Method and device for tuning controller parameters in a servo system, and computing device

Abstract

The present application relates to the technical field of controller parameter tuning, and discloses a method and device for tuning controller parameters in a servo system, and a computing device. The tuning method includes: sweeping the frequency characteristics of the controlled object in the servo system, and determining the open-loop transfer function for the controlled object according to the frequency characteristics; determining the full-band constraint boundary for the servo system according to the constraint conditions of the user on the stability and disturbance rejection of the servo system; making the real part and the imaginary part of the coordinates of the open-loop transfer function equal to the coordinates of the full-band constraint boundary, and making the slopes of the open-loop transfer function and the full-band constraint boundary equal at the intersection point, to determine a full-rank system of equations; solving the full-rank system of equations to obtain the target solution set of the controller parameters, and screening out the target controller parameters from the target solution set according to the maximum bandwidth criterion. The present application can reduce the production costs of time and manpower increased by re-designing the controller parameters when replacing the controlled object, and improve the production efficiency of industrial manufacturing.

Description

Technical Field

[0001] This application relates to the technical field of controller parameter tuning, for example, to a method and device for tuning controller parameters in a servo system, and a computing device. Background Art

[0002] In the related art, for the diverse scenarios of industrial manufacturing, the differences between different controlled objects are significant. For the controlled objects corresponding to the outer loop (i.e., speed and position loops) of the servo system, the characteristics of the load side need to be considered. When modeling, the influence of flexible transmission links (such as elastic shafts, gearboxes, ball screws, and their transmission belts, etc.) often needs to be considered. Therefore, when replacing the controlled object in the servo system, it is necessary to redesign the controller parameters of the servo system.

[0003] In the process of implementing the embodiments of the present disclosure, it is found that at least the following problems exist in the related art:

[0004] Frequently redesigning controller parameters will increase time and labor costs. Therefore, how to provide a general controller parameter tuning method to reduce the time and labor production costs increased by redesigning controller parameters when replacing the controlled object and improve the production efficiency of industrial manufacturing has become a technical problem that urgently needs to be solved. Summary of the Invention

[0005] To have a basic understanding of some aspects of the disclosed embodiments, a simple summary is given below. The summary is not a general review, nor is it intended to identify key / important constituent elements or delineate the protection scope of these embodiments, but rather serves as a preface to the subsequent detailed description.

[0006] The embodiments of the present disclosure provide a method and device for tuning controller parameters in a servo system, and a computing device, which can reduce the time and labor production costs increased by redesigning controller parameters when replacing the controlled object and improve the production efficiency of industrial manufacturing.

[0007] In some embodiments, the method for tuning controller parameters in a servo system includes: sweeping the frequency characteristics of the controlled object in the servo system to determine the controlled object and the open-loop transfer function for the controlled object; determining the full-frequency band constraint boundary for the servo system according to the user's constraint conditions on the stability and disturbance rejection of the servo system; making the real and imaginary parts of the coordinates of the open-loop transfer function equal to the coordinates of the full-frequency band constraint boundary, and making the slopes of the open-loop transfer function and the full-frequency band constraint boundary equal at the intersection point to determine a full-rank system of equations; solving the full-rank system of equations to obtain the target solution set of the controller parameters, and screening out the target controller parameters from the target solution set according to the maximum bandwidth criterion.

[0008] Optionally, the constraint conditions for the stability of the servo system include: closed-loop amplitude constraint, phase margin constraint, and gain margin constraint; the constraint conditions for the disturbance rejection of the servo system include: disturbance rejection performance constraint; according to the user's constraint conditions for the stability and disturbance rejection of the servo system, determine the full-band constraint boundary of the servo system, including: according to the upper limit value of the closed-loop amplitude constraint, use the open-loop transfer function of the servo system to draw a closed-loop amplitude circle; limit the gain margin and phase margin of the closed-loop amplitude circle according to the phase margin constraint and the gain margin constraint to determine the stability constraint boundary; construct a disturbance rejection constraint circle according to the disturbance rejection performance constraint, and on the basis of the stability constraint boundary, extend the maximum phase line and connect the arc segment of the disturbance rejection constraint circle to determine the full-band constraint boundary.

[0009] Optionally, solving the full-rank equation set to obtain the target solution set of the controller parameters includes: receiving the angle step and frequency step input by the user; solving the full-rank equation set based on the angle step and frequency step according to a preset search algorithm to obtain the target solution set of the controller parameters.

[0010] Optionally, screening out the target controller parameters from the target solution set according to the maximum bandwidth criterion includes: for each solution in the target solution set, calculate the frequency when the closed-loop amplitude of the servo system first decays to the set decibel as the bandwidth of the servo system; select the solution corresponding to the maximum bandwidth in the target solution set as the target controller parameters.

[0011] Optionally, before screening out the target controller parameters from the target solution set according to the maximum bandwidth criterion, the tuning method further includes: correcting the target solution set.

[0012] Optionally, correcting the target solution set includes: determining the frequency points to be corrected corresponding to each solution in the target solution set; calculating the complex plane coordinates of the open-loop transfer function at the frequency points to be corrected; in the case where the complex plane coordinates are within the stability constraint boundary of the servo system, removing the solution corresponding to the frequency point to be corrected from the target solution set.

