Two-dimensional trajectory cooperative tracking system and method for H-bridge precision motion mechanism

Abstract

The invention discloses a two-dimensional trajectory cooperative tracking system and method for an H-bridge precision motion mechanism, and relates to the technical field of precision numerical control. The X-axis feedback control part comprises a feedback controller Gcx and a nominal object Px, the Y-axis feedback control part comprises a feedback controller Gcy and a nominal object Py, the coupling control part comprises an X-axis coupling gain, a Y-axis coupling gain and a robust cross coupling controller, and estimated contour errors epsilon c and epsilon 0 are obtained through cross coupling control or not. And establishing an estimated contour error equivalent feedback loop, subtracting the equivalent feedback loop output from the non-coupling estimated contour error epsilon 0 to obtain a cross-coupling estimated contour error epsilon c, inputting the cross-coupling estimated contour error epsilon c to a robust cross-coupling controller to obtain an equivalent robust cross-coupling controller output, and obtaining an equivalent feedback loop output through an equivalent controlled object. The method can effectively improve the tracking precision of the trajectory, has the characteristic of adapting to any trajectory input, can carry out offline design, is simple in design method, and is beneficial to practical application.

Description

Technical Field

[0001] The invention relates to the technical field of precision numerical control, and in particular to a two-dimensional trajectory collaborative tracking system and method for an H-bridge type precision motion mechanism. Background Art

[0002] As a high-end intelligent equipment, high-precision computer numerical control system is an important part of the advanced manufacturing technology field, and the CNC machining of high-precision parts relies on high-precision collaborative control technology. Therefore, the research on high-precision two-dimensional trajectory collaborative tracking method is of great significance to promote the development of CNC technology and advanced manufacturing industry.

[0003] In order to solve the motion coupling problem of multi-axis systems, it is necessary to design a variable gain cross-coupling controller based on single-axis tracking control to compensate for contour errors in real time. However, the traditional variable gain cross-coupling controller has the following problems: (1) The traditional control method is not accurate enough to meet some high-precision parts processing scenarios; (2) Its controller parameters only meet the accuracy requirements of a single trajectory, but for different parts processing scenarios, this parameter cannot guarantee the contour accuracy of all input trajectories in multiple scenarios; (3) The parameters of the traditional PID cross-coupling controller need to be debugged online, which consumes a lot of debugging time. Summary of the invention

[0004] In order to solve the shortcomings of the background technology, the present invention provides a two-dimensional trajectory collaborative tracking system and method for an H-bridge type precision motion mechanism, which can effectively improve the tracking accuracy of the trajectory, has the characteristics of adapting to arbitrary trajectory input, can be designed offline, has a simple design method, and is conducive to practical applications.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A two-dimensional trajectory collaborative tracking system of an H-bridge precision motion mechanism includes an X-axis feedback control part S1, a Y-axis feedback control part S2 and a coupling control part S3. The X-axis feedback control part S1 includes an X-axis feedback controller G cx with the X-axis nominal object P x The Y-axis feedback control part S2 includes a Y-axis feedback controller G cy with the Y axis nominal object P y , the coupling control part S3 includes an X-axis coupling gain C x , Y-axis coupling gain C y with a robust cross-coupling controller C;

[0007] The two-dimensional motion trajectory is decomposed into the X-axis reference trajectory input X r and Y axis reference trajectory input Y r , the X-axis reference trajectory input X rOutput position X o The X-axis position error signal E is obtained by subtracting x , the Y-axis reference trajectory input Y r Output position Y o The Y-axis position error signal E is obtained by subtracting y , the X-axis position error signal E x Input to the X-axis feedback controller G cx , the Y-axis position error signal E y Input to the Y-axis feedback controller G cy ;

[0008] X-axis position error signal E x and Y-axis position error signal E y and the X-axis coupling gain C x and the Y-axis coupling gain C y After multiplication, the difference is obtained to obtain the cross-coupling estimated contour error ε c , the cross-coupling estimated profile error ε c The output of the robust cross-coupling controller C is respectively coupled to the X-axis coupling gain C x and Y-axis coupling gain C y multiply;

[0009] X-axis position error signal E x Through the X-axis feedback controller G cx The output of the robust cross-coupling controller C and the X-axis coupling gain C x Subtract the multiplication results to get the X-axis controller output U x , Y-axis position error signal E y Through the Y-axis feedback controller G cy The output of the robust cross-coupling controller C and the Y-axis coupling gain C y The results are added to get the Y-axis controller output U y , the X-axis controller output U x The nominal object P on the X axis x Get the X-axis output position X o , the Y-axis controller output U y The Y axis nominal object P y Get the Y axis output position Y o .

