A vehicle-mounted two-axis servo control method based on asymmetric cross coupling

Abstract

This invention discloses a vehicle-mounted two-axis servo control method based on asymmetric cross-coupling, comprising: real-time acquisition of azimuth and pitch disturbance angular rates of a two-axis turntable; obtaining filtered azimuth and pitch disturbance angular rates using filters; obtaining azimuth and pitch disturbance angles using integrators; constructing a command planning controller to obtain azimuth and pitch rotation angles; obtaining the pitch axis compensation coefficient based on the target trajectory curve and constructing a cross-coupling controller; constructing azimuth and pitch position controllers and obtaining azimuth and pitch speed control commands; obtaining azimuth and pitch disturbance compensation angular velocities corresponding to the filtered azimuth and pitch disturbance angular rates; and using an asymmetric cross-coupling strategy to decouple and compensate the azimuth and pitch axis speed input commands to achieve the following motion of the target trajectory curve. This method can effectively compensate for position deviations caused by disturbances, improve the synchronization performance of the two axes, and exhibit good dynamic response and stability.

Description

Technical Field

[0001] This invention belongs to the field of multi-axis servo control technology, specifically relating to a vehicle-mounted two-axis servo control method based on asymmetric cross coupling. Background Technology

[0002] A two-axis rotary table is a precision mechanical device that enables rotational motion on two mutually perpendicular axes. These two axes are commonly referred to as the azimuth axis and the elevation axis, corresponding to rotation in the horizontal and vertical directions, respectively.

[0003] Two-axis turntables are precision rotating devices specifically designed for installation on vehicles. They are used to support and manipulate various types of sensors, cameras, antennas, weapon systems, and other equipment. They provide stable and precise aiming, tracking, and smooth operation while the vehicle is in motion, ensuring these devices can effectively perform their functions. These turntables are widely used in security monitoring, emergency response, scientific research, and other fields.

[0004] The vehicle-mounted two-axis servo system is introduced into the design of two-axis turntables as a key active control system. This system ensures that the load can maintain a stable attitude under various dynamic conditions and can quickly follow commands by precisely controlling the relative motion between two key axes (usually the pitch axis and the azimuth axis).

[0005] In such vehicle-mounted two-axis servo systems, tracking accuracy and anti-interference capability are crucial performance indicators, typically used to evaluate the system's dynamic response and stability. These systems usually mount load devices, such as optical sights or weapon systems, on the pitch axis. The testing method involves sending a pre-set target curve command from a host computer to control the load device to perform precise curved movements, while simultaneously applying disturbances to the base of the two-axis platform. This method comprehensively evaluates the response speed and stability of the vehicle-mounted two-axis servo system, ensuring it maintains high performance under complex dynamic conditions.

[0006] Two main problems need to be addressed in this type of testing. The first is maintaining the stable pointing of the laser pointer on the pitch axis under disturbances. The traditional approach is to install an inertial measurement unit (IMU) on the vehicle body, measuring the vehicle's attitude angles and combining this with coordinate transformation to stabilize the laser pointer's pointing in inertial space. While this method provides some stability in certain applications, it has significant shortcomings in applications with high precision and real-time requirements. The communication cycle of traditional IMUs is typically limited to a few hundred hertz (Hz), which is particularly insufficient in high-precision control systems requiring millisecond-level response. The low data update rate leads to feedback lag in the control system, thus affecting the overall control performance and stability. Furthermore, to convert attitude information in the vehicle's coordinate system into pointing in inertial space, traditional methods rely on complex floating-point matrix operations. This not only increases the processor load but also significantly prolongs the execution time of the control algorithm, making it difficult to meet the extremely high real-time requirements of applications.

[0007] In addition to the above, a common approach to the first problem is to use a rate gyroscope to integrate the disturbance angular rate into an angle and then compensate for it. While this method provides a relatively simple and intuitive way to perform attitude compensation and can be effective in certain scenarios, its inherent integral delay and accumulated error problems limit its performance under high-precision and fast-response requirements. The second problem is how to effectively reduce contour errors during two-axis coordinated motion. Traditional methods use two-axis synchronization algorithms, such as cross-coupling control, to reduce contour errors. Conventional cross-coupling algorithms perform poorly when handling complex trajectories (such as sine curves), especially at key points of the trajectory (such as peaks and troughs), where large contour errors tend to occur. This not only affects the tracking accuracy of the system but may also lead to a slow and unsmooth system response. Therefore, an onboard two-axis servo control method based on asymmetric cross-coupling is proposed. Summary of the Invention

[0008] The purpose of this invention is to address the above-mentioned problems by proposing an on-board two-axis servo control method based on asymmetric cross coupling, which can improve the dynamic response capability and stability of the two-axis turntable.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] This invention proposes an on-board two-axis servo control method based on asymmetric cross-coupling, applied to a two-axis turntable. The two-axis turntable is mounted on the vehicle body and used to drive the load to rotate around the azimuth and pitch axes, which are perpendicular. The on-board two-axis servo control method based on asymmetric cross-coupling includes:

[0011] S1. Real-time acquisition of azimuth and pitch disturbance angular rates of the two-axis turntable;

[0012] S2. Input the output signal of the first filter from the previous moment, the azimuth disturbance angular rate, and the current azimuth disturbance angular rate into the first filter for filtering to obtain the filtered azimuth disturbance angular rate ω at the current moment. yf The output signal of the second filter from the previous moment, along with the pitch disturbance angular rate and the current pitch disturbance angular rate, are input into the second filter for filtering to obtain the filtered pitch disturbance angular rate ω at the current moment. pf ;

[0013] S3. Integrate the azimuth and pitch disturbance angular rates from time zero to the current time using an integrator to obtain the azimuth disturbance angle θ at the current time. yt and pitch disturbance angle θ pt ;

[0014] S4. Construct a command planning controller. The command planning controller is used to obtain the current orientation rotation angle of the two-axis turntable based on the target trajectory curve. And pitch and rotation angle β;

[0015] S5. Obtain the pitch axis compensation coefficient K at the current moment based on the target trajectory curve. cy And construct a cross-coupled controller;

[0016] S6. Construct the azimuth position controller and pitch position controller, and record the current azimuth rotation angle. Azimuth disturbance angle θ yt The azimuth angular displacement is used as the input to the azimuth position controller to obtain the azimuth velocity control command ω at the current moment. yu The current pitch rotation angle β and pitch disturbance angle θ are used to determine the current pitch angle rotation angle β and pitch disturbance angle θ. pt The pitch angular displacement is used as the input to the pitch position controller to obtain the pitch velocity control command ω at the current moment. pu ;

[0017] S7. Based on the filtered azimuth perturbation angular rate ω at the current moment yf and the filtered pitch disturbance angular rate ω pf This corresponds to obtaining the azimuth disturbance compensation angular velocity ω at the current moment. yc and pitch disturbance compensation angular velocity ω pc ;

[0018] S8. An asymmetric cross-coupling strategy is used to decouple and compensate the azimuth and pitch axis velocity input commands at the current moment, achieving the target trajectory curve following motion. The asymmetric cross-coupling strategy involves decoupling and compensating the azimuth axis by an amount ω. ys As the azimuth axis velocity input command, the pitch axis decoupling compensation amount ω ps As the pitch axis speed input command, where:

[0019] Azimuth axis decoupling compensation amount ω ys The formula is as follows:

[0020] ω ys =ω yu -ω yc +C x *u

[0021] Pitch axis decoupling compensation ω ps The formula is as follows:

[0022] ω ps =ω pu -ω pc +K cy *u

[0023] In the formula, C x denoted as the azimuth cross-coupling factor, and u is the output of the cross-coupling controller.