[0013] Optionally, determining the frequency points to be corrected corresponding to each solution in the target solution set includes: determining the phase angle range of the stability constraint boundary of the servo system; calculating the phase angle of each solution in the target solution set at each frequency point; using the frequency points with the phase angle within the phase angle range as the frequency points to be corrected.

[0014] In some embodiments, a device for tuning controller parameters in a servo system includes: a frequency sweeping module configured to sweep the frequency characteristics of a controlled object in the servo system to determine the controlled object and the open-loop transfer function for the controlled object; a constraint module configured to determine the full-band constraint boundary for the servo system according to the user's constraint conditions on the stability and disturbance rejection of the servo system; a determination module configured to make the real and imaginary parts of the coordinates of the open-loop transfer function equal to those of the coordinates of the full-band constraint boundary, and make the slopes of the open-loop transfer function and the full-band constraint boundary equal at the intersection point to determine a full-rank equation set; and a solution module configured to solve the full-rank equation set to obtain a target solution set of controller parameters and screen out target controller parameters from the target solution set according to the maximum bandwidth criterion.

[0015] In some embodiments, a device for tuning controller parameters in a servo system includes a processor and a memory storing program instructions, and the processor is configured to be able to execute the method for tuning controller parameters in a servo system as described above.

[0016] In some embodiments, a computing device includes: a device body; and the device for tuning controller parameters in a servo system as described above, which is disposed on the device body.

[0017] The method, device, and computing device for tuning controller parameters in a servo system provided by the embodiments of the present disclosure can achieve the following technical effects:

[0018] In the embodiments of the present disclosure, after replacing the controlled object in the servo system, the frequency characteristics of the controlled object are obtained by a frequency sweeping method, and the open-loop transfer function for the controlled object is determined according to the frequency characteristics. The full-band constraint boundary is constructed according to the user's constraint conditions on the stability and disturbance rejection of the servo system. A full-rank equation set for the servo system is constructed according to the open-loop transfer function and the full-band constraint. Finally, a target solution set is obtained by solving the full-rank equation set, and target controller parameters for the replaced controlled object are screened out from the target solution set according to the maximum bandwidth criterion. In this way, when replacing the controlled object in the servo system, it is not necessary for the user to manually measure the relevant parameters of the controlled object and establish relevant models. Nor is it necessary to rely on experience for multiple trials and errors as in traditional tuning methods. Therefore, the embodiments of the present disclosure can reduce the production costs of time and manpower increased by re-designing controller parameters and improve the production efficiency of industrial manufacturing.

[0019] The above general description and the following description are only exemplary and explanatory, and are not used to limit this application. Description of the Drawings

[0020] One or more embodiments are exemplarily illustrated by corresponding drawings. These exemplary illustrations and the drawings do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are shown as similar elements. The drawings do not constitute a scale limitation, and wherein:

[0021] Figure 1 is a schematic diagram of a method for tuning controller parameters in a servo system provided by an embodiment of the present disclosure;

[0022] Figure 2 is a schematic diagram of a unit negative feedback closed-loop system provided by an embodiment of the present disclosure;

[0023] Figure 3 is a schematic diagram of a stability region satisfying closed-loop amplitude constraints provided by an embodiment of the present disclosure;

[0024] Figure 4 is a schematic diagram of a stability region satisfying closed-loop amplitude constraints and gain margin constraints provided by an embodiment of the present disclosure;

[0025] Figure 5 is a schematic diagram of a stability region satisfying closed-loop amplitude constraints, gain margin constraints, and phase margin constraints provided by an embodiment of the present disclosure;

[0026] Figure 6 is a schematic diagram of a stability region satisfying closed-loop amplitude constraints, gain margin constraints, phase margin constraints, and disturbance rejection performance constraints provided by an embodiment of the present disclosure;

[0027] Figure 7 is a schematic diagram of a process for solving a full-rank equation set based on angle step and frequency step provided by an embodiment of the present disclosure;

[0028] Figure 8 is a schematic diagram of another method for tuning controller parameters in a servo system provided by an embodiment of the present disclosure;

[0029] Figure 9 is a schematic diagram of a process for correcting a target solution set provided by an embodiment of the present disclosure;

[0030] Figure 10 is a schematic diagram of a device for tuning controller parameters in a servo system provided by an embodiment of the present disclosure;

[0031] Figure 11 is a schematic diagram of a device for tuning controller parameters in a servo system provided by an embodiment of the present disclosure. Detailed implementation manners

[0032] In order to understand the features and technical content of the embodiments of the present disclosure in more detail, the implementation of the embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings. The attached drawings are only for reference and explanation, and are not used to limit the embodiments of the present disclosure. In the following technical descriptions, for the sake of explanation, numerous details are provided to give a full understanding of the disclosed embodiments. However, one or more embodiments can still be implemented without these details. In other cases, well-known structures and devices may be shown in a simplified manner to simplify the drawings.

[0033] In the description of the embodiments of the present disclosure, the terms "first", "second", etc. in the specification, claims and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so as to implement the embodiments of the present disclosure described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion.

[0034] Unless otherwise specified, the term "a plurality of" features means two or more.

[0035] In the embodiments of the present disclosure, the character " / " features indicate that the objects before and after are in an "or" relationship. For example, the A / B feature means: A or B.