[0010] Furthermore, when the robust cross-coupling controller C is not working, a coupling-free estimated contour error ε0 is obtained.

[0011] A two-dimensional trajectory collaborative tracking method for an H-bridge type precision motion mechanism comprises the following steps:

[0012] Step 1: Solve the cross-coupling estimated contour error ε c And the uncoupled estimated contour error ε0:

[0013]

[0014] Step 2: Estimating the cross-coupling contour error ε c Compared with the uncoupled estimated contour error ε0, the transfer function T of the estimated contour error is obtained:

[0015]

[0016] Among them, C x = sinφ,C y =cosφ, φ is the angle between the two-dimensional motion trajectory and the X-coordinate axis;

[0017] Establish an estimated contour error equivalent feedback loop, including a robust cross-coupling controller C and an equivalent controlled object K, the uncoupled estimated contour error ε0 minus the equivalent feedback loop output Y e The cross-coupling estimated contour error ε is obtained c , and then input to the robust cross-coupling controller C to obtain the equivalent robust cross-coupling controller output U e , the equivalent robust cross-coupled controller output U e The equivalent feedback loop output Y is obtained through the equivalent controlled object K. e , define the equivalent open-loop transfer function G o =CK;

[0018] Step 3: Select the full-band vector w all ={w l ,w h},w l is the low frequency band vector, w h is the vector of the medium and high frequency band, and the equivalent controlled object is traversed from φ∈[0,0.5π] with the change dφ as the interval to obtain the frozen linear time-invariant equivalent controlled object set K i , w all Substitute each element into the set K i From the transfer function elements of each linear time-invariant equivalent controlled object in, we can obtain w all Under each element, the amplitude and phase of each linear time-invariant equivalent controlled object are plotted. All the obtained function points are plotted in the form of phase as the horizontal axis and amplitude as the vertical axis to form a Nichols diagram as the template of the equivalent controlled object. The linear time-invariant equivalent controlled object transfer function with the minimum amplitude in the sample diagram of each frequency band is found as the nominal transfer function K of the equivalent controlled object. nominal ;

[0019] Step 4: Vector w in the low frequency bandl Perform sensitivity limitation and limit the upper sensitivity boundary M:

[0020]

[0021] Among them, M is a constant, C(jw l ) is w l The complex value of the transfer function of the robust cross-coupled controller in each element, K i (jw l ) is w l The set K of elements i The complex value of the transfer function of each linear time-invariant equivalent controlled object;

[0022] In the full frequency band vector w all Perform stability constraints and limit the boundary function T u :

[0023]

[0024] Among them, T u (jw all ) is w all The complex value of the transfer function of the boundary function in each element, C(jw all ) is w all The complex value of the transfer function of the robust cross-coupled controller in each element, K i (jw all ) is w all The set K of elements i The complex value of the transfer function of each linear time-invariant equivalent controlled object;

[0025] Step 5: In the sensitivity limitation and stability limitation process, the low-frequency vector w l and the full-band vector w all The equivalent open-loop transfer function under the condition of l and w all The elements, phases and amplitudes of the traversal are traversed in three dimensions. In all the traversed phases, the complex values ​​of each point are compared with the complex values ​​of the nominal transfer function of the equivalent controlled object of each point traversing the low-frequency band and full-frequency band elements to obtain w l and w all The complex value of the transfer function C(jw l ) and C(jw all ), respectively, through sensitivity limitation and stability limitation, find the amplitude extreme points under each phase, respectively at w l and w allIn each element, the amplitude extreme points under all phases are connected to obtain the boundaries of sensitivity constraints and stability constraints, and the boundaries are composited to obtain the Nichols diagram of the composite boundary;