[0024] Preferably, the two-axis turntable includes a platform, an azimuth ring, a pitch support, a pitch mount, a first fiber optic gyroscope, a second fiber optic gyroscope, a first motor, a second motor, a first driver, and a second driver. The platform is connected to the vehicle body. The first motor is mounted on the platform and drives the azimuth ring to rotate around the azimuth axis. The pitch support is connected to the azimuth ring. The second motor is mounted on the pitch support and drives the pitch mount to rotate around the pitch axis. The first fiber optic gyroscope is connected to the platform, and the second fiber optic gyroscope is connected to the pitch support. The first driver is electrically connected to the first motor, and the second driver is electrically connected to the second motor. The detection result of the first fiber optic gyroscope is the azimuth axis disturbance angular rate, and the detection result of the second fiber optic gyroscope is the pitch axis disturbance angular rate.

[0025] Preferably, both the first filter and the second filter are bilinear low-pass filters, and perform the following operations:

[0026] S21. The analog transfer function H(s) is established using a first-order Butterworth low-pass filter, as shown in the following formula:

[0027]

[0028] In the formula, ω c Let ω be the cutoff angular frequency, and ω c =2πf c fc Let s be the cutoff frequency, and s be the first complex variable;

[0029] S22, Calculate the frequency pre-distortion ω a The formula is as follows:

[0030]

[0031] In the formula, ω d For the ideal discrete-time angular frequency, and ω d =2πf c T is the sampling period;

[0032] S23. Replace the cutoff angular frequency ω in the analog transfer function H(s). c Frequency predistortion ω a The first complex variable s is The discrete transfer function H(z) is obtained by performing a bilinear transformation, as shown in the following formula:

[0033]

[0034] In the formula, z is the second complex variable;

[0035] S24. Establish the difference equation:

[0036] Let the first intermediate variable The discrete transfer function H(z) is then expressed as:

[0037]

[0038] because Where X(z) is the input signal after z-transformation, and Y(z) is the output signal after z-transformation, we can obtain:

[0039]

[0040] Then, an inverse z-transform is performed, that is, y[t] replaces Y(z), x[t] replaces X(z), and x(t-1) replaces X(z). -1 y(t-1) replaces Y(z)z -1 The difference equation can then be obtained, as shown in the following formula:

[0041]

[0042] In the formula, y[t] is the output signal of the filter at time t, y[t-1] is the output signal of the filter at time t-1, x[t] is the input signal of the filter at time t, x[t-1] is the input signal of the filter at time t-1, and z -1 Let z be the -1 power of the second complex variable;

[0043] S25. Obtain the filtered azimuth disturbance angular rate and the filtered pitch disturbance angular rate at the current moment respectively, based on the difference equation, as the output signals of the corresponding filters, where:

[0044] Filtered azimuth perturbation angular velocity ω at time t yf [t], the formula is as follows:

[0045]

[0046] Filtered pitch disturbance angular rate ω at time t pf [t], the formula is as follows:

[0047]

[0048] In the formula, ω yf [t-1] represents the filtered azimuth perturbation angular velocity at time t-1, ω yt [t] represents the azimuth perturbation angular velocity at time t, ω yt [t-1] represents the azimuth perturbation angular velocity at time t-1, ω pf [t-1] represents the filtered pitch disturbance angular rate at time t-1, ω pt [t] represents the pitch disturbance angular rate at time t, ω pt [t-1] represents the pitch disturbance angular rate at time t-1.

[0049] Preferably, the azimuth disturbance angular rate and pitch disturbance angular rate from time zero to the current time are integrated using an integrator to obtain the azimuth disturbance angle θ at the current time. yt and pitch disturbance angle θ pt The details are as follows:

[0050] azimuth perturbation angle θ at time t yt (t), the formula is as follows:

[0051]

[0052] Pitch angle θ at time t pt (t), the formula is as follows:

[0053]

[0054] In the formula, ω yt [n] represents the azimuth perturbation angular velocity at time n, ω pt [n] represents the pitch disturbance angular rate at time n, where n = 0 to t, and f is the sampling frequency.

[0055] Preferably, the instruction planning controller performs the following operations:

[0056] S41. Establish a target coordinate system o1x1y1 on the projection plane where the target trajectory curve is located. The origin o1 of the target coordinate system is the point on the projection plane pointed to by the load of the two-axis turntable in the initial state. The vertical upward is the y1 axis and the horizontal rightward is the x1 axis.

[0057] S42. A fixed-period sampling method is used to sample the target trajectory curve to obtain several sampling points and the coordinates of the corresponding sampling points;

[0058] S43. Calculate the azimuth rotation angle at the current moment based on the coordinates of the current sampling point P. And the pitch rotation angle β, the formula is as follows:

[0059]

[0060] l′ 2 =x 2 +l 2

[0061] In the formula, l is the distance between the load and the projection plane and is a constant, l′ is the second intermediate variable, (x0, y0) is the coordinate of the current sampling point P, x0 is the abscissa of the current sampling point P, y0 is the ordinate of the current sampling point P, and the current time is the time to reach the current sampling point P, which is also the target point at the current time.

[0062] Preferably, based on the filtered azimuth perturbation angular rate ω at the current moment yf and the filtered pitch disturbance angular rate ω pf This corresponds to obtaining the azimuth disturbance compensation angular velocity ω at the current moment. yc and pitch disturbance compensation angular velocity ω pc ,in:

[0063] Current azimuth disturbance compensation angular velocity ω yc The formula is as follows:

[0064] ω yc =K u1 *ω yf

[0065]

[0066] In the formula, K u1 R is the azimuth angular rate compensation coefficient. y K1 is the gear ratio of the first motor, K1 is the azimuth compensation proportional control coefficient, the unit of azimuth disturbance compensation angular velocity is 0.0001 rps, and the unit of filtered azimuth disturbance angular rate is ° / s.

[0067] The pitch disturbance compensation angular velocity ω at the current moment pc The formula is as follows:

[0068] ω pc =K u2 *ω pf

[0069]

[0070] In the formula, K u2 R is the pitch angular rate compensation coefficient. p K is the gear ratio of the second motor, K2 is the pitch compensation proportional control coefficient, the pitch disturbance compensation angular velocity is in units of 0.0001 rps, and the filtered pitch disturbance angular rate is in units of ° / s.