[0036] The term "and / or" is a description of the associated relationship of an object, and the feature indicates that three relationships can exist. For example, A and / or B, the feature means: A or B, or, the three relationships of A and B.

[0037] The term "corresponding" can refer to an associated relationship or a binding relationship. A corresponding to B means that there is an associated relationship or a binding relationship between A and B.

[0038] It should be noted that, without conflict, the embodiments in the embodiments of the present disclosure and the features in the embodiments can be combined with each other.

[0039] As Figure 1 shown, the embodiments of the present disclosure provide a method for tuning the controller parameters in a servo system. The execution subject of the tuning method can be a processor, and the tuning method includes:

[0040] S101, the processor sweeps the frequency characteristics of the controlled object in the servo system, and determines the open-loop transfer function for the controlled object according to the frequency characteristics.

[0041] Specifically, the servo system belongs to a unit negative feedback closed-loop system, and its specific structure is as Figure 2As shown, by using chirp as the injected swept-frequency signal and setting the target frequency range and frequency step of the frequency sweep, the swept-frequency result of the controlled object under the discrete linear frequency set can be obtained. After performing a series of processes on the swept-frequency result, the frequency characteristics of the controlled object can be determined.

[0042] Specifically, the swept-frequency result of the controlled object under the discrete linear frequency set is expressed by the following expression (1):

[0043] Ω = {ω start , ···, ω end}, (1);

[0044] where Ω is the swept-frequency result of the controlled object, ω start is the starting step of the frequency, and ω end is the ending step of the frequency.

[0045] Specifically, the frequency characteristics of the controlled object are expressed by the following expression (2):

[0046] H(jω) = X H (ω) + jY H (ω), (2);

[0047] where H(jω) is the frequency characteristics of the controlled object, X H (ω) is the real part of the controlled object, and Y H (ω) is the imaginary part of the controlled object.

[0048] Specifically, the real part and the imaginary part of the controlled object are expressed by the following expression (3):

[0049]

[0050] where |H(jω)| and ∠H(jω) are the amplitude and phase angle of the controlled object, respectively.

[0051] Specifically, by substituting the frequency characteristics of the controlled object into the corresponding expression of the open-loop transfer function, the open-loop transfer function for the controlled object can be determined.

[0052] S102. The processor determines the full-frequency band constraint boundary for the servo system according to the user's constraint conditions on the stability and disturbance rejection of the servo system.

[0053] Specifically, the stability constraint condition for the servo system mainly focuses on whether the servo system can quickly return to the original equilibrium state or fluctuate within an allowable range when subjected to external disturbances or internal parameter changes. The disturbance rejection constraint condition mainly focuses on the resistance ability of the servo system to external disturbances.

[0054] Specifically, the stability constraint boundary of the servo system can be determined according to the stability constraint conditions of the servo system. On the basis of the stability constraint boundary, the stability constraint boundary can be further restricted according to the disturbance rejection constraint conditions of the servo system, and then the full-band constraint boundary of the servo system can be determined.

[0055] Optionally, the constraint conditions for the stability of the servo system include: closed-loop amplitude constraint, phase margin constraint, and gain margin constraint; the constraint conditions for the disturbance rejection of the servo system include: disturbance rejection performance constraint; determining the full-band constraint boundary of the servo system according to the constraint conditions of the user for the stability and disturbance rejection of the servo system includes: drawing a closed-loop amplitude circle using the open-loop transfer function of the servo system according to the upper limit value of the closed-loop amplitude constraint; restricting the gain margin and phase margin of the closed-loop amplitude circle according to the phase margin constraint and the gain margin constraint to determine the stability constraint boundary; constructing a disturbance rejection constraint circle according to the disturbance rejection performance constraint, and on the basis of the stability constraint boundary, extending the maximum phase line and connecting the arc segment of the disturbance rejection constraint circle to determine the full-band constraint boundary.

[0056] Specifically, the closed-loop transfer function is an important representation of the stability of the servo system, which is specifically reflected in the resonance peak and bandwidth parameters. When the closed-loop amplitude is too high, the servo system will generate severe vibrations, causing irreversible damage to the controlled object. Therefore, in order to ensure the stability of the servo system, a constant upper limit value W greater than 1 needs to be set for the closed-loop amplitude threshold1 (i.e., the upper limit value of the closed-loop amplitude constraint), and the obtained inequality is represented by the following expression (4):

[0057]

[0058] where jω represents the complex frequency, feedback(jω) is the feedback signal at the complex frequency, reference(jω) is the reference signal at the complex frequency, L(jω) is the open-loop transfer function of the servo system, and there is L(jω) = X L (ω) + jY L (ω).

[0059] Specifically, substituting L(jω) = X L (ω) + jY L (ω) into the above expression (4), it can be rewritten as the following expression (5):

[0060]

[0061] Specifically, when the expression (5) is satisfied and the equal sign holds, the expression (4) appears as a circle in the Nyquist diagram, and this circle is the closed-loop amplitude circle.

[0062] Exemplarily, taking the upper limit value W of the closed-loop amplitude constraint as threshold1 = 1.93 as an example, the corresponding closed-loop amplitude circle is as Figure 3 shown.