[0026] Step 6: Design a robust cross-coupling controller in the Nichols diagram of the composite boundary:

[0027]

[0028] Among them, K g is the robust cross-coupled controller gain, z i is the zero point of the robust cross-coupling controller, p j is the pole of the robust cross-coupling controller, m is the number of zeros of the robust cross-coupling controller, and n is the number of poles of the robust cross-coupling controller;

[0029] The equivalent nominal open-loop transfer function CK obtained by multiplying the nominal transfer function of the robust cross-coupled controller and the equivalent controlled object is nominal , in the low frequency band vector w l Each element and the full-band vector w all All elements satisfy the composite boundary conditions.

[0030] Furthermore, in step 3, the low-frequency vector w l =(2π×0, 2π×20]rad / s, mid-high frequency vector w l =(2π×20, 2π×5000]rad / s.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows: compared with the disadvantages of low controller tracking accuracy, long debugging time and parameters only applicable to a single trajectory of the traditional cross-coupling control method, the present invention establishes an equivalent feedback loop based on the cross-coupling control method of the tangent approximation model, and designs a robust cross-coupling controller based on the quantitative feedback theory for the time-varying equivalent controlled object, which can effectively improve the tracking accuracy of the two-dimensional trajectory of the H-bridge precision motion mechanism, and has strong adaptability to arbitrary trajectory input of the system, has the advantages of offline design and reduced online debugging time, and the design method is simple, which is more conducive to practical application in high-precision numerical control systems and has good application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of an H-bridge type precision motion mechanism;

[0033] Figure 2 is a cross-coupling control block diagram of the system of the present invention;

[0034] Figure 3 is a non-cross-coupling control block diagram of the system of the present invention;

[0035] Figure 4 is a control block diagram of an estimated contour error equivalent feedback loop of the system of the present invention;

[0036] Figure 5 is an equivalent controlled object template diagram in the embodiment;

[0037] Figure 6 is a sensitivity limiting condition boundary diagram in the embodiment;

[0038] Figure 7 is a stability limiting condition boundary diagram in an embodiment;

[0039] Figure 8 is a Nichols diagram of an equivalent nominal open-loop transfer function based on a composite boundary design in an embodiment;

[0040] Fig. 9 is the circular trajectory simulation result under different control strategies in the embodiment;

[0041] Fig.10 1 and 2 are the simulation results of corner trajectories under different control strategies in the embodiment. DETAILED DESCRIPTION

[0042] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0043] Conventional H-bridge precision motion mechanism combined with Figure 1 As shown in the figure, a two-dimensional trajectory collaborative tracking system of H-bridge precision motion mechanism is proposed for this mechanism. Figure 2 As shown, it includes an X-axis feedback control part S1, a Y-axis feedback control part S2 and a coupling control part S3, which is a cross-coupling control, wherein:

[0044] The X-axis feedback control part S1 includes an X-axis feedback controller G cx with the X-axis nominal object P x The Y-axis feedback control part S2 includes a Y-axis feedback controller G cy with the Y axis nominal object P y , the coupling control part S3 includes an X-axis coupling gain C x , Y-axis coupling gain C y with a robust cross-coupled controller C.

[0045] The two-dimensional motion trajectory is decomposed into the X-axis reference trajectory input X rand Y axis reference trajectory input Y r , the X-axis reference trajectory input X r Output position X o The X-axis position error signal E is obtained by subtracting x , the Y-axis reference trajectory input Y r Output position Y o The Y-axis position error signal E is obtained by subtracting y , the X-axis position error signal E x Input to the X-axis feedback controller G cx , the Y-axis position error signal E y Input to the Y-axis feedback controller G cy At the same time, the X-axis position error signal E x and Y-axis position error signal E y All are input to the coupling control part S3.

[0046] X-axis position error signal E x and Y-axis position error signal E y and the X-axis coupling gain C x and the Y-axis coupling gain C y After multiplication, the difference is obtained to obtain the cross-coupling estimated contour error ε c , the cross-coupling estimated profile error ε c The output of the robust cross-coupling controller C is respectively coupled to the X-axis coupling gain C x and Y-axis coupling gain C y After multiplication, they are re-input into the X-axis feedback control part S1 and the Y-axis feedback control part S2 respectively.

