A tracking derivative control guidance method for high dynamic vehicles

Abstract

The application discloses a tracking differential control guidance method applied to a high-dynamic aircraft, which is guided and controlled by a three-dimensional guidance model considering the dynamic characteristics of an autopilot, can optimize the "differential expansion" problem generated in a traditional backstepping control process, and compared with a dynamic surface guidance law applying a first-order low-pass filter to solve the problem, the guidance control method adopts a tracking differentiator to perform differential processing on a virtual control variable generated in a backstepping design process, so that the obtained result has higher precision, thereby generating higher control precision, and realizing the guidance control with higher precision.

Description

Technical Field

[0001] This invention relates to guidance and control of highly dynamic aircraft, and more specifically to a tracking differential control guidance method for highly dynamic aircraft. Background Technology

[0002] In recent years, with the enhancement of target mobility and defense capabilities, research on guidance methods has gradually deepened. The classic proportional guidance method is difficult to design guidance methods for multi-order guidance models that take into account the dynamic characteristics of autopilots.

[0003] Traditional backstepping control methods use direct differentiation to solve for the derivatives of the virtual control variables needed in the next design step. However, when the virtual control variables change rapidly, direct differentiation causes the solved derivative variables to "expand" rapidly, affecting the control process.

[0004] Although dynamic surface control methods can filter virtual control variables to obtain the derivatives of approximate virtual control variables for the next step, the accuracy is difficult to guarantee, making it difficult to apply in practical engineering.

[0005] For the reasons mentioned above, the inventors have conducted in-depth research on guidance methods for tracking targets by high-dynamic aircraft, in order to design a differential control guidance method for tracking high-dynamic aircraft that can solve the above problems. Summary of the Invention

[0006] To overcome the above problems, the inventors conducted intensive research and designed a tracking differential control guidance method for high-dynamic aircraft. This method uses a three-dimensional guidance model that considers the dynamic characteristics of the autopilot for guidance control, which can optimize the "differential expansion" problem generated in the traditional backstepping control process. At the same time, compared with the dynamic surface guidance law that uses a first-order low-pass filter to solve the same problem, the guidance control method uses a tracking differentiator to differentiate the virtual control variables generated in the backstepping design process, resulting in higher accuracy of the obtained results and thus higher control accuracy, achieving higher precision guidance control; thus completing the present invention.

[0007] Specifically, the purpose of this invention is to provide a tracking differential control guidance method for high-dynamic aircraft.

[0008] In this guidance method, control commands for the aircraft are obtained in real time and transmitted to the servo motors on the aircraft. The servo motors then operate according to the control commands to adjust the aircraft's flight state, thereby enabling the aircraft to hit the target.

[0009] The control command is obtained through the following formula (a):

[0010]

[0011] Where u represents a control command.

[0012] K3 represents the design parameters.

[0013] s3 indicates error surface three.

[0014] ξ represents the damping ratio.

[0015] ω n Indicates the undamped natural frequency.

[0016] x3 represents the first derivative of the normal acceleration of the aircraft along the line of sight between the aircraft and the target.

[0017] x2 represents the normal acceleration of the aircraft along the line of sight between the aircraft and the target.

[0018] The dummy variable derivative represents the first derivative of the normal acceleration of the tracking aircraft along the line of sight to the target.

[0019] The error surface s3 is obtained by the following formula (ii):

[0020] s3 = x3 - x 3d (two)

[0021] Where x3 represents the first derivative of the aircraft's normal acceleration along the line of sight between the aircraft and the target; Indicates a Mε The derivative; Indicates a Mη The derivative of a Mε a represents the component of the aircraft's acceleration on the Y-axis in the line-of-sight coordinate system. Mη This represents the component of the aircraft's acceleration on the Z-axis in the line-of-sight coordinate system;

[0022] x 3d This represents the virtual control variable that needs to be tracked in x3.

[0023] Wherein, the x 3d We obtain it through the following formula (iii):

[0024]

[0025] Where K2 represents the design parameters,

[0026] s2 represents error surface two.

[0027] x represents the value obtained by the tracking differentiator. 2d The derivative of .

[0028] The error surface s2 is obtained by the following equation (iv):

[0029] s2=x2-x 2d (Four)

[0030] Where x2 represents the normal acceleration of the aircraft along the line of sight to the target; x2 = [a Mε a Mη ] T ;a Mε a represents the component of the aircraft's acceleration on the Y-axis in the line-of-sight coordinate system. Mη This represents the component of the aircraft's acceleration on the Z-axis in the line-of-sight coordinate system;

[0031] x 2d This represents the virtual control variable that needs to be tracked in x2.