[0063] Specifically, referring to Figure 3 it can be known that the distance between the intersection point of the closed-loop amplitude circle and the negative real axis closer to the origin and the coordinate (-1, j0) corresponds to the gain margin, which is expressed by the following expression (6):

[0064]

[0065] where GM is the gain margin, the center of (4) represents the center of the closed-loop amplitude circle obtained by expression (4), and the radius of (4) represents the radius of the closed-loop amplitude circle obtained by expression (4).

[0066] Specifically, referring to Figure 3 it can be known that the coordinates of the intersection point of the closed-loop amplitude circle and the unit circle in the complex plane are (-cos(PM), -jsin(PM)), and the angle between this intersection point and the negative real axis represents the phase margin. It is expressed by the following expression (7):

[0067]

[0068] where PM is the phase margin.

[0069] Specifically, based on the above expressions (6) and (7), it can be known that there is a certain relationship between the upper limit value of the closed-loop amplitude constraint and the gain margin and the phase margin. Therefore, the user can set the upper limit value of the closed-loop amplitude constraint according to the preset gain margin and phase margin.

[0070] Specifically, in order to expand the phase margin at a single point to a full-band constraint, the embodiments of the present disclosure introduce two phase rays starting from the origin and having an angle of with the negative real axis (such as the dashed line A in Figure 4 ). Setting as the phase margin input by the user, the stability region defined by the closed-loop amplitude constraint cannot be compatible with the phase margin, resulting in damage to the stability of the servo system. Therefore, in order to take into account the phase margin input by the user and the effectiveness of the closed-loop amplitude constraint, it is necessary to set as the maximum phase of the closed-loop amplitude circle. In this case, is expressed by the following expression (8):

[0071]

[0072] where is the phase margin constraint on the closed-loop amplitude circle.

[0073] Specifically, connect the maximum phase line shown in Figure 4 with the closed-loop amplitude circle, and the closed-loop amplitude circle can be further restricted by the phase margin constraint. Specifically, after further restricting the closed-loop amplitude circle by the phase margin constraint, an excessive gain margin will be introduced, and it is difficult for the servo system to reach this standard. If you want to reach this standard, you need to sacrifice the dynamic response performance of the servo system. Therefore, in the embodiments of the present disclosure, a gain margin constraint will also be performed to establish a gain constraint circle, adjust the gain margin to a user-defined level, and reduce the excessive gain margin.

[0074] Specifically, to establish a gain constraint circle that is compatible with the phase margin constraint defined in

[0075] Let the gain constraint circle be tangent to the maximum phase line. Therefore, the center of the gain constraint circle is located on the negative real axis, and the specific situation is as shown in Figure 5 shown.

[0076] Specifically, in order to make the established gain constraint circle satisfy the gain margin, let the coordinates of the intersection point of the gain constraint circle and the negative real axis closer to the origin be (-X circle2 , j0), and this point needs to satisfy the following expression (9):

[0077]

[0078] Specifically, according to expression (9), X circle2 = 10 -GM / 20 . Let the radius of the gain constraint circle be R circle2 , then the center coordinates of the gain constraint circle can be determined as (-10 -GM / 20 _R circle2 , j0). Based on the same idea as expression (8), Figure 6 in is calculated through the following expression (10):

[0079]

[0080] where is the phase margin constraint for the gain constraint circle, the radius of circle2 represents the radius of the gain constraint circle, and the center of circle2 represents the center of the gain constraint circle.

[0081] Specifically, based on the above expression (10), the expression (11) for calculating the radius of the gain constraint circle can be derived:

[0082] ​

[0083] wherein, R circle2 is the radius of the gain constraint circle.

[0084] Specifically, based on the above expressions (10) and (11), the analytical formula of the gain constraint circle can be determined, which is represented by the following expression (12):

[0085]

[0086] Specifically, as Figure 5 shown, on the basis of the boundary obtained by further restricting the closed-loop amplitude circle through the phase margin constraint, removing the area on the right side of the gain constraint circle can obtain the stability constraint boundary.

[0087] It should be noted that if the gain margin preset by the user is less than the gain margin defined in the closed-loop amplitude constraint, after the gain margin constraint, the part on the right side of the closed-loop amplitude circle that needs to be removed, and at this time the maximum phase line is shortened to a point, and the final stability constraint boundary is the same as Figure 3 the situation shown.

[0088] Specifically, the stability constraint boundary can ensure the stability of the servo system. However, in the low-frequency range, more attention is paid to the disturbance rejection performance of the servo system. Therefore, the embodiments of the present disclosure also set a disturbance rejection performance constraint and constructed a disturbance rejection constraint circle to impose the disturbance rejection performance constraint.

[0089] Specifically, first, the sensitivity function needs to be introduced. The sensitivity function is used to evaluate the sensitivity of the servo system to low-frequency disturbance signals. When its amplitude is too high, the disturbance rejection ability of the servo system weakens, resulting in an increase in the tracking error. Therefore, the embodiments of the present disclosure also set an upper limit W threshold2 for the amplitude of the sensitivity function. The sensitivity function is represented by the following expression (13):

[0090]

[0091] wherein, jω represents the complex frequency, error(jω) is the error signal at the complex frequency, reference(jω) is the reference signal at the complex frequency, and |1 + L(jω)| is the distance from the open-loop transfer function to the point (-1, j0) in the complex plane. The design of the disturbance rejection constraint circle aims to increase this distance as much as possible in the low-frequency range, thereby reducing the amplitude of the sensitivity function and improving the disturbance rejection ability of the servo system. To simplify the user setting process, in the embodiments of the present disclosure, the disturbance rejection constraint circle is directly constructed based on the conventional margins (phase margin and gain margin) without additional parameter configuration.