[0071] Preferably, the cross-coupled controller is constructed as follows:

[0072] S51. Calculate the contour error ε at the current moment, using the following formula:

[0073] ε=-sinθ*e y +cosθ*e p

[0074] In the formula, ε represents the actual arrival point P at the current time. r To the target point P t The distance between the secants, e y For azimuth tracking error, e p The pitch tracking error is θ, where θ is the target point P at the current moment. t The angle between the secant and the x-axis of the target coordinate system;

[0075] S52, Assume ε = -C x *e y +C y *e p And based on the formula in step S51, the mathematical expression for the cross-coupling factor is obtained:

[0076] C x =sinθ,C y =cosθ

[0077] In the formula, the cross-coupling factor includes the azimuth cross-coupling factor C. x and pitch cross-coupling factor C y ;

[0078] S53. Obtain the output of the cross-coupled controller at the corresponding time according to the cross-coupling control algorithm. The cross-coupling control algorithm adopts the PID control algorithm, and its mathematical expression is as follows:

[0079]

[0080] In the formula, u(t) is the output of the cross-coupled controller at time t, ε(t) is the input of the cross-coupled controller at time t, i.e., the profile error at time t. Similarly, ε(i) is the input of the cross-coupled controller at time i, i = 0 to t-1, ε(t-1) is the input of the cross-coupled controller at time t-1, and k p k is the proportional coefficient of the cross-coupled controller. i k represents the integral coefficient of the cross-coupled controller. d These are the differential coefficients of the cross-coupled controller.

[0081] Preferably, the pitch axis compensation coefficient K is obtained based on the target trajectory curve at the current moment. cy The formula is as follows:

[0082]

[0083] In the formula, y t Let P be the target point at time t. t The ordinate, y t-1 Let P be the target point at time t-1. t-1 The ordinate is H, where H is the proportional adjustment coefficient, and the target point P at time t is... t and the target point P at time t-1 t-1 All of these are points on the target trajectory curve.

[0084] Preferably, both the azimuth position controller and the pitch position controller are PID controllers.

[0085] Preferably, the current azimuth is rotated by an angle. Azimuth disturbance angle θ yt The azimuth angular displacement is used as the input to the azimuth position controller to obtain the azimuth velocity control command ω at the current moment. yu The current pitch rotation angle β and pitch disturbance angle θ are used to determine the current pitch angle rotation angle β and pitch disturbance angle θ. pt The pitch angular displacement is used as the input to the pitch position controller to obtain the pitch velocity control command ω at the current moment. pu The formula is as follows:

[0086] ω yu =K yp *K yu (θ yr -θ yt )-K yp *E y

[0087] ω pu =K pp *K pu (θpr -θ pt )-K pp *E p

[0088] In the formula, K yp K is the proportional control parameter for the azimuth position controller. yu K is the conversion factor from azimuth rotation angle units to azimuth angular displacement units. pp K is the proportional control parameter for the pitch position controller. pu θ is the conversion factor from pitch rotation units to pitch angular displacement units. yr The controller output command is planned according to the current instruction, that is, the current orientation rotation angle. E y The azimuth angular displacement is obtained from the encoder feedback of the first motor, θ. pr The controller output command is planned for the current instruction, i.e., the current pitch-to-rotation angle β, E. p The pitch angular displacement is obtained from the encoder feedback of the second motor.

[0089] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0090] This method uses fiber optic gyroscopes to sense the azimuth and pitch disturbance angular rates of a two-axis turntable, achieves stable control through disturbance angular rate compensation, and optimizes the synchronous control of the two-axis turntable based on an asymmetric cross-coupling strategy, wherein:

[0091] Stable control achieved through disturbance angular rate compensation specifically involves obtaining filtered azimuth and pitch disturbance angular rates by applying filters to the azimuth and pitch disturbance angular rates respectively, obtaining the azimuth and pitch disturbance angles by using integrators, and then compensating the inputs of the corresponding drivers with the filtered azimuth and pitch disturbance angular rates after proportional control. At the same time, the azimuth and pitch disturbance angles are fed back to the inputs of the corresponding position controllers. This can effectively compensate for position deviations caused by disturbances in the two-axis turntable, improve the synchronization performance of the two axes, and further reduce the generation of contour errors.

[0092] The synchronous control of a two-axis turntable optimized based on an asymmetric cross-coupling strategy includes: constructing a command planning controller to obtain azimuth and pitch rotation angles; obtaining the pitch axis compensation coefficient based on the target trajectory curve and constructing a cross-coupling controller; constructing azimuth and pitch position controllers, and using the azimuth rotation angle, azimuth disturbance angle, and azimuth angular displacement as inputs to the azimuth position controller to obtain the azimuth velocity control command, and using the pitch rotation angle, pitch disturbance angle, and pitch angular displacement as inputs to the pitch position controller to obtain the pitch velocity control command; and based on the filtered azimuth... The disturbance angular rate and the filtered pitch disturbance angular rate are used to obtain the azimuth disturbance compensation angular velocity and pitch disturbance compensation angular velocity, respectively. An asymmetric cross-coupling strategy is adopted for the azimuth axis velocity input command and the pitch axis velocity input command at the current moment. The azimuth axis decoupling compensation amount and the pitch axis decoupling compensation amount are used as the azimuth axis velocity input command and the pitch axis velocity input command, respectively, to achieve the following motion of the target trajectory curve. That is, the azimuth axis velocity input command and the pitch axis velocity input command are used as the input of the azimuth axis and pitch axis driver to complete the compensation, which can improve the dynamic response capability, stability and accuracy of the two-axis turntable. Attached Figure Description

[0093] Figure 1 The flowchart shows the vehicle-mounted two-axis servo control method based on asymmetric cross coupling according to the present invention.

[0094] Figure 2 This is a schematic diagram of the structure of the two-axis rotary table of the present invention;

[0095] Figure 3 This is a schematic diagram illustrating the principle of solving the azimuth and pitch rotation angles of the present invention.

[0096] Figure 4 This is a control block diagram of the two-axis rotary table of the present invention;

[0097] Figure 5 This is a schematic diagram illustrating the principle of contour error calculation in this invention;

[0098] Figure 6 This is a comparison diagram of the effects of single-axis disturbance angular rate compensation and disturbance angle compensation in this invention;

[0099] Figure 7 This is a comparison chart of the contour errors of existing techniques and the method of this invention.

[0100] Reference numerals in the attached figures: 1. Stage; 2. Azimuth mount; 3. Pitch support; 4. Pitch mount; 5. First fiber optic gyroscope; 6. Second fiber optic gyroscope. Detailed Implementation

[0101] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0102] It should be noted that, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of the application.