[0047] X-axis position error signal E x Through the X-axis feedback controller G cx The output of the robust cross-coupling controller C and the X-axis coupling gain C x Subtract the multiplication results to get the X-axis controller output U x , Y-axis position error signal E y Through the Y-axis feedback controller G cy The output of the robust cross-coupling controller C and the Y-axis coupling gain C y The results are added to get the Y-axis controller output U y , the X-axis controller output U x The nominal object P on the X axis x Get the X-axis output position X o , the Y-axis controller output U y The Y axis nominal object P y Get the Y axis output position Y o .

[0048] When the robust cross-coupling controller C is set to 0, it is equivalent to no cross-coupling control. Figure 3 As shown, compared with the cross-coupling control, its robust cross-coupling controller C does not work, and the uncoupled estimated contour error ε0 is obtained.

[0049] like Figure 2 to Figure 4 As shown, based on quantitative feedback theory, according to Figure 2 The cross-coupling control block diagram shown in Figure 3 The cross-coupling-free control block diagram shown and Figure 4 The control block diagram of the estimated contour error equivalent feedback loop is shown in FIG. A two-dimensional trajectory collaborative tracking method of an H-bridge type precision motion mechanism is proposed, including the following steps:

[0050] Step 1: Solve the cross-coupling estimated contour error ε for the cross-coupling and no cross-coupling of the two-dimensional trajectory collaborative tracking system of the H-bridge precision motion mechanism. c and the uncoupled estimated contour error ε0, which is in the following form:

[0051]

[0052]

[0053] Step 2: Estimating the cross-coupling contour error ε c Compared with the uncoupled estimated contour error ε0, the transfer function T of the estimated contour error is obtained, which is as follows:

[0054]

[0055] Among them, C x = sinφ,C y =cosφ, φ is the angle between the two-dimensional motion trajectory and the X-coordinate axis, which changes with the two-dimensional motion trajectory.

[0056] The transfer function T of the estimated contour error is the same as the sensitivity function of the traditional feedback control system. Based on this, an equivalent feedback loop of the estimated contour error is established. Figure 4 As shown, it includes a robust cross-coupled controller C and an equivalent controlled object K, wherein the uncoupled estimated contour error ε0 minus the equivalent feedback loop output Y e The cross-coupling estimated contour error ε is obtained c , and then input to the robust cross-coupling controller C to obtain the equivalent robust cross-coupling controller output U e , the equivalent robust cross-coupled controller output U e The equivalent feedback loop output Y is obtained through the equivalent controlled object K. e , define the equivalent open-loop transfer function Go =CK, an effective way to reduce the estimated contour error is to reduce the sensitivity function amplitude of the equivalent feedback loop;

[0057] Step 3: Select the full-band vector w all ={w l ,w h}, where w l is the low frequency band vector, w l =(2π×0, 2π×20]rad / s, w h is the mid-high frequency band vector, w l =(2π×20, 2π×5000]rad / s, according to the change parameter φ of the equivalent controlled object K, the equivalent controlled object is traversed from φ∈[0,0.5π] with the change amount dφ as the interval, and the frozen linear time-invariant equivalent controlled object set K is obtained i , w all Substitute each element into the set K i From the transfer function elements of each linear time-invariant equivalent controlled object in, we can obtain w all Under each element, the amplitude and phase of each linear time-invariant equivalent controlled object are plotted. All the obtained function points are plotted in the form of phase as the horizontal axis and amplitude as the vertical axis to form a Nichols diagram as the template of the equivalent controlled object. The linear time-invariant equivalent controlled object transfer function with the minimum amplitude in the sample diagram of each frequency band is found as the nominal transfer function K of the equivalent controlled object. nominal , used for the subsequent design of robust cross-coupling controller C;

[0058] Step 4: In order to reduce the estimated contour error, the vector w in the low frequency band l The upper sensitivity boundary M of the equivalent feedback control is limited by the following method:

[0059]

[0060] The above formula is the sensitivity limiting formula, and we can find w l The robust cross-coupling controller C(jw l ), let it be the equivalent controlled object K in each linear time invariant i (jw l ) satisfies the sensitivity limiting formula, which is the sensitivity limiting process. Among them, M is a constant, C(jw l ) is w l The complex value of the transfer function of the robust cross-coupled controller in each element, K i (jw l ) is w l The set K of elements i The complex value of the transfer function of each linear time-invariant equivalent controlled object.

