Three-axis stabilized platform body angular velocity weak coupling controller gain design method

Abstract

The invention provides a gain design method of a three-axis stabilized platform body angular velocity weak coupling controller. Firstly, rotational inertia of a table body, an inner frame and an outer frame in three directions is measured respectively; secondly, designing a servo control loop controller; and establishing a table body angular velocity closed-loop control transfer function matrix, and adjusting gain coefficients of servo loop controllers of the outer frame shaft and the inner frame shaft according to off-diagonal coupling terms. The traditional controller design neglects the difference between servo control loop gains of an inner frame shaft and an outer frame shaft, and does not consider table body angular velocity cross coupling errors introduced due to different rotational inertia of the controller and a frame. According to the method, a complete servo loop table body angular velocity closed-loop control transfer function is established to obtain a transfer function relationship among a table body angular velocity coupling error item, the frame rotational inertia and the controller, and the gain of the controller is adjusted through the transfer function relationship to effectively eliminate the table body angular velocity cross coupling error. And the steady-state precision of the angular velocity of the table body is improved.

Description

Technical Field

[0001] The invention relates to a controller design method, in particular to a gain design method for a weak-coupling controller of an angular velocity of a three-axis stable platform, belongs to the field of servo loop control, and can be used for stable control of a servo loop in a platform system. Background Art

[0002] The control accuracy of the servo loop of the three-axis stabilized platform is an important basis for reflecting the accuracy level of the inertial platform, and the accuracy level of the inertial platform determines the navigation accuracy of the vehicle.

[0003] The three-axis stabilized platform is a multi-input and multi-output system, and there is a complex cross-coupling relationship between its input and output. Therefore, the design of the inertial platform servo loop controller is crucial to the overall control accuracy of the platform. During the design process, not only the use environment and index requirements should be considered, but also the cross-coupling error of the platform angular velocity introduced by the frame rotation inertia and the different controller designs should be analyzed.

[0004] Traditional controller design generally considers closed-loop system stability, steady-state error, stability to parameter changes, cross-coupling of angular velocity and torque, dynamic performance, etc., but ignores the difference in servo control loop gain between the inner frame axis and the outer frame axis due to different controller designs and frame rotational inertia. This difference will lead to cross-coupling errors in the angular velocity of the table.

[0005] Therefore, how to design the servo loop controller and adjust the appropriate controller gain value is very meaningful to reduce the cross-coupling error of the platform angular velocity and improve the control accuracy. Summary of the invention

[0006] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and provide a gain design method for a weak-coupling controller of the angular velocity of a three-axis stabilized platform, which can reduce the cross-coupling error of the angular velocity of the platform introduced due to the different rotational inertia of the controller and the frame, thereby improving the control accuracy of the platform.

[0007] The technical solution provided by the present invention is:

[0008] A gain design method for a weak-coupling controller of an angular velocity of a three-axis stabilized platform, comprising:

[0009] The three-axis stable platform is measured to obtain the x p ,y p 、z p Moment of inertia of the shaft Internal frame pair Moment of inertia of the shaft External frame pair Moment of inertia of the shaft

[0010] The measured rotation angle β of the table axis zk ;

[0011] The servo control loop controller G of the three-axis stable platform body axis, inner frame axis and outer frame axis are designed respectively. cz (s), G cy (s), G cx (s);

[0012] Establishing a closed-loop control transfer function matrix of the angular velocity of the stage, and obtaining a non-diagonal coupling term H(s), wherein the non-diagonal coupling term H(s) is a transfer function relationship between the servo control loop controller of the inner frame axis and the outer frame axis and the frame rotation inertia;

[0013] According to the off-diagonal coupling term H(s), adjust the inner frame axis servo control loop gain coefficient K cy and the outer frame axis servo loop gain factor K cx , eliminating the cross-coupling error of the table angular velocity.

[0014] Preferably, the table axis rotation angle β zk The measurement method is as follows:

[0015] Install the sensor on the table axis to measure the rotation angle of the inner frame around the table axis, which is the table axis rotation angle β zk .

[0016] Preferably, the PID parameters are adjusted by the robust response time method to obtain the servo control loop controllers of the three-axis stable platform body axis, inner frame axis and outer frame axis, in the following form:

[0017]

[0018] Where i is x, y, z, K ci Represents the controller gain coefficient, G ci (s) represents the controller transfer function.