[0103] like Figures 1-7 As shown, an on-board two-axis servo control method based on asymmetric cross-coupling is applied to a two-axis turntable. The two-axis turntable is mounted on the vehicle body and is used to drive the load to rotate around the azimuth and pitch axes. The azimuth and pitch axes are perpendicular. The on-board two-axis servo control method based on asymmetric cross-coupling includes:

[0104] S1. Real-time acquisition of the azimuth and pitch disturbance angular rates of the two-axis turntable.

[0105] In one embodiment, the two-axis turntable includes a platform 1, an azimuth ring 2, a pitch support 3, a pitch mount 4, a first fiber optic gyroscope 5, a second fiber optic gyroscope 6, a first motor, a second motor, a first driver, and a second driver. The platform 1 is connected to the vehicle body. The first motor is mounted on the platform 1 and is used to drive the azimuth ring 2 to rotate around the azimuth axis. The pitch support 3 is connected to the azimuth ring 2. The second motor is mounted on the pitch support 3 and is used to drive the pitch mount 4 to rotate around the pitch axis. The first fiber optic gyroscope 5 is connected to the platform 1, and the second fiber optic gyroscope 6 is connected to the pitch support 3. The first driver is electrically connected to the first motor, and the second driver is electrically connected to the second motor. The detection result of the first fiber optic gyroscope 5 is the azimuth axis disturbance angular rate, and the detection result of the second fiber optic gyroscope 6 is the pitch axis disturbance angular rate.

[0106] like Figure 2As shown, this embodiment of the two-axis turntable includes a platform 1, an azimuth mount 2, a pitch support 3, a pitch mount 4, a first fiber optic gyroscope 5, a second fiber optic gyroscope 6, a first motor, a second motor, a first driver, and a second driver. The platform 1 provides support for structures such as the azimuth mount 2, the pitch support 3, the pitch mount 4, and the fiber optic gyroscopes. It can also mount control boards, drivers (such as servo drivers), and motors, and can be fixed to a movable carrier, such as a vehicle body, through mounting holes. The platform 1 is rigidly connected to the vehicle body. The azimuth mount 2 can rotate around the azimuth axis under the drive of the first motor, with a rotation range generally from 0° to 360°. The pitch support 3 is connected to the azimuth mount 2, and the pitch mount 4 can rotate around the pitch axis under the drive of the second motor, with a rotation range generally from -10° to 70°. The rotation of the azimuth mount 2 and the pitch mount 4 is generally driven by the rotation of the motor driving the meshing of mechanical gears. In this embodiment, the movement of the two rotation axes (azimuth axis and pitch axis, which are perpendicular to each other) of the two-axis turntable is controlled by the control board sending control commands to the servo driver. After receiving the control commands, the servo driver drives the motor to rotate, which in turn drives the gears to mesh, ultimately transmitting the rotational transmission to the rotation axes of the two-axis turntable. The first fiber optic gyroscope 5 is used to detect the azimuth axis disturbance angular rate of the platform 1, and the second fiber optic gyroscope 6 is used to detect the pitch axis disturbance angular rate of the pitch support 3, which are the azimuth and pitch disturbance angular rates of the two-axis turntable, and also the azimuth and pitch disturbance angular rates of the vehicle body.

[0107] Figure 2 In this system, the vehicle coordinate system o′x′y′z′ is a moving coordinate system fixed on platform 1, while the geodetic coordinate system OXYZ is a fixed coordinate system. The attitude of platform 1 will change due to disturbances. Stability refers to maintaining the azimuth and pitch stability of the load mounted on the pitch seat 4 in the geodetic coordinate system OXYZ by adjusting the angles of the azimuth seat 2 and the pitch seat 4 when platform 1 is disturbed. The azimuth and pitch directions refer to two rotational directions parallel to the OZ and OX rotation axes in the geodetic coordinate system OXYZ, such as... Figure 2 In the diagram, L1 represents the azimuth axis, L2 represents the pitch axis, L3 represents the azimuth direction, and L4 represents the pitch direction. Initially, the vehicle coordinate system o′x′y′z′ and the geodetic coordinate system OXYZ can be aligned through translation.

[0108] Fiber optic gyroscopes (fiber optic rate gyroscopes) are installed on stage 1 and pitch support 3 respectively to sense the angular rates of disturbance in the azimuth and pitch directions of the two-axis turntable. The azimuth disturbance angular rate of the two-axis turntable refers to the rotational angular rate of stage 1 with o′z′ of the moving coordinate system on stage 1 as the rotation axis, and the pitch disturbance angular rate of the two-axis turntable refers to the rotational angular rate of stage 1 with o′x′ of the moving coordinate system on stage 1 as the rotation axis.

[0109] When evaluating the stability and following performance of a vehicle-mounted two-axis servo system (two-axis turntable), the load on the pitch mount 4 can be replaced with a visible light source (such as a laser pointer). The performance is measured by recording the motion trajectory projected onto the projection plane by the visible light source. Generally, a sinusoidal signal with a preset amplitude and frequency is used as the command trajectory (target trajectory curve). By comparing the motion trajectories recorded on the projection plane, the stability and following performance of the two-axis turntable can be obtained.

[0110] S2. Input the output signal of the first filter from the previous moment, the azimuth disturbance angular rate, and the current azimuth disturbance angular rate into the first filter for filtering to obtain the filtered azimuth disturbance angular rate ω at the current moment. yf The output signal of the second filter from the previous moment, along with the pitch disturbance angular rate and the current pitch disturbance angular rate, are input into the second filter for filtering to obtain the filtered pitch disturbance angular rate ω at the current moment. pf .

[0111] In one embodiment, both the first filter and the second filter are bilinear low-pass filters, and perform the following operations:

[0112] S21. The analog transfer function H(s) is established using a first-order Butterworth low-pass filter, as shown in the following formula:

[0113]

[0114] In the formula, ω c Let ω be the cutoff angular frequency, and ω c =2πf c f c Let s be the cutoff frequency, and s be the first complex variable;

[0115] S22, Calculate the frequency pre-distortion ω a The formula is as follows:

[0116]

[0117] In the formula, ω d For the ideal discrete-time angular frequency, and ω d =2πf c T is the sampling period;

[0118] S23. Replace the cutoff angular frequency ω in the analog transfer function H(s). c Frequency predistortion ω a The first complex variable s is The discrete transfer function H(z) is obtained by performing a bilinear transformation, as shown in the following formula:

[0119]

[0120] In the formula, z is the second complex variable;

[0121] S24. Establish the difference equation:

[0122] Let the first intermediate variable The discrete transfer function H(z) is then expressed as:

[0123]

[0124] because Where X(z) is the input signal after z-transformation, and Y(z) is the output signal after z-transformation, we can obtain:

[0125]

[0126] Then, an inverse z-transform is performed, that is, y[t] replaces Y(z), x[t] replaces X(z), and x(t-1) replaces X(z). -1 y(t-1) replaces Y(z)z -1 The difference equation can then be obtained, as shown in the following formula:

[0127]