[0032] Wherein, the x 2d Obtained through the following formula (5):

[0033] x 2d =K1s1+f(x1)+d (V)

[0034] Where K1 represents the design parameters,

[0035] s1 represents error surface one.

[0036] f(x1) represents the polynomial term in the nonlinear system excluding the design variables and unknown variables.

[0037] d represents the normal acceleration of the target along the line of sight between the aircraft and the target. Preferably, d = [a Tε a Tη ] T ;a Tε a represents the component of the target's acceleration on the Y-axis in the line-of-sight coordinate system. Tη This represents the component of the target's acceleration along the Z-axis in the line-of-sight coordinate system.

[0038] The error surface s1 is obtained by the following equation (vi):

[0039] s1 = x1 - 0 (VI)

[0040] Where x1 represents the normal relative velocity between the aircraft and the target along the line of sight; x1 = [V ε V η ] T Vε represents the Y-axis component of the relative velocity between the aircraft and the target in the line-of-sight coordinate system. η This represents the component of the relative velocity between the aircraft and the target on the Z-axis in the line-of-sight coordinate system.

[0041] Wherein, f(x1) is obtained by the following equation (VII):

[0042]

[0043] Among them, V r This represents the component of the relative velocity between the aircraft and the target on the X-axis in the line-of-sight coordinate system.

[0044] V ε This represents the component of the relative velocity between the aircraft and the target on the Y-axis in the line-of-sight coordinate system.

[0045] V η This represents the Z-axis component of the relative velocity between the aircraft and the target in the line-of-sight coordinate system.

[0046] ε represents the line-of-sight angle relative to the target with the aircraft as the origin;

[0047] r represents the relative distance between the aircraft and the target.

[0048] The beneficial effects of this invention include:

[0049] The tracking differential control guidance method for high-dynamic aircraft provided by the present invention uses a tracking differentiator to differentiate the virtual control variables generated during the backstepping design process, so that the obtained results have higher accuracy, thereby producing higher control accuracy and realizing higher precision guidance control. Attached Figure Description

[0050] Figure 1 The virtual control quantity x is shown in the embodiments and comparative examples of this application. 2d Schematic diagram showing changes over time;

[0051] Figure 2 The virtual control quantity x is shown in the embodiments and comparative examples of this application. 3d A diagram illustrating the changes over time. Detailed Implementation

[0052] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0053] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0054] According to the tracking differential control guidance method for high-dynamic aircraft provided by the present invention, the control command of the aircraft is obtained in real time, and the control command is transmitted to the servo motor on the aircraft. The servo motor operates according to the control command to adjust the flight state of the aircraft, thereby enabling the aircraft to hit the target.

[0055] The control command is obtained by using a three-dimensional guidance model that considers the dynamic characteristics of the driver's instrument. The control command is represented by u = [u...]. ε u η ] T It means, u ε This represents the control command in the pitch direction within the line-of-sight coordinate system, u. η This indicates the control command in the yaw direction in the line-of-sight coordinate system.

[0056] In a preferred embodiment, the control command is obtained by the following formula (a):

[0057]

[0058] Where u represents a control command.

[0059] K3 represents the design parameter, and its preferred value is 8;

[0060] s3 indicates error surface three.

[0061] ξ represents the damping ratio, and its preferred value is 0.8;

[0062] ω n This represents the undamped natural frequency, and its preferred value is 220.

[0063] x3 represents the first derivative of the aircraft's normal acceleration along the line of sight between the aircraft and the target.

[0064] x2 represents the normal acceleration of the aircraft along the line of sight between the aircraft and the target.

[0065] The dummy variable derivative represents the first derivative of the normal acceleration of the tracking aircraft along the line of sight of the target.

[0066] In a preferred embodiment, the error surface s3 is obtained by the following equation (ii):

[0067] s3 = x3 - x 3d (two)

[0068] Where x3 represents the first derivative of the normal acceleration of the aircraft along the line of sight between the aircraft and the target; preferably,

[0069] x 3dThis represents the virtual control variable that needs to be tracked in the nonlinear system x3.

[0070] In this application, in the line-of-sight coordinate system formed by the aircraft and the target, (a Tr ,a Tε ,a Tη (a) represents the target's acceleration. Mr ,a Mε ,a Mη The acceleration of the aircraft is represented by , and the relative velocity between the aircraft and the target can be expressed as:

[0071]

[0072] Indicates a Mε The derivative; Indicates a Mη The derivative of .