[0019] Preferably, a transfer function matrix of the platform angular velocity closed-loop control is established, specifically:

[0020] The transfer function expression of the closed-loop control of the platform angular velocity is as follows:

[0021]

[0022] Among them, ω po (s) is the output angular velocity of the stage, ω pi (s) is the input angular velocity of the platform, is the transformation matrix from the frame axis coordinate system to the table body coordinate system, J A-1 is the inverse matrix of the frame moment of inertia, is the frame active inertia decoupling matrix, G c (s) is the controller transfer function, is the transformation matrix from the table coordinate system to the frame axis coordinate system, For the points link;

[0023]

[0024] β yk is the rotation angle of the outer frame around the inner frame axis;

[0025] Substituting the above sub-items into the transfer function expression of the platform angular velocity closed-loop control, we get the transfer function matrix of the platform angular velocity closed-loop control:

[0026]

[0027] Preferably, the off-diagonal coupling term H(s) of the stage angular velocity closed-loop control transfer function matrix is ​​expressed as:

[0028]

[0029] Preferably, the inner frame axis servo control loop gain coefficient K is adjusted according to the off-diagonal coupling term H(s) cy and the outer frame axis servo loop gain factor K cx , specifically:

[0030] Let H(s) = 0, then we have

[0031]

[0032] Preferably, the three-axis stable platform includes a base, an outer frame, an inner frame and a platform body, and the corresponding base body coordinate system x b y b z b , External frame body coordinate system Internal frame body coordinate system and the platform body coordinate system x p y p z p ; The origins of the four coordinate systems coincide, and the z coordinate system of the platform body p Axis and inner frame body coordinate system The axes coincide with each other, and the coordinate system of the inner frame body Axis and external frame body coordinate system The axes coincide, the coordinate system of the outer frame The x axis and the base body coordinate system b Axes coincide.

[0033] The advantages of the present invention compared with the prior art are as follows:

[0034] The existing controller design ignores the difference in servo control loop gain between the inner frame axis and the outer frame axis, and does not consider the cross-coupling error of the platform angular velocity introduced by the different moments of inertia between the controller and the frame. The present invention establishes a complete servo loop platform angular velocity closed-loop control transfer function, obtains the transfer function relationship between the platform angular velocity coupling error and the frame moment of inertia and the controller, and adjusts the controller gain through the transfer function model, which can effectively improve the control accuracy of the platform angular velocity. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a process flow chart of the method of the present invention;

[0036] Figure 2 It is the table body angular velocity error curve diagram when the controller gain of the servo control loop of the outer frame axis and the inner frame axis is taken at different multiples;

[0037] Figure 3 is the power spectrum density curve of the X gyroscope direction angle. DETAILED DESCRIPTION

[0038] The present invention mainly establishes a complete servo loop table angular velocity closed-loop control transfer function, obtains the transfer function relationship between the table angular velocity coupling error and the frame rotational inertia and the controller, and adjusts the controller gain through the transfer function model, which can effectively improve the steady-state accuracy of the table angular velocity.

[0039] The three-axis stable platform includes a base, an outer frame, an inner frame and a platform body. The corresponding base body coordinate system x b y b z b , External frame body coordinate system Internal frame body coordinate system and the platform body coordinate system x p y p z p ; The origins of the four coordinate systems coincide, and the z coordinate system of the platform body p Axis and inner frame body coordinate system The axes coincide with each other, and the coordinate system of the inner frame body Axis and external frame body coordinate system The axes coincide, the coordinate system of the outer frame The x axis and the base body coordinate system b Axes coincide.

[0040] The process flow chart of the method of the present invention is as follows Figure 1 As shown, the implementation steps are as follows:

[0041] (1) Measure the x-axis of the three-axis stable platform p ,y p 、z p Moment of inertia of the shaft Internal frame pair Moment of inertia of the shaft External frame pair Moment of inertia of the shaft

[0042] (2) Measure the rotation angle β of the table axis zk ;

[0043] (3) Design the servo control loop controller G for the three-axis stabilized platform body axis, inner frame axis, and outer frame axis cz (s), G cy (s), G cx (s);

[0044] (4) Establishing the closed-loop control transfer function matrix of the table angular velocity, and obtaining the off-diagonal coupling term H(s), the off-diagonal coupling term H(s) is the transfer function relationship between the servo control loop controller of the inner frame axis and the outer frame axis and the frame rotational inertia.