[0128] In the formula, y[t] is the output signal of the filter at time t, y[t-1] is the output signal of the filter at time t-1, x[t] is the input signal of the filter at time t, x[t-1] is the input signal of the filter at time t-1, and z -1 Let z be the -1 power of the second complex variable;

[0129] S25. Obtain the filtered azimuth disturbance angular rate and the filtered pitch disturbance angular rate at the current moment respectively, based on the difference equation, as the output signals of the corresponding filters, where:

[0130] Filtered azimuth perturbation angular velocity ω at time t yf [t], the formula is as follows:

[0131]

[0132] Filtered pitch disturbance angular rate ω at time t pf [t], the formula is as follows:

[0133]

[0134] In the formula, ω yf [t-1] represents the filtered azimuth perturbation angular velocity at time t-1, ω yt [t] represents the azimuth perturbation angular velocity at time t, ω yt[t-1] represents the azimuth perturbation angular velocity at time t-1, ω pf [t-1] represents the filtered pitch disturbance angular rate at time t-1, ω pt [t] represents the pitch disturbance angular rate at time t, ω pt [t-1] represents the pitch disturbance angular rate at time t-1.

[0135] In this process, both the first and second filters are digital filters. If a bilinear low-pass filter is selected, it is constructed by converting a continuous-time domain filter, such as a first-order Butterworth low-pass filter, into the time domain.

[0136] S3. Integrate the azimuth and pitch disturbance angular rates from time zero to the current time using an integrator to obtain the azimuth disturbance angle θ at the current time. yt and pitch disturbance angle θ pt .

[0137] In one embodiment, the azimuth disturbance angular rate and pitch disturbance angular rate from time zero to the current time are integrated using an integrator to obtain the azimuth disturbance angle θ at the current time. yt and pitch disturbance angle θ pt The details are as follows:

[0138] azimuth perturbation angle θ at time t yt (t), the formula is as follows:

[0139]

[0140] Pitch angle θ at time t pt (t), the formula is as follows:

[0141]

[0142] In the formula, ω yt [n] represents the azimuth perturbation angular velocity at time n, ω pt [n] represents the pitch disturbance angular rate at time n, where n = 0 to t, and f is the sampling frequency.

[0143] Among them, such as Figure 4 As shown, the azimuth disturbance angle θ at the current moment yt The azimuth disturbance angular rate from time zero to the current time is integrated using the first integrator, and the pitch disturbance angle θ at the current time is obtained. pt The pitch disturbance angular rate from time zero to the current time is integrated using the second integrator, ω. yt ω represents the azimuth perturbation angular rate at the corresponding moment. ptThis represents the pitch disturbance angular rate at the corresponding moment.

[0144] S4. Construct a command planning controller. The command planning controller is used to obtain the current orientation rotation angle of the two-axis turntable based on the target trajectory curve. And the pitch and rotation angle β.

[0145] In one embodiment, the instruction planning controller performs the following operations:

[0146] S41. Establish a target coordinate system o1x1y1 on the projection plane where the target trajectory curve is located. The origin o1 of the target coordinate system is the point on the projection plane pointed to by the load of the two-axis turntable in the initial state. The vertical upward is the y1 axis and the horizontal rightward is the x1 axis.

[0147] S42. A fixed-period sampling method is used to sample the target trajectory curve to obtain several sampling points and the coordinates of the corresponding sampling points;

[0148] S43. Calculate the azimuth rotation angle at the current moment based on the coordinates of the current sampling point P. And the pitch rotation angle β, the formula is as follows:

[0149]

[0150] l′ 2 =x 2 +l 2

[0151] In the formula, l is the distance between the load and the projection plane and is a constant, l′ is the second intermediate variable, (x0, y0) is the coordinate of the current sampling point P, x0 is the abscissa of the current sampling point P, y0 is the ordinate of the current sampling point P, and the current time is the time to reach the current sampling point P, which is also the target point at the current time.

[0152] The controller is designed based on the target trajectory curve. For example, in this embodiment, the target trajectory curve is a sine curve. Figure 3 As shown, a target coordinate system o1x1y1 is established on the projection plane S. The origin o1 of the target coordinate system is the point on the projection plane S pointed to by the load (laser pointer) of the two-axis turntable in the initial state. The vertical direction upward is the y1 axis, and the horizontal direction to the right is the x1 axis. When the pitch axis rotates by an angle β and the azimuth axis is in the initial position, the point o0 of the visible light source on the pitch mount 4 hits the projection plane S at a position P", and its distance from the x1 axis is h. When the azimuth axis rotates by an angle β, the target coordinate system is established on the projection plane S. Subsequently, the light spot is not point P′ at a distance h from the x1 axis, but rather point P at a greater distance from the x1 axis. This demonstrates that obtaining the azimuth and pitch rotation angles from points on the target trajectory curve requires further geometric analysis to achieve more precise tracking accuracy.

[0153] Specifically, the distance from the emission point o0 of the visible light source on the elevation mount 4 to the projection plane S is l, which remains constant during the test. The target trajectory curve is decomposed into a series of points on the projection plane S using a fixed-period sampling method. The horizontal and vertical coordinates of the sampled points are known quantities. The azimuth and pitch rotation angles are calculated based on the coordinates of the sampled points. Subsequently, the azimuth rotation angle... (i.e., the angle that the direction ring 2 needs to rotate) is the target command θ output by the command planning controller to the azimuth position controller. yr The pitch rotation angle β (the angle that pitch mount 4 needs to rotate) is used as the target command θ output by the command planning controller to the pitch position controller. pr .

[0154] S5. Obtain the pitch axis compensation coefficient K at the current moment based on the target trajectory curve. cy And construct a cross-coupled controller.

[0155] In one embodiment, the pitch axis compensation coefficient K at the current moment is obtained based on the target trajectory curve. cy The formula is as follows:

[0156]

[0157] In the formula, y t Let P be the target point at time t. t The ordinate, y t-1 Let P be the target point at time t-1. t-1 The ordinate is H, where H is the proportional adjustment coefficient, and the target point P at time t is... t and the target point P at time t-1 t-1 All of these are points on the target trajectory curve.

[0158] In one embodiment, the cross-coupled controller is constructed as follows:

[0159] S51. Calculate the contour error ε at the current moment, using the following formula:

[0160] ε=-sinθ*e y +cosθ*e p

[0161] In the formula, ε represents the actual arrival point P at the current time. r To the target point P tThe distance between the secants, e y For azimuth tracking error, e p The pitch tracking error is θ, where θ is the target point P at the current moment. t The angle between the secant and the x-axis of the target coordinate system;

[0162] S52, Assume ε = -C x *e y +C y *e p And based on the formula in step S51, the mathematical expression for the cross-coupling factor is obtained:

[0163] C x =sinθ,C y =cosθ

[0164] In the formula, the cross-coupling factor includes the azimuth cross-coupling factor C. x and pitch cross-coupling factor C y ;

[0165] S53. Obtain the output of the cross-coupled controller at the corresponding time according to the cross-coupling control algorithm. The cross-coupling control algorithm adopts the PID control algorithm, and its mathematical expression is as follows:

[0166]

[0167] In the formula, u(t) is the output of the cross-coupled controller at time t, ε(t) is the input of the cross-coupled controller at time t, i.e., the profile error at time t. Similarly, ε(i) is the input of the cross-coupled controller at time i, i = 0 to t-1, ε(t-1) is the input of the cross-coupled controller at time t-1, and k p k is the proportional coefficient of the cross-coupled controller. i k represents the integral coefficient of the cross-coupled controller. d These are the differential coefficients of the cross-coupled controller.