[0073] Preferably, the line-of-sight coordinate system formed by the aircraft and the target is defined as follows: with the center of gravity of the aircraft as the origin, the line connecting the center of gravity of the aircraft and the center of gravity of the target as the X-axis, the direction from the aircraft to the target as positive, the yaw direction of the aircraft as the Y-axis and the pitch direction of the aircraft as the Z-axis during the flight of the aircraft along the X-axis.

[0074] In a preferred embodiment, the x 3d Obtained through the following formula (iii):

[0075]

[0076] Wherein, K2 represents the design parameter, and preferably, its value is 6;

[0077] s2 represents error surface two.

[0078] x represents the value obtained by the tracking differentiator. 2d The derivative of .

[0079] The tracking differentiator can be represented as:

[0080]

[0081] Where R2 takes the value 20; the function F(·) can be expressed as:

[0082] F(h1,h2)=υ(h1)+υ(h2)

[0083]

[0084] constant a i >0, (i=2,3);

[0085] By tracking the differentiator, we can obtain... Approximate value z 22 In this application, To replace.

[0086] In a preferred embodiment, the error surface s2 is obtained by the following equation (iv):

[0087] s2=x2-x 2d (Four)

[0088] Where x2 represents the normal acceleration of the aircraft's line of sight to the target; x2 = [a Mε a Mη ] T ;

[0089] x 2d This represents the virtual control variable that needs to be tracked in x2.

[0090] In a preferred embodiment, the x 2d Obtained through the following formula (5):

[0091] x 2d =K1s1+f(x1)+d (V)

[0092] Where K1 represents the design parameters,

[0093] s1 represents error surface one.

[0094] f(x1) represents the polynomial term in the nonlinear system excluding the design variables and unknown variables.

[0095] d represents the normal acceleration of the target along the line of sight between the aircraft and the target. Preferably, d = [a Tε a Tη ] T .

[0096] In a preferred embodiment, the error surface s1 is obtained by the following equation (vi):

[0097] s1 = x1 - 0 (VI)

[0098] Where x1 represents the normal relative velocity between the aircraft and the target along the line of sight; x1 = [V ε V η ] T .

[0099] In a preferred embodiment, f(x1) is obtained by the following equation (vii):

[0100]

[0101] Among them, V r This represents the component of the relative velocity between the aircraft and the target on the X-axis in the line-of-sight coordinate system.

[0102] V ε This represents the component of the relative velocity between the aircraft and the target on the Y-axis in the line-of-sight coordinate system.

[0103] V η This represents the Z-axis component of the relative velocity between the aircraft and the target in the line-of-sight coordinate system.

[0104] ε represents the line-of-sight angle relative to the target with the aircraft as the origin;

[0105] r represents the relative distance between the aircraft and the target.

[0106] Experimental Example

[0107] The initial position of the aircraft is (0 0 0), the initial position of the target is (3km 3km 3km), the initial velocity of the aircraft is 600m / s, and the target has a sinusoidal acceleration, a. T =(0 0-20sin(πt / 2)m / s 2 ),

[0108] The tracking differential control guidance method for high-dynamic aircraft is adopted for guidance and control of the aircraft, wherein the control command is obtained in real time through the following equation (I):

[0109]

[0110] Among them, the error surface 3s3 is obtained by the following formula (ii):

[0111] s3 = x3 - x 3d (two)

[0112] x 3d Obtained through the following formula (iii):

[0113]

[0114] Error surface 2 s2 is obtained by the following equation (iv):

[0115] s2=x2-x 2d (Four)

[0116] x 2d Obtained through the following formula (5):

[0117] x 2d =K1s1+f(x1)+d (V)

[0118] Error surface s1 is obtained by the following equation (vi):

[0119] s1 = x1 - 0 (VI)

[0120] f(x1) is obtained through the following equation (VII):

[0121]

[0122] The design parameters K1 is set to 4, K2 to 6, and K3 to 8; ω n ξ indicates that the undamped natural frequency is 220 Hz; ξ indicates that the damping ratio is 0.8.

[0123] The final accuracy of the guidance terminal was 0.073m.

[0124] Comparative Example

[0125] Based on the exact same initial conditions as the experimental example, namely, the initial position of the aircraft is (0 0 0), the initial position of the target is (3km 3km 3km), the initial velocity of the aircraft is 600m / s, and the target has a sinusoidal acceleration, a T =(00 -20sin(πt / 2)m / s 2 ),

[0126] The guidance law DSCG designed using the traditional dynamic surface control method was used to guide and control the aircraft, and the final guidance terminal accuracy was 0.178m.