[0045] (5) According to the off-diagonal coupling term H(s), adjust the inner frame axis servo control loop gain coefficient K cy and the outer frame axis servo loop gain factor K cx , eliminating the cross-coupling error of the table angular velocity.

[0046] Table axis rotation angle β zk The measurement method is as follows:

[0047] Install the sensor on the table axis to measure the rotation angle of the inner frame around the table axis, which is the table axis rotation angle β zk .

[0048] In step (3), the PID parameters are adjusted by the robust response time method to obtain the servo control loop controllers of the three-axis stable platform body axis, inner frame axis and outer frame axis, which are in the following form:

[0049]

[0050] Where i is x, y, z, K ci Represents the controller gain coefficient, G ci (s) represents the controller transfer function.

[0051] In step (4), the platform angular velocity closed-loop control transfer function matrix is ​​established to obtain the off-diagonal coupling term H(s), which is specifically:

[0052] The transfer function expression of the closed-loop control of the platform angular velocity is as follows:

[0053]

[0054] Among them, ω po (s) is the output angular velocity of the stage, ω pi (s) is the input angular velocity of the platform, is the transformation matrix from the frame axis coordinate system to the table body coordinate system, J A -1 is the inverse matrix of the frame moment of inertia, is the frame active inertia decoupling matrix, G c (s) is the controller function, is the transformation matrix from the table coordinate system to the frame axis coordinate system, For the points link;

[0055]

[0056] Substituting the above sub-items into the transfer function expression of the platform angular velocity closed-loop control, we get the transfer function matrix of the platform angular velocity closed-loop control:

[0057]

[0058] Among them, the off-diagonal coupling term H(s) of the closed-loop control transfer function matrix of the platform angular velocity is expressed as

[0059]

[0060] In step (5), the inner frame axis servo control loop gain coefficient K is adjusted according to the off-diagonal coupling term H(s). cy and the outer frame axis servo loop gain factor K cx , specifically:

[0061] Let H(s) = 0, then we have

[0062] There are three cases where the above formula is established:

[0063] First, β zk = ±90°;

[0064] Second, β zk =0° or 180°;

[0065] third,

[0066] The first two cases are special cases because the table axis can work at any angle; if the third case can be made always true, the effect of the off-diagonal coupling term on the table angular velocity will be weakened.

[0067] When the third situation is established, there is

[0068] Taking into account the response speed of the inner and outer frames, generally, the cutoff frequency of the outer frame axis servo control loop is at least about 2Hz lower than the cutoff frequency of the inner frame axis servo control loop. Therefore, the relationship between the servo control loop gain of the outer frame axis and the inner frame axis is as follows.

[0069]

[0070] When the above relationship is satisfied, the cross-coupling error of the table angular velocity introduced by the difference between the inner and outer frame axis servo control loops can be reduced.

[0071] The initial state of the platform is that the platform axis angle is 45°, and the inner frame axis and outer frame axis angle are both 0°. Let the servo loop controllers of the outer frame and the inner frame have gains that satisfy K and cx =0.6K cy , K cx =1.2K cy , K cx =2.0K cy , where K cx =1.2K cy According to the above three gain relationships, a 0.5sin(πt) interference signal is injected into the Y gyroscope direction, and three servo control loops perform closed-loop feedback control based on angular velocity. Figure 2 The table angular velocity error curve is shown when the servo loop controller gain of the outer frame axis and the inner frame axis is taken at different multiples. Figure 2 It can be seen that when K is satisfied cx =1.2K cy When K cx =0.6K cy or K cx =2.0K cy When the angular velocity error of the outer frame platform is greater than K cx =1.2K cy It can be seen that the controller gain difference between the inner and outer frame axis servo control loops is too large or too small, which is not optimal. The controller gain needs to be adjusted according to the proportional relationship of the frame rotation inertia to eliminate the cross-coupling error of the table angular velocity.

[0072] Figure 3 is the power spectrum density curve of the X gyroscope direction angle. FFT analysis is performed on the measured X gyroscope direction angle curve data. At 0.5Hz and 1Hz frequencies, the black curve (K cx =0.6K cy ) and the blue curve (K cx =2.0Kcy ) compared to the red curve (K cx =1.2K cy ) power spectrum density is the smallest, indicating that the coupling degree of the gyroscope angular velocity in the X and Y directions is the smallest.