[0168] Specifically, a cross-coupled controller (CCC) is designed based on the target trajectory curve. An asymmetric cross-coupling strategy is used, where the output of the cross-coupled controller is multiplied by the corresponding coupling coefficient and compensated for at the inputs of the azimuth and pitch axis drivers (first and second drivers). Specifically, as follows... Figure 4 As shown, P t Point P is the desired location to reach at time t. t-1 Point P is the desired location to reach at time t-1. t P t-1 All points are locations on the desired trajectory (target trajectory curve), P r The point is the actual point reached at time t. In this embodiment, the desired point P is used.t The secant is used instead of the tangent, i.e., P is used. t P t-1 As the desired point P t The tangent line is used to define the contour error, and the contour error ε at time t is defined as the actual arrival point P at the current time. r To the target point P t secant P t P t-1 The distance between them, where θ is the target point P at the current moment. t secant P t P t-1 The angle between the cross-coupled controller and the horizontal axis x1 of the target coordinate system. The output u of the cross-coupled controller is decoupled and compensated to the corresponding axis through a cross-coupled control algorithm to reduce contour error. The preferred cross-coupled control algorithm is a PID control algorithm, or other cross-coupled control algorithms well known to those skilled in the art.

[0169] S6. Construct the azimuth position controller and pitch position controller, and record the current azimuth rotation angle. Azimuth disturbance angle θ yt The azimuth angular displacement is used as the input to the azimuth position controller to obtain the azimuth velocity control command ω at the current moment. yu The current pitch rotation angle β and pitch disturbance angle θ are used to determine the current pitch angle rotation angle β and pitch disturbance angle θ. pt The pitch angular displacement is used as the input to the pitch position controller to obtain the pitch velocity control command ω at the current moment. pu .

[0170] In one embodiment, both the azimuth position controller and the pitch position controller are PID controllers.

[0171] In one embodiment, the current azimuth is rotated by an angle. Azimuth disturbance angle θ yt The azimuth angular displacement is used as the input to the azimuth position controller to obtain the azimuth velocity control command ω at the current moment. yu The current pitch rotation angle β and pitch disturbance angle θ are used to determine the current pitch angle rotation angle β and pitch disturbance angle θ. pt The pitch angular displacement is used as the input to the pitch position controller to obtain the pitch velocity control command ω at the current moment. pu The formula is as follows:

[0172] ω yu =K yp *K yu (θ yr -θ yt )-K yp *E y

[0173] ω pu =K pp *K pu (θ pr -θ pt )-K pp *E p

[0174] In the formula, K yp K is the proportional control parameter for the azimuth position controller. yu K is the conversion factor from azimuth rotation angle units to azimuth angular displacement units. pp K is the proportional control parameter for the pitch position controller. pu θ is the conversion factor from pitch rotation units to pitch angular displacement units. yr The controller output command is planned according to the current instruction, that is, the current orientation rotation angle. E y The azimuth angular displacement is obtained from the encoder feedback of the first motor, θ. pr The controller output command is planned for the current instruction, i.e., the current pitch-to-rotation angle β, E. p The pitch angular displacement is obtained from the encoder feedback of the second motor.

[0175] Specifically, both the azimuth position controller and the pitch position controller are implemented based on PID controllers and can suppress the corresponding position controller outputs caused by disturbances.

[0176] S7. Based on the filtered azimuth perturbation angular rate ω at the current moment yf and the filtered pitch disturbance angular rate ω pf This corresponds to obtaining the azimuth disturbance compensation angular velocity ω at the current moment. yc and pitch disturbance compensation angular velocity ω pc .

[0177] In one embodiment, based on the filtered azimuth perturbation angular rate ω at the current moment yf and the filtered pitch disturbance angular rate ω pf This corresponds to obtaining the azimuth disturbance compensation angular velocity ω at the current moment. yc and pitch disturbance compensation angular velocity ω pc ,in:

[0178] Current azimuth disturbance compensation angular velocity ω yc The formula is as follows:

[0179] ω yc =K u1 *ω yf

[0180]

[0181] In the formula, K u1 R is the azimuth angular rate compensation coefficient. y K1 is the gear ratio of the first motor, K1 is the azimuth compensation proportional control coefficient, the unit of azimuth disturbance compensation angular velocity is 0.0001 rps, and the unit of filtered azimuth disturbance angular rate is ° / s.

[0182] The pitch disturbance compensation angular velocity ω at the current moment pc The formula is as follows:

[0183] ω pc =K u2 *ω pf

[0184]

[0185] In the formula, K u2 R is the pitch angular rate compensation coefficient. p K is the gear ratio of the second motor, K2 is the pitch compensation proportional control coefficient, the pitch disturbance compensation angular velocity is in units of 0.0001 rps, and the filtered pitch disturbance angular rate is in units of ° / s.

[0186] Specifically, the filtered azimuth disturbance angular rate and the filtered pitch disturbance angular rate are converted to units, multiplied by the corresponding proportional control coefficient, and then compensated to the input of the corresponding driver.

[0187] S8. An asymmetric cross-coupling strategy is used to decouple and compensate the azimuth and pitch axis velocity input commands at the current moment, achieving the target trajectory curve following motion. The asymmetric cross-coupling strategy involves decoupling and compensating the azimuth axis by an amount ω. ys As the azimuth axis velocity input command, the pitch axis decoupling compensation amount ω ps As the pitch axis speed input command, where:

[0188] Azimuth axis decoupling compensation amount ω ys The formula is as follows:

[0189] ω ys =ω ys -ω yc +C x *u

[0190] Pitch axis decoupling compensation ω ps The formula is as follows:

[0191] ω ps =ω pu -ω pc +Kcy *u

[0192] In the formula, C x denoted as the azimuth cross-coupling factor, and u is the output of the cross-coupling controller.

[0193] This method employs an asymmetric cross-coupling strategy to control the two-axis turntable. The output of the position controller, the disturbance compensation angular velocity, and the output of the cross-coupling controller are used as input commands for the driver. These three are linearly superimposed and used as reference commands for the driver, thereby controlling the two-axis turntable.