[0127] Furthermore, the intermediate variables required for the control command, i.e., the virtual control quantity, are obtained from the experimental and comparative examples, and this virtual control quantity x is continuously tracked. 2d =[x 2dε x 2dη ] T x 3d =[x 3dε x 3dη ] T The virtual control quantity obtained in Experiment Example 1 is represented by the letter TDG, which is the blue dashed line in the figure. In the comparative example, the virtual control quantity corresponding to DSCG is the green dotted line.

[0128] The results of retrieving virtual control quantities are as follows Figure 1 and Figure 2 As shown, according to the retrieved results, the approximate value of the virtual control variable obtained by using the TDG guidance method is closer to the original variable than the approximate value in DSCG, which further ensures the accuracy of the entire control process and thus achieves a better guidance effect.

[0129] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A tracking differential control guidance method for a high dynamic aircraft, characterized in that, in the guidance method, a control command of the aircraft is obtained in real time, and the control command is transmitted to a rudder on the aircraft in real time, the rudder works according to the control command to adjust the flight state of the aircraft, so that the aircraft hits the target; the control command is obtained by the following formula (I): Wherein, u represents the control command, K3 represents a design parameter, s3 represents an error surface three, ξ represents a damping ratio, ω n represents the undamped natural frequency, x3 represents the first derivative of the normal acceleration of the line of sight of the aircraft on the line of sight of the aircraft and the target, x2 represents the normal acceleration of the line of sight of the aircraft on the line of sight of the aircraft and the target, virtual variable derivative representing the first derivative of the aircraft line-of-sight acceleration on the line-of-sight of the aircraft to the target; the error surface three s3 is obtained by the following formula (II): where x3represents the first derivative of the aircraft normal acceleration on the line of sight to the target; represents the derivative of a Mε represents the derivative of a Mη represents the derivative of a Mε represents the component of the aircraft acceleration in the Y axis in the line of sight coordinate system; Mη represents the component of the aircraft acceleration in the Z axis in the line of sight coordinate system;​ x 3d virtual control variables that the variables in x3 need to track; The x 3d By the following formula (three): Wherein, K2 represents a design parameter, s2 represents an error surface two, represents the derivative of x 2d obtained by tracking differentiator.

2. The tracking differential control guidance method for a high dynamic aircraft according to claim 1, characterized in that, the error surface two s2 is obtained by the following formula (IV): s2 = x2 - x 2d (iv) where x2represents the normal acceleration of the aircraft on the line of sight to the target; x2= [a Mε a Mη ] Τ ; a Mε represents the component of the acceleration of the aircraft in the Y axis in the line of sight coordinate system, a Mη represents the component of the acceleration of the aircraft in the Z axis in the line of sight coordinate system; x 2d x2represents the virtual control variables that the variables need to track.

3. The tracking differential control guidance method for a high dynamic aircraft according to claim 2, characterized in that, The x 2d By the following formula (five): x 2d = K1s1+ f(x1) + d(five) wherein K1 represents a design parameter, s1 represents an error surface one, f(x1) represents a polynomial term of a non-linear system except design variables and unknown variables, d represents the normal acceleration of the target on the line of sight of the aircraft and the target, d = [a Tε a Tη ] Τ ; aTε represents the component of the acceleration of the target in the line of sight coordinate system on the Y axis, a Tη represents the component of the acceleration of the target in the line of sight coordinate system on the Z axis.

4. The tracking differential control guidance method for a high dynamic aircraft according to claim 3, characterized in that, the error surface one s1 is obtained by the following formula (VI): s1 = x1-0 (VI) wherein x1represents the normal relative velocity of the aircraft and the target on the line of sight, x1=[V ε V η ] Τ ; V represents the component of the relative velocity of the aircraft and the target in the Y axis in the line of sight coordinate system, V η represents the component of the relative velocity of the aircraft and the target in the Z axis in the line of sight coordinate system.

5. The tracking differential control guidance method for a high dynamic aircraft according to claim 3, characterized in that, the f(x1) is obtained by the following formula (VII): where V r represents the component of the relative velocity of the aircraft and the target in the line-of-sight coordinate system in the X axis; V ε represents the component of the relative velocity of the aircraft and the target in the line-of-sight coordinate system in the Y axis; V η represents the component of the relative velocity of the aircraft and the target in the line-of-sight coordinate system in the Z axis; ε represents the angle of the line of sight of the aircraft relative to the target with the aircraft as the origin; r represents the relative distance between the aircraft and the target.

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