[0092] Specifically, to make the disturbance rejection constraint circle compatible with the phase margin requirement and effectively constrain the low-frequency band below the phase margin, the disturbance rejection constraint circle is designed to be tangent to the maximum phase line. Then, the center of the disturbance rejection constraint circle is located on the negative real axis. The specific situation is as Figure 6 shown.

[0093] Specifically, as Figure 6 shown, find a point on the negative real axis to the left of the point (-1, j0). The distance from this point to (-1, j0) is equal to the user-defined gain margin, and let this point be the intersection of the disturbance rejection constraint circle and the negative real axis farther from the origin. Suppose the coordinates of this point are (-X circle3 , j0). Then, the following expression (14) can be determined:

[0094]

[0095] Specifically, according to expression (14), X circle3 = 10 GM / 20 . Suppose the radius of the gain constraint circle is R circle3 . Then, the center coordinates of the disturbance rejection constraint circle can be determined as (-10 GM / 20 +R circle3 , j0). Based on the same idea as expression (8), Figure 6 in is calculated through the following expression (15):

[0096]

[0097] where is the phase margin constraint on the disturbance rejection constraint circle, the radius of circle3 represents the radius of the disturbance rejection constraint circle, and the center of circle3 represents the center of the disturbance rejection constraint circle.

[0098] Specifically, based on the above expression (15), the expression (16) for calculating the radius of the disturbance rejection constraint circle can be derived:

[0099]

[0100] where R circle3 is the radius of the disturbance rejection constraint circle.

[0101] Specifically, based on the above expressions (15) and (16), the analytical formula of the disturbance rejection constraint circle can be determined, which is shown by the following expression (17):

[0102]

[0103] Specifically, the arc segment of the anti-disturbance constraint circle to the left of the tangent point corresponds to a larger |1 + L(jω)| value. Therefore, selecting this arc segment as the boundary can impose a stronger anti-disturbance constraint. On the basis of the stability constraint boundary, extend the maximum phase line and connect this arc segment to determine the final full-frequency band constraint boundary.

[0104] S103. The processor makes the real and imaginary parts of the coordinates of the open-loop transfer function equal to those of the full-frequency band constraint boundary, and makes the slopes of the open-loop transfer function and the full-frequency band constraint boundary equal at the intersection point to determine a full-rank equation set.

[0105] Specifically, the coordinates of the open-loop transfer function of the servo system at a certain frequency ω are (X H , jY H ), and the coordinates of the full-frequency band constraint boundary are (X qft , jY qft ). Making the real and imaginary parts of these two coordinates equal respectively can obtain an equation set with a rank of 2. However, the undetermined parameters of the controller in the servo system include ω 0 , K p and K i . Therefore, this equation set has an under-rank problem. Thus, the embodiment of the present disclosure additionally adds the condition that the slopes of the open-loop transfer function and the full-frequency band constraint boundary are equal at the intersection point.

[0106] Specifically, when determining the full-rank equation set, it is first necessary to determine the coordinate selection range on the full-frequency band constraint boundary. Specifically, in order to ensure that the phase margin and gain margin of the servo system are close to the preset values, the arc segment on the rightmost side of the full-frequency band constraint boundary connecting the phase margin and the gain margin can be selected as this range. Therefore, this arc segment can be determined as the selection interval of (X qft , jY qft ). The values of X qft and Y qft can be determined by applying the coordinate points on the gain constraint circle through the following expression (18):

[0107]

[0108] where θ is the polar angle between the line connecting the center of the gain constraint circle to (X qft , jY qft ) and the real axis, and its initial angle θ start is and the termination angle θ end is 0 rad. On this basis, according to the tangent equation of the gain constraint circle at this point, the tangent slope here is shown in the following expression (19):

[0109]

[0110] Specifically, after determining the coordinate selection range on the full-band constraint boundary, it is necessary to determine the coordinates and slope of the open-loop transfer function in the complex plane. Among them, the low-pass filter in the controller adopts a first-order form, as shown in the following expression (20):

[0111]

[0112] where ω 0 is the cut-off frequency, X lpf and Y lpf are the real part and the imaginary part of the low-pass filter respectively. On this basis, the PI controller adopted in the embodiments of the present disclosure can be expressed by the following expression (21):

[0113]

[0114] Specifically, based on expression (20), expression (21) and the frequency characteristics of the controlled object, the open-loop transfer function of the servo system can be expressed by the following expression (22).

[0115]

[0116] where:

[0117] The real part X L and the imaginary part Y L of the open-loop transfer function are shown in the following expression (23):

[0118]

[0119] The slope k ol of the open-loop transfer function in the complex plane is shown in the following expression (24):

[0120]

[0121] Specifically, after determining the coordinates and slope of the open-loop transfer function in the complex plane, let k ol = k qft , after numerical simplification, a quartic equation about ω 0 can be obtained, as shown in expression (25a). Let the real part and the imaginary part of the coordinates of the open-loop transfer function and the boundary be equal respectively, and an analytical formula as shown in expression (25b) can be obtained through numerical simplification. Expressions (25a) and (25b) are full-rank equation systems obtained by making the real part and the imaginary part of the coordinates of the open-loop transfer function equal to the real part and the imaginary part of the coordinates of the full-band constraint boundary, and making the slope of the open-loop transfer function equal to the slope of the full-band constraint boundary at the intersection point.