[0073] The present invention obtains the off-diagonal coupling term H(s) by establishing a closed-loop control transfer function model of a servo control loop, thereby adjusting the controller gain of the servo control loop of the inner frame axis and the outer frame axis, reducing the cross-coupling error of the angular velocity of the table introduced due to the different rotational inertia of the controller and the frame, and improving the control accuracy of the table.

[0074] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A method for designing the gain of a weak-coupling controller for the angular velocity of a three-axis stabilized platform, characterized in that include: The three-axis stable platform is measured to obtain the x p ,y p 、z p Moment of inertia of the shaft Internal frame pair Moment of inertia of the shaft External frame pair Moment of inertia of the shaft The measured rotation angle β of the table axis zk ; The servo control loop controller G of the three-axis stable platform body axis, inner frame axis and outer frame axis are designed respectively. cz (s), G cy (s), G cx (s); Establishing a closed-loop control transfer function matrix of the angular velocity of the stage, and obtaining a non-diagonal coupling term H(s), wherein the non-diagonal coupling term H(s) is a transfer function relationship between the servo control loop controller of the inner frame axis and the outer frame axis and the frame rotation inertia; According to the off-diagonal coupling term H(s), adjust the inner frame axis servo control loop gain coefficient K cy and the outer frame axis servo loop gain factor K cx , eliminating the cross-coupling error of the table angular velocity.

2. The method for designing the gain of the angular velocity weak coupling controller of a three-axis stabilized platform according to claim 1, characterized in that: Table axis rotation angle β zk The measurement method is as follows: Install the sensor on the table axis to measure the rotation angle of the inner frame around the table axis, which is the table axis rotation angle β zk .

3. The method for designing the gain of the angular velocity weak coupling controller of a three-axis stabilized platform according to claim 1, characterized in that: The robust response time method is used to tune the PID parameters, and the servo control loop controllers of the three-axis stable platform body axis, inner frame axis and outer frame axis are obtained in the following form: Where i is x, y, z, K ci Represents the controller gain coefficient, G ci (s) represents the controller transfer function.

4. The method for designing the gain of the angular velocity weak coupling controller of a three-axis stabilized platform according to claim 1, characterized in that: The closed-loop control transfer function matrix of the platform angular velocity is established, which is as follows: The transfer function expression of the closed-loop control of the platform angular velocity is as follows: Among them, ω po (s) is the output angular velocity of the stage, ω pi (s) is the input angular velocity of the platform, is the transformation matrix from the frame axis coordinate system to the table body coordinate system, is the inverse matrix of the frame moment of inertia, is the frame active inertia decoupling matrix, G c (s) is the controller transfer function, is the transformation matrix from the table coordinate system to the frame axis coordinate system, For the points link; β yk is the rotation angle of the outer frame around the inner frame axis; Substituting the above sub-items into the transfer function expression of the platform angular velocity closed-loop control, we get the transfer function matrix of the platform angular velocity closed-loop control:

5. The method for designing the gain of the angular velocity weak coupling controller of a three-axis stabilized platform according to claim 1, characterized in that: The expression of the off-diagonal coupling term H(s) of the transfer function matrix of the platform angular velocity closed-loop control is:

6. The method for designing the gain of the angular velocity weak coupling controller of a three-axis stabilized platform according to claim 1, characterized in that: According to the off-diagonal coupling term H(s), adjust the inner frame axis servo control loop gain coefficient K cy and the outer frame axis servo loop gain factor K cx , specifically: Let H(s) = 0, then we have 7. The method for designing the gain of the angular velocity weak coupling controller of a three-axis stabilized platform according to claim 1, characterized in that: The three-axis stable platform includes a base, an outer frame, an inner frame and a platform body. The corresponding base body coordinate system x b y b z b , External frame body coordinate system Internal frame body coordinate system and the platform body coordinate system x p y p z p ; The origins of the four coordinate systems coincide, and the z coordinate system of the platform body p Axis and inner frame body coordinate system The axes coincide with each other, and the coordinate system of the inner frame body Axis and external frame body coordinate system The axes coincide, the coordinate system of the outer frame The x axis and the base body coordinate system b Axes coincide.

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