[0061] In order to ensure the stability of the equivalent feedback loop, the amplitude of the transfer function is limited. all The bounding function T u , boundary function T u Based on the empirical formula of the second-order system and the design of adding system zeros and poles, the limiting method is as follows:

[0062]

[0063] The above formula is a stability limiting formula. Find w all The robust cross-coupling controller C(jw all ), let it be the equivalent controlled object K in each linear time invariant i (jw all ) satisfies the stability limitation formula, which is a stability limitation process. Among them, T u (jw all ) is w all The complex value of the transfer function of the boundary function in each element, C(jw all ) is w all The complex value of the transfer function of the robust cross-coupled controller in each element, K i (jw all ) is w all The set K of elements i The complex value of the transfer function of each linear time-invariant equivalent controlled object;

[0064] Step 5: In the sensitivity limitation process, the low-frequency vector w l The equivalent open-loop transfer function under the transfer function value G o (jw l )=C(jw l )K(jw l ) is written in plural form Let it be in w l The elements, phases and amplitudes of the traversal are traversed in three dimensions. In all the traversed phases, the complex values ​​of each point are compared with the complex values ​​of the nominal transfer function of the equivalent controlled object of the traversal of the low-frequency elements at each point to obtain w l The complex value of the transfer function C(jw l ), through the sensitivity limit formula, find the amplitude extreme point under each phase, that is, the amplitude extreme point under each phase satisfies that all the elements of the equivalent controlled object set just meet the sensitivity limit formula at the amplitude extreme point, in w l In each element, the amplitude extreme points under all phases are connected to obtain the boundary of the sensitivity limit condition; in the stability limit process, the full-band vector w all The equivalent open-loop transfer function under the transfer function value G o (jw all)=C(jw all )K(jw all ) is written in plural form Let it be in w all The elements, phases and amplitudes of the traversal are traversed in three dimensions. In all the traversed phases, the complex values ​​of each point are compared with the complex values ​​of the nominal transfer function of the equivalent controlled object of each point traversing the full-band elements to obtain w all The complex value of the transfer function C(jw all ), through the stability limit formula, find the amplitude extreme point under each phase, that is, the amplitude extreme point under each phase satisfies the stability limit formula of each equivalent controlled object set element at the amplitude extreme point, all In each element, the amplitude extreme points under all phases are connected to obtain the boundary of the stability limitation condition.

[0065] Afterwards, the boundary of the sensitivity constraint condition is combined with the boundary of the stability constraint condition to obtain the Nichols diagram of the composite boundary;

[0066] Step 6: In the Nichols diagram of the composite boundary, the robust cross-coupling controller is designed as:

[0067]

[0068] Among them, K g is the robust cross-coupled controller gain, z i is the zero point of the robust cross-coupling controller, p j is the pole of the robust cross-coupled controller, m is the number of zeros of the robust cross-coupled controller, and n is the number of poles of the robust cross-coupled controller.

[0069] Finally, the equivalent nominal open-loop transfer function CK obtained by multiplying the nominal transfer function of the robust cross-coupled controller with the equivalent controlled object is nominal , in the low frequency band vector w l Each element and the full-band vector w all All elements satisfy the composite boundary conditions.