[0122]

[0123] where, bi denote as the coefficient, and b i is a function of the frequency ω and the polar angle θ.

[0124] S104, the processor solves the full-rank equation set to obtain the target solution set of the controller parameters, and filters out the target controller parameters from the target solution set according to the maximum bandwidth criterion.

[0125] In the embodiments of the present disclosure, after replacing the controlled object in the servo system, the frequency characteristics of the controlled object are obtained by the frequency sweep method, and the open-loop transfer function for the controlled object is determined according to the frequency characteristics. The full-band constraint boundary is constructed according to the constraints of the user on the stability and anti-interference of the servo system. The full-rank equation set of the servo system is constructed according to the open-loop transfer function and the full-band constraint. Finally, the target solution set is obtained by solving the full-rank equation set, and the target controller parameters for the replaced controlled object are filtered out from the target solution set according to the maximum bandwidth criterion. In this way, when replacing the controlled object in the servo system, it is not necessary for the user to manually measure the relevant parameters of the controlled object and establish relevant models. Nor is it necessary to rely on experience for multiple trial and errors as in the traditional tuning method. Therefore, the embodiments of the present disclosure can reduce the production costs of time and manpower increased by redesigning the controller parameters and improve the production efficiency of industrial manufacturing.

[0126] Optionally, solving the full-rank equation set to obtain the target solution set of the controller parameters includes: receiving the angle step and the frequency step input by the user; solving the full-rank equation set based on the angle step and the frequency step according to the preset search algorithm to obtain the target solution set of the controller parameters.

[0127] Specifically, solving the full-rank equation set is an iterative solution process, gradually solving each solution suitable as the controller parameter until the polar angle θ of the open-loop transfer function is greater than the end angle.

[0128] Exemplarily, the iterative process of solving the full-rank equation set based on the angle step and the frequency step according to the preset search algorithm to obtain the target solution set of the controller parameters is as Figure 7 shown.

[0129] Optionally, filtering out the target controller parameters from the target solution set according to the maximum bandwidth criterion includes: for each solution in the target solution set, calculating the frequency when the closed-loop amplitude of the servo system first decays to the set decibel as the bandwidth of the servo system; selecting the solution corresponding to the maximum bandwidth in the target solution set as the target controller parameter.

[0130] Specifically, for each solution in the target solution set, the frequency at which the closed-loop amplitude of the servo system first decays to the set decibels can reflect the response speed of the servo system. Therefore, the frequency at which the closed-loop amplitude of the servo system first decays to the set decibels can be calculated as the bandwidth of the servo system under this solution.

[0131] Optionally, the value range of the set decibels is from -3 dB to 0.707 dB. Specifically, the closed-loop amplitude of the servo system is calculated according to the following expression (26).

[0132]

[0133] where M cl (ω) is the closed-loop amplitude of the servo system, |L(jω)| is the open-loop transfer function value of each solution in the target solution set at each frequency point, and ∠L(jω) is the phase angle of each solution in the target solution set at each frequency point.

[0134] Specifically, the open-loop transfer function value of each solution in the target solution set at each frequency point is calculated according to the following expression (27):

[0135]

[0136] Specifically, the phase angle of each solution in the target solution set at each frequency point is calculated according to the following expression (28):

[0137] ∠L(jω) = tan -1 (Y L / X L ), Expression (28);

[0138] Exemplarily, taking the set decibels as 0.707 dB as an example, when M cl (ω) first decays to 0.707, record this frequency as ω m , if the frequency step ω step is set small enough (for example, 2.5 Hz), the bandwidth ω bw can be approximated as (ω m + ω m-1 ) / 2, where ω m = ω m-1 + ω step .

[0139] Specifically, since the larger the bandwidth, the stronger the response ability of the servo system to high-frequency signals, and the higher the tracking accuracy and stability, it is necessary to select the solution corresponding to the maximum bandwidth in the target solution set as the target controller parameter.

[0140] Another embodiment of the present disclosure provides another method for tuning the controller parameters in a servo system, such as Figure 8As shown, the tuning method includes:

[0141] S801, a processor scans the frequency characteristics of a controlled object in a frequency servo system, and determines an open-loop transfer function for the controlled object according to the frequency characteristics.

[0142] S802: The processor determines a full-band constraint boundary for the servo system according to user constraints on the stability and anti-interference performance of the servo system.

[0143] S803, the processor makes the real and imaginary parts of the coordinates of the open-loop transfer function and the full-band constraint boundary equal, makes the slopes of the open-loop transfer function and the full-band constraint boundary at the intersection point equal, and determines the full-rank equation group.

[0144] S804: The processor solves the full-rank equation group to obtain a target solution set of controller parameters, and corrects the target solution set.

[0145] Specifically, when the controlled object exhibits multi-resonant modal characteristics, although the full-rank equations can locally ensure that the open-loop transfer function does not cross the stability boundary at the intersection, there is still a risk of crossing the boundary within the range of other resonant modes, causing the obtained solution to fail. Therefore, after determining the Mu Bai solution set, the target solution set needs to be corrected.

