 q1 q2 q3] T , the desired attitude quaternion is q d =[q d0 q d1 q d2 q d3 ] T ; Define state variable x = qq d ,but Design the composite non-singular fixed-time convergent composite sliding surface as follows: in, p,q are odd numbers, and x is qq d , quaternion error, sliding surface parameters λ>0, m>0, n>0, switching line δ∈(0,1) of the composite sliding surface, k1>0, k2>0, p, q are odd numbers greater than 0; The designed sliding mode reaching law is: Among them, p2,q2 are positive odd numbers, It can be less than 1, v is a reaching law, and η1 and η2 are positive numbers; The control law is obtained by feedback linearization: Where, E = f(q) g(J); Since the E matrix is ​​a 4×3 column-full matrix, the inverse operation needs to be replaced by the pseudo-inverse operation, and the formula is as follows: AND -1 =(And T ·AND) -1 ·AND T (2.2) Fast and accurate differentiator In order to make full use of the controller input signal, that is, the information of the desired angle, and integrate it into the controller; Make an estimate; design the input variable of the differentiator to be u = q d , the output variable is The following control law is used to ensure the convergence of the differentiator Where sgn(x,k)=|x k *sign(x), α1, α2, α3, α4, α5 are odd numbers, k1, k2, k3, k4, k5 are positive numbers; The input of the fast and accurate differentiator is q d =[q d0 q d1 q d2 q d3 ] T , the output is its derivatives of various orders (2.3) Dilated Observer When considering model uncertainty and external disturbance, the modeling uncertainty and disturbance are abstracted as a whole Simplify the model to The virtual control quantity is: In this method, the input state of ESO is q = [q0 q1 q2 q3] T The input control quantity of ESO is the virtual control quantity virtual_control The output of ESO is Then compensate it into the control law to get the final control law 3. The quaternion-based fixed-time agile turning attitude control method for an aircraft according to claim 1 or 2, characterized in that: The method is used for a control system of an initial program turning section for realizing large off-axis launch and over-the-shoulder launch of a fourth-generation air-to-air missile, a program turning process of an initial vertical launch of a missile, an initial agile turning process of an air-to-air missile or an over-the-shoulder launch process, a terminal guidance rapid maneuvering penetration of an attacking missile, or a rapid attitude adjustment during a terminal interception of an intercepting missile.

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