[0194] like Figure 6 As shown, when a disturbance with an amplitude of 2° and a frequency of 1Hz is applied to platform 1, the existing disturbance angle compensation method and the disturbance angular rate compensation method of this invention are used respectively. The disturbance angle obtained by the existing disturbance angle compensation method can be obtained through the integrator in step S3. Through comparative simulation experiments, it is verified that the disturbance angular rate compensation method provided by this invention has a lower angle error and higher stability accuracy than the existing disturbance angle compensation method. For example, for a single-axis (azimuth axis or pitch axis) disturbance experiment, the figure shows the disturbance applied to the azimuth direction. The angle error is the difference between the azimuth rotation angle and the azimuth angle of platform 1. The azimuth angle of platform 1 is specifically the angle between the o′x′ axis of the vehicle coordinate system o′x′y′z′ and the OX axis of the geodetic coordinate system OXYZ, or the angle between the o′y′ axis of the vehicle coordinate system o′x′y′z′ and the OY axis of the geodetic coordinate system OXYZ. Ideally, it should be 0 if there is no error.

[0195] like Figure 7 As shown, simulation experiments have verified that the method provided by this invention (improved cross coupling, i.e., asymmetric cross coupling) can further reduce contour errors compared to existing methods (conventional cross coupling).

[0196] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0197] The embodiments described above are merely specific and detailed examples of the embodiments described in this application, and should not be construed as limiting the scope of the application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the appended claims.

Claims

1. A vehicle-mounted two-axis servo control method based on asymmetric cross-coupling, applied to a two-axis turntable, wherein the two-axis turntable is mounted on the vehicle body and used to drive the load to rotate around the azimuth axis and the pitch axis, wherein the azimuth axis and the pitch axis are perpendicular, characterized in that: The on-board two-axis servo control method based on asymmetric cross coupling includes: S1. Real-time acquisition of azimuth and pitch disturbance angular rates of the two-axis turntable; S2. Input the output signal of the first filter from the previous moment, the azimuth disturbance angular rate, and the current azimuth disturbance angular rate into the first filter for filtering to obtain the filtered azimuth disturbance angular rate ω at the current moment. yf The output signal of the second filter from the previous moment, along with the pitch disturbance angular rate and the current pitch disturbance angular rate, are input into the second filter for filtering to obtain the filtered pitch disturbance angular rate ω at the current moment. pf ; S3. Integrate the azimuth and pitch disturbance angular rates from time zero to the current time using an integrator to obtain the azimuth disturbance angle θ at the current time. yt and pitch disturbance angle θ pt ; S4. Construct an instruction planning controller, which is used to obtain the azimuth rotation angle of the two-axis turntable at the current moment according to the target trajectory curve. And pitch and rotation angle β; S5. Obtain the pitch axis compensation coefficient K at the current moment based on the target trajectory curve. cy And construct a cross-coupled controller; S6. Construct the azimuth position controller and pitch position controller, and record the current azimuth rotation angle. Azimuth disturbance angle θ yt The azimuth angular displacement is used as the input to the azimuth position controller to obtain the azimuth velocity control command ω at the current moment. yu The current pitch rotation angle β and pitch disturbance angle θ are used to determine the current pitch angle rotation angle β and pitch disturbance angle θ. pt The pitch angular displacement is used as the input to the pitch position controller to obtain the pitch velocity control command ω at the current moment. pu ; S7. Based on the filtered azimuth perturbation angular rate ω at the current moment yf and the filtered pitch disturbance angular rate ω pf This corresponds to obtaining the azimuth disturbance compensation angular velocity ω at the current moment. yc and pitch disturbance compensation angular velocity ω pc ; S8. An asymmetric cross-coupling strategy is used to decouple and compensate the azimuth and pitch axis velocity input commands at the current moment to achieve the following motion of the target trajectory curve. The asymmetric cross-coupling strategy involves decoupling and compensating the azimuth axis by an amount ω. ys As the azimuth axis velocity input command, the pitch axis decoupling compensation amount ω ps As the pitch axis speed input command, where: Azimuth axis decoupling compensation amount ω ys The formula is as follows: oh ys =ω yu -oh yc +C x *u Pitch axis decoupling compensation ω ps The formula is as follows: oh ps =ω pu -oh pc +K cy *u In the formula, C x denoted as the azimuth cross-coupling factor, and u is the output of the cross-coupling controller.

2. The on-board two-axis servo control method based on asymmetric cross coupling as described in claim 1, characterized in that: The two-axis turntable includes a platform (1), an azimuth ring (2), a pitch support (3), a pitch mount (4), a first fiber optic gyroscope (5), a second fiber optic gyroscope (6), a first motor, a second motor, a first driver, and a second driver. The platform (1) is connected to the vehicle body. The first motor is mounted on the platform (1) and is used to drive the azimuth ring (2) to rotate around the azimuth axis. The pitch support (3) is connected to the azimuth ring (2). The second motor is mounted on the pitch support (3) and is used to drive the pitch mount (4) to rotate around the pitch axis. The first fiber optic gyroscope (5) is connected to the platform (1). The second fiber optic gyroscope (6) is connected to the pitch support (3). The first driver is electrically connected to the first motor. The second driver is electrically connected to the second motor. The detection result of the first fiber optic gyroscope (5) is the azimuth axis disturbance angular rate. The detection result of the second fiber optic gyroscope (6) is the pitch axis disturbance angular rate.

3. The on-board two-axis servo control method based on asymmetric cross coupling as described in claim 2, characterized in that: Both the first and second filters are bilinear low-pass filters, and they perform the following operations: S21. The analog transfer function H(s) is established using a first-order Butterworth low-pass filter, as shown in the following formula: In the formula, ω c Let ω be the cutoff angular frequency, and ω c =2πf c f c Let s be the cutoff frequency, and s be the first complex variable; S22, Calculate the frequency pre-distortion ω a The formula is as follows: In the formula, ω d For the ideal discrete-time angular frequency, and ω d =2πf c T is the sampling period; S23. Replace the cutoff angular frequency ω in the analog transfer function H(s). c Frequency predistortion ω a The first complex variable s is The discrete transfer function H(z) is obtained by performing a bilinear transformation, as shown in the following formula: In the formula, z is the second complex variable; S24. Establish the difference equation: Let the first intermediate variable The discrete transfer function H(z) is then expressed as: because Where X(z) is the input signal after z-transformation, and Y(z) is the output signal after z-transformation, we can obtain: Then, an inverse z-transform is performed, that is, y[t] replaces Y(z), x[t] replaces X(z), and x(t-1) replaces X(z). -1 y(t-1) replaces Y(z)z -1 The difference equation can then be obtained, as shown in the following formula: In the formula, y[t] is the output signal of the filter at time t, y[t-1] is the output signal of the filter at time t-1, x[t] is the input signal of the filter at time t, x[t-1] is the input signal of the filter at time t-1, and z -1 Let z be the -1 power of the second complex variable; S25. Obtain the filtered azimuth disturbance angular rate and the filtered pitch disturbance angular rate at the current moment respectively, based on the difference equation, as the output signals of the corresponding filters, where: Filtered azimuth perturbation angular velocity ω at time t yf [t], the formula is as follows: Filtered pitch disturbance angular rate ω at time t pf [t], the formula is as follows: In the formula, ω yf [t-1] represents the filtered azimuth perturbation angular velocity at time t-1, ω yt [t] represents the azimuth perturbation angular velocity at time t, ω yt [t-1] represents the azimuth perturbation angular velocity at time t-1, ω pf [t-1] represents the filtered pitch disturbance angular rate at time t-1, ω pt [t] represents the pitch disturbance angular rate at time t, ω pt [t-1] represents the pitch disturbance angular rate at time t-1.