[0146] Optionally, the target solution set is corrected, including: determining a frequency point to be corrected corresponding to each solution in the target solution set; calculating the complex plane coordinates of the open-loop transfer function at the frequency point to be corrected; and removing the solution corresponding to the frequency point to be corrected from the target solution set when the complex plane coordinates are within the stability constraint boundary of the servo system.

[0147] Optionally, determining the frequency point to be corrected corresponding to each solution in the target solution set includes: determining the phase angle range of the stability constraint boundary of the servo system; calculating the phase angle of each solution in the target solution set at each frequency point; and taking the frequency point whose phase angle is within the phase angle range as the frequency point to be corrected.

[0148] Specifically, although the reliability of the algorithm can be ensured by correcting each frequency point of each solution in the target solution set, this will significantly prolong the execution time of the algorithm. Therefore, the embodiment of the present disclosure introduces a phase angle criterion to optimize this process. Specifically, according to the above expression (8), the phase angle range of the stability constraint boundary is

[0149] Specifically, correcting the target solution set is also an iterative process, and the overall process can be described as follows: Figure 9 shown.

[0150] S805: The processor selects target controller parameters from the target solution set according to the maximum bandwidth criterion.

[0151] In the embodiments of the present disclosure, after obtaining the target solution set of the controller parameters by solving the full-rank equation set, the target solution set will be corrected. In this way, the accuracy of the determined target solution set is improved, and further the accuracy of the final target controller parameters is improved.

[0152] Combined with Figure 10 As shown in, the embodiments of the present disclosure provide a security evaluation device 1000 for a large model, including: a frequency sweeping module 1001, a constraint module 1002, a determination module 1003, and a solution module 1004. The frequency sweeping module 1001 is configured to sweep the frequency characteristics of the controlled object in the servo system and determine the open-loop transfer function for the controlled object according to the frequency characteristics. The constraint module 1002 is configured to determine the full-band constraint boundary for the servo system according to the constraint conditions of the user on the stability and anti-interference of the servo system. The determination module 1003 is configured to make the real part and the imaginary part of the coordinates of the open-loop transfer function equal to the coordinates of the full-band constraint boundary, and make the slopes of the open-loop transfer function and the full-band constraint boundary equal at the intersection point, and determine the full-rank equation set. The solution module 1004 is configured to solve the full-rank equation set to obtain the target solution set of the controller parameters and screen out the target controller parameters from the target solution set according to the maximum bandwidth criterion.

[0153] Combined with Figure 11 As shown in, the embodiments of the present disclosure provide a device 1100 for tuning the controller parameters in a servo system, including: a processor 1101 and a memory 1102. Optionally, the device may further include a communication interface 1103 and a bus 1104. Among them, the processor 1101, the communication interface 1103, and the memory 1102 can complete mutual communication through the bus 1104. The communication interface 1103 can be used for information transmission. The processor 1101 can call the logic instructions in the memory 1102 to execute the method for tuning the controller parameters in the servo system in the above embodiments.

[0154] In addition, when the logic instructions in the above-mentioned memory 1102 are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0155] The memory 1102, as a computer-readable storage medium, can be used to store software programs and computer-executable programs, such as the program instructions / modules corresponding to the methods in the embodiments of the present disclosure. The processor 1101 executes functional applications and data processing by running the program instructions / modules stored in the memory 1102, that is, implements the method for tuning the controller parameters in the servo system in the above embodiments.

[0156] The memory 1102 may include a program storage area and a data storage area. Among them, the program storage area may store an operating system and application programs required for at least one function; the data storage area may store data created according to the use of the terminal device, etc. In addition, the memory 1102 may include a high-speed random access memory and may also include a non-volatile memory.

[0157] An embodiment of the present disclosure provides a computing device, including: a device body; a device for tuning controller parameters in a servo system as described above, disposed on the device body.

[0158] An embodiment of the present disclosure provides a computer-readable storage medium storing computer-executable instructions, and the computer-executable instructions are configured to execute the above-mentioned security evaluation method for large models.

[0159] The technical solution of the embodiment of the present disclosure may be embodied in the form of a software product. The computer software product is stored in a storage medium and includes one or more instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the embodiment of the present disclosure. The foregoing storage medium may be a non-transitory storage medium, such as: a USB flash drive, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk, or an optical disc, etc., which are various media that can store program codes.

[0160] The above description and the accompanying drawings fully illustrate the embodiments of the present disclosure, enabling those skilled in the art to practice them. Other embodiments may include structural, logical, electrical, process, and other changes. The embodiments merely represent possible variations. Unless explicitly required, individual components and functions are optional, and the order of operations may vary. Parts and features of some embodiments may be included in or replace parts and features of other embodiments. Moreover, the terms used in this application are only for describing the embodiments and do not limit the claims. As used in the description of the embodiments and the claims, unless the context clearly indicates otherwise, the singular forms "a", "an", and "the" are intended to also include the plural forms. Similarly, as used in this application, the term "and / or" refers to any and all possible combinations of one or more of the associated listed items. Additionally, when used in this application, the term "comprise" and its variants "comprises" and / or "comprising" etc. mean the presence of the stated features, wholes, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or groupings of these. Without further limitation, an element defined by the statement "comprising one..." does not exclude the presence of additional identical elements in the process, method, or apparatus that includes the element. Herein, each embodiment may focus on the differences from other embodiments, and the same or similar parts among the embodiments may be referred to each other. For the methods, products, etc. disclosed in the embodiments, if they correspond to the method parts disclosed in the embodiments, the relevant parts may refer to the description of the method parts.