[0070] Example

[0071] In the cross-coupling control established in this embodiment, the single-degree-of-freedom feedback controller G cx , G cy and the single-degree-of-freedom nominal object P x , P y They are as follows:

[0072]

[0073] Based on the above cross-coupling control, an equivalent feedback loop is established and an equivalent controlled object is obtained. The following are selected:

[0074] w l =2πf l ,

[0075] f l ={0.1Hz,0.5Hz,1Hz,10Hz},

[0076] w all =2πf all ,

[0077] f all ={0.1Hz,0.5Hz,1Hz,10Hz,35Hz,100Hz,1000Hz},

[0078] Let dφ=0.025π, design boundary function T u for:

[0079]

[0080] According to the above specific implementation steps, the equivalent controlled object template is obtained as follows: Figure 5 As shown, the sensitivity limit boundary diagram is as follows Figure 6 As shown in , the boundaries of each element in the low frequency band coincide in the Nichols diagram. The stability limit condition boundary diagram is shown in Figure 7 shown.

[0081] Design the robust cross-coupled controller C as:

[0082]

[0083] Nichols diagram of equivalent nominal open-loop transfer function based on composite boundary design Figure 8 shown.

[0084] In order to illustrate the advantages of this method over the traditional method in that it has high tracking accuracy and can satisfy any trajectory input, the reference circular trajectory and angular trajectory are input respectively without changing the controller parameters, and the output results are combined with Fig. 9 and Fig.10 Its tracking trajectory index is the root mean square error index: for circular trajectory, the root mean square error of non-coupling control is 2.53μm, the root mean square error of traditional PID cross-coupling control is 1.15μm, and the root mean square error of quantitative feedback cross-coupling control is 0.74μm; for angular trajectory, the root mean square error of non-coupling control is 5.66μm, the root mean square error of traditional PID cross-coupling control is 6.06μm, and the root mean square error of quantitative feedback cross-coupling control is 4.07μm.

[0085] In summary, it can be seen that the two-dimensional trajectory collaborative tracking system and method of the H-bridge precision motion mechanism proposed in the present invention has better tracking performance than the traditional method, meets the conditions for inputting any trajectory, and can be designed offline.

[0086] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0087] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A two-dimensional trajectory collaborative tracking system of an H-bridge type precision motion mechanism, comprising an X-axis feedback control part S1 and a Y-axis feedback control part S2, wherein the X-axis feedback control part S1 comprises an X-axis feedback controller G cx with the X-axis nominal object P x The Y-axis feedback control part S2 includes a Y-axis feedback controller G cy with the Y axis nominal object P y , characterized in that: The system further comprises a coupling control part S3, wherein the coupling control part S3 comprises an X-axis coupling gain C x , Y-axis coupling gain C y with a robust cross-coupling controller C; The two-dimensional motion trajectory is decomposed into the X-axis reference trajectory input X r and Y axis reference trajectory input Y r , the X-axis reference trajectory input X r Output position X o The X-axis position error signal E is obtained by subtracting x , the Y-axis reference trajectory input Y r Output position Y o The Y-axis position error signal E is obtained by subtracting y , the X-axis position error signal E x Input to the X-axis feedback controller G cx , the Y-axis position error signal E y Input to the Y-axis feedback controller G cy ; X-axis position error signal E x and Y-axis position error signal E y and the X-axis coupling gain C x and the Y-axis coupling gain C y After multiplication, the difference is obtained to obtain the cross-coupling estimated contour error ε c , the cross-coupling estimated profile error ε c The output of the robust cross-coupling controller C is respectively coupled to the X-axis coupling gain C x and Y-axis coupling gain C y multiply; X-axis position error signal E x Through the X-axis feedback controller G cx The output of the robust cross-coupling controller C and the X-axis coupling gain C x Subtract the multiplication results to get the X-axis controller output U x , Y-axis position error signal E y Through the Y-axis feedback controller G cy The output of the robust cross-coupling controller C and the Y-axis coupling gain C y The results are added to get the Y-axis controller output U y , the X-axis controller output U x The nominal object P on the X axis x Get the X-axis output position X o , the Y-axis controller output U y The Y axis nominal object P y Get the Y axis output position Y o .

2. The two-dimensional trajectory collaborative tracking system of an H-bridge type precision motion mechanism according to claim 1, characterized in that: When the robust cross-coupling controller C is not working, a coupling-free estimated contour error ε0 is obtained.