4. The on-board two-axis servo control method based on asymmetric cross coupling as described in claim 1, characterized in that: The azimuth and pitch disturbance angular rates are integrated using integrators to obtain the azimuth disturbance angle θ at the current moment. yt and pitch disturbance angle θ pt The details are as follows: azimuth perturbation angle θ at time t yt (t), the formula is as follows: Pitch angle θ at time t pt (t), the formula is as follows: In the formula, ω yt [n] represents the azimuth perturbation angular velocity at time n, ω pt [n] represents the pitch disturbance angular rate at time n, where n = 0 to t, and f is the sampling frequency.

5. The on-board two-axle servo control method based on asymmetric cross coupling as described in claim 1, characterized in that: The instruction planning controller performs the following operations: S41. Establish a target coordinate system o1x1y1 on the projection plane where the target trajectory curve is located. The origin o1 of the target coordinate system is the point on the projection plane pointed to by the load of the two-axis turntable in the initial state. The vertical upward direction is the y1 axis and the horizontal rightward direction is the x1 axis. S42. A fixed-period sampling method is used to sample the target trajectory curve to obtain several sampling points and the coordinates of the corresponding sampling points; S43. Calculate the azimuth rotation angle at the current moment based on the coordinates of the current sampling point P. And the pitch rotation angle β, the formula is as follows: l′ 2 ＝x 2 +l 2 In the formula, l is the distance between the load and the projection plane and is a constant, l′ is the second intermediate variable, (x0, y0) is the coordinate of the current sampling point P, x0 is the abscissa of the current sampling point P, y0 is the ordinate of the current sampling point P, and the current time is the time to reach the current sampling point P, which is also the target point at the current time.

6. The on-board two-axis servo control method based on asymmetric cross coupling as described in claim 2, characterized in that: Based on the filtered azimuth perturbation angular rate ω at the current moment yf and the filtered pitch disturbance angular rate ω pf This corresponds to obtaining the azimuth disturbance compensation angular velocity ω at the current moment. yc and pitch disturbance compensation angular velocity ω pc ,in: Current azimuth disturbance compensation angular velocity ω yc The formula is as follows: oh yc =K u1 *oh yf In the formula, K u1 R is the azimuth angular rate compensation coefficient. y K1 is the gear ratio of the first motor, K1 is the azimuth compensation proportional control coefficient, the unit of azimuth disturbance compensation angular velocity is 0.0001 rps, and the unit of filtered azimuth disturbance angular rate is ° / s. The pitch disturbance compensation angular velocity ω at the current moment pc The formula is as follows: oh pc =K u2 *oh pf In the formula, K u2 R is the pitch angular rate compensation coefficient. p K is the gear ratio of the second motor, K2 is the pitch compensation proportional control coefficient, the pitch disturbance compensation angular velocity is in units of 0.0001 rps, and the filtered pitch disturbance angular rate is in units of ° / s.

7. The on-board two-axis servo control method based on asymmetric cross coupling as described in claim 1, characterized in that: The process of constructing the cross-coupled controller is as follows: S51. Calculate the contour error ε at the current moment, using the following formula: ε=-sinθ*e y +cosθ*e p In the formula, ε represents the actual arrival point P at the current time. r To the target point P t The distance between the secants, e y For azimuth tracking error, e p The pitch tracking error is θ, where θ is the target point P at the current moment. t The angle between the secant and the x-axis of the target coordinate system; S52, Assume ε = -C x *e y +C y *e p And based on the formula in step S51, the mathematical expression for the cross-coupling factor is obtained: C x =sinθ,C y =cosθ In the formula, the cross-coupling factor includes the azimuth cross-coupling factor C. x and pitch cross-coupling factor C y ; S53. Obtain the output of the cross-coupled controller at the corresponding time according to the cross-coupling control algorithm. The cross-coupling control algorithm adopts the PID control algorithm, and its mathematical expression is as follows: In the formula, u(t) is the output of the cross-coupled controller at time t, ε(t) is the input of the cross-coupled controller at time t, i.e., the profile error at time t. Similarly, ε(i) is the input of the cross-coupled controller at time i, i = 0 to t-1, ε(t-1) is the input of the cross-coupled controller at time t-1, and k p k is the proportional coefficient of the cross-coupled controller. i k represents the integral coefficient of the cross-coupled controller. d These are the differential coefficients of the cross-coupled controller.

8. The on-board two-axle servo control method based on asymmetric cross coupling as described in claim 1, characterized in that: The compensation coefficient K for the pitch axis at the current moment is obtained based on the target trajectory curve. cy The formula is as follows: In the formula, y t Let P be the target point at time t. t The ordinate, y t-1 Let P be the target point at time t-1. t-1 The ordinate is H, where H is the proportional adjustment coefficient, and the target point P at time t is... t and the target point P at time t-1 t-1 All of these are points on the target trajectory curve.

9. The on-board two-axis servo control method based on asymmetric cross coupling as described in claim 2, characterized in that: Both the azimuth position controller and the pitch position controller are PID controllers.

10. The on-board two-axis servo control method based on asymmetric cross coupling as described in claim 9, characterized in that: The current orientation is rotated by an angle. Azimuth disturbance angle θ yt The azimuth angular displacement is used as the input to the azimuth position controller to obtain the azimuth velocity control command ω at the current moment. yu The current pitch rotation angle β and pitch disturbance angle θ are used to determine the current pitch angle rotation angle β and pitch disturbance angle θ. pt The pitch angular displacement is used as the input to the pitch position controller to obtain the pitch velocity control command ω at the current moment. pu The formula is as follows: oh yu =K yp *K yu (i yr -θ yt )-K yp *E y oh pu =K pp *K pu (i pr -θ pt )-K pp *E p In the formula, K yp K is the proportional control parameter for the azimuth position controller. yu K is the conversion factor from azimuth rotation angle units to azimuth angular displacement units. pp K is the proportional control parameter for the pitch position controller. pu θ is the conversion factor from pitch rotation units to pitch angular displacement units. yr The controller output command is planned according to the current instruction, that is, the current orientation rotation angle. E y The azimuth angular displacement is obtained from the encoder feedback of the first motor, θ. pr The controller output command is planned for the current instruction, i.e., the current pitch-to-rotation angle β, E. p The pitch angular displacement is obtained from the encoder feedback of the second motor.

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