3. A two-dimensional trajectory collaborative tracking method for an H-bridge precision motion mechanism, characterized in that: According to the system of claim 2, the two-dimensional trajectory collaborative tracking method thereof comprises the following steps: Step 1: Solve the cross-coupling estimated contour error ε c And the uncoupled estimated contour error ε0: Step 2: Estimating the cross-coupling contour error ε c Compared with the uncoupled estimated contour error ε0, the transfer function T of the estimated contour error is obtained: Among them, C x = sinφ,C y =cosφ, φ is the angle between the two-dimensional motion trajectory and the X-coordinate axis; Establish an estimated contour error equivalent feedback loop, including a robust cross-coupling controller C and an equivalent controlled object K, the uncoupled estimated contour error ε0 minus the equivalent feedback loop output Y e The cross-coupling estimated contour error ε is obtained c , and then input to the robust cross-coupling controller C to obtain the equivalent robust cross-coupling controller output U e , the equivalent robust cross-coupled controller output U e The equivalent feedback loop output Y is obtained through the equivalent controlled object K. e , define the equivalent open-loop transfer function G o =CK; Step 3: Select the full-band vector w all ={w l ,w h },w l is the low frequency band vector, w h is the vector of the medium and high frequency band, and the equivalent controlled object is traversed from φ∈[0,0.5π] with the change dφ as the interval to obtain the frozen linear time-invariant equivalent controlled object set K i , w all Substitute each element into the set K i From the transfer function elements of each linear time-invariant equivalent controlled object in, we can obtain w all Under each element, the amplitude and phase of each linear time-invariant equivalent controlled object are plotted. All the obtained function points are plotted in the form of phase as the horizontal axis and amplitude as the vertical axis to form a Nichols diagram as the template of the equivalent controlled object. The linear time-invariant equivalent controlled object transfer function with the minimum amplitude in the sample diagram of each frequency band is found as the nominal transfer function K of the equivalent controlled object. nominal ; Step 4: Vector w in the low frequency band l Perform sensitivity limitation and limit the upper sensitivity boundary M: Among them, M is a constant, C(jw l ) is w l The complex value of the transfer function of the robust cross-coupled controller in each element, K i (jw l ) is w l The set K of elements i The complex value of the transfer function of each linear time-invariant equivalent controlled object; In the full frequency band vector w all Perform stability constraints and limit the boundary function T u : Among them, T u (jw all ) is w all The complex value of the transfer function of the boundary function in each element, C(jw all ) is w all The complex value of the transfer function of the robust cross-coupled controller in each element, K i (jw all ) is w all The set K of elements i The complex value of the transfer function of each linear time-invariant equivalent controlled object; Step 5: In the sensitivity limitation and stability limitation process, the low-frequency vector w l and the full-band vector w all The equivalent open-loop transfer function under the condition of l and w all The elements, phases and amplitudes of the traversal are traversed in three dimensions. In all the traversed phases, the complex values ​​of each point are compared with the complex values ​​of the nominal transfer function of the equivalent controlled object of each point traversing the low-frequency band and full-frequency band elements to obtain w l and w all The complex value of the transfer function C(jw l ) and C(jw all ), respectively, through sensitivity limitation and stability limitation, find the amplitude extreme points under each phase, respectively at w l and w all In each element, the amplitude extreme points under all phases are connected to obtain the boundaries of sensitivity constraints and stability constraints, and the boundaries are composited to obtain the Nichols diagram of the composite boundary; Step 6: Design a robust cross-coupling controller in the Nichols diagram of the composite boundary: Among them, K g is the robust cross-coupled controller gain, z i is the zero point of the robust cross-coupling controller, p j is the pole of the robust cross-coupling controller, m is the number of zeros of the robust cross-coupling controller, and n is the number of poles of the robust cross-coupling controller; The equivalent nominal open-loop transfer function CK obtained by multiplying the nominal transfer function of the robust cross-coupled controller and the equivalent controlled object is nominal , in the low frequency band vector w l Each element and the full-band vector w all All elements satisfy the composite boundary conditions.

4. The method for collaboratively tracking a two-dimensional trajectory of an H-bridge precision motion mechanism according to claim 3, characterized in that: In step 3, the low frequency band vector w l =(2π×0, 2π×20]rad / s, mid-high frequency vector w l =(2π×20, 2π×5000]rad / s.

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