[0161] Those skilled in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner may depend on the specific application and design constraints of the technical solution. The technician can use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of the embodiments of the present disclosure. The technician can clearly understand that for the convenience and brevity of description, the specific working processes of the systems, devices, and units described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0162] In the embodiments disclosed herein, the disclosed methods, products (including but not limited to devices, equipment, etc.) can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units can be merely a logical function division. In actual implementation, there can be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Additionally, the displayed or discussed couplings or direct couplings or communication connections to each other can be through some interfaces. The indirect coupling or communication connection of devices or units can be in electrical, mechanical, or other forms. The units described as separate components can be or can not be physically separated. The components displayed as units can be or can not be physical units, that is, they can be located in one place or can be distributed to multiple network units. Some or all of the units can be selected according to actual needs to implement this embodiment. Additionally, in the embodiments of the present disclosure, the various functional units can be integrated in one processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit.

[0163] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to embodiments of the present disclosure. In this regard, each block in the flowchart or block diagram can represent a module, a program segment, or a part of code, and the module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions marked in the blocks can occur in a different order than marked in the accompanying drawings. For example, two consecutive blocks can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, which can depend on the functions involved. In the descriptions corresponding to the flowcharts and block diagrams in the accompanying drawings, the operations or steps corresponding to different blocks can also occur in a different order than disclosed in the description. Sometimes, there is no specific order between different operations or steps. For example, two consecutive operations or steps can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, which can depend on the functions involved. Each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

Claims

1. A method for setting controller parameters in a servo system, characterized in that: include: The frequency characteristics of the controlled object in the swept frequency servo system, and the open-loop transfer function for the controlled object is determined according to the frequency characteristics; According to the user's constraints on the stability and anti-interference of the servo system, determine the full-band constraint boundary of the servo system; The real and imaginary parts of the coordinates of the open-loop transfer function and the full-band constraint boundary are made equal, and the slopes of the open-loop transfer function and the full-band constraint boundary at the intersection point are made equal, and the full-rank equation system is determined; The full-rank equations are solved to obtain the target solution set of controller parameters, and the target controller parameters are selected from the target solution set according to the maximum bandwidth criterion.

2. The setting method according to claim 1, characterized in that: The constraints on the stability of the servo system include: closed-loop amplitude constraint, phase margin constraint and gain margin constraint; the constraints on the anti-interference performance of the servo system include: anti-interference performance constraint; according to the user's constraints on the stability and anti-interference of the servo system, determine the full-band constraint boundaries of the servo system, including: According to the upper limit of the closed-loop amplitude constraint, a closed-loop amplitude circle is drawn using the open-loop transfer function of the servo system; According to the phase margin constraint and the gain margin constraint, the gain margin and the phase margin of the closed-loop amplitude circle are restricted to determine the stability constraint boundary; An anti-interference constraint circle is constructed according to the anti-interference performance constraint, and on the basis of the stability constraint boundary, the maximum phase line is extended and connected to the arc segment of the anti-interference constraint circle to determine the full-band constraint boundary.

3. The setting method according to claim 1, characterized in that: Solve the full-rank equations to obtain the target solution set of controller parameters, including: Receive the angle step and frequency step input by the user; According to the preset search algorithm, the full-rank equations are solved based on the angle step and frequency step to obtain the target solution set of the controller parameters.

4. The setting method according to claim 1, characterized in that: The target controller parameters are selected from the target solution set according to the maximum bandwidth criterion, including: For each solution in the target solution set, the frequency at which the closed-loop amplitude of the servo system decays to a set decibel for the first time is calculated as the bandwidth of the servo system; The solution corresponding to the maximum bandwidth in the target solution set is selected as the target controller parameter.

5. The setting method according to any one of claims 1 to 4, characterized in that: Before selecting the target controller parameters from the target solution set according to the maximum bandwidth criterion, the tuning method further includes: Correct the target solution set.

6. The setting method according to claim 5, characterized in that: Correct the target solution set, including: Determine the frequency point to be corrected corresponding to each solution in the target solution set; Calculate the complex plane coordinates of the open-loop transfer function at the frequency point to be corrected; When the complex plane coordinates are within the stability constraint boundary of the servo system, the solution corresponding to the frequency point to be corrected is removed from the target solution set.

7. The setting method according to claim 6, characterized in that: Determine the frequency point to be corrected corresponding to each solution in the target solution set, including: Determine the phase angle range of the stability constraint boundary of the servo system; Calculate the phase angle of each solution in the target solution set at each frequency point; The frequency point whose phase angle is within the phase angle range is taken as the frequency point to be corrected.

8. A device for setting controller parameters in a servo system, characterized in that: include: A frequency sweep module, configured to sweep the frequency characteristics of a controlled object in the frequency servo system, and determine an open-loop transfer function for the controlled object according to the frequency characteristics; A constraint module is configured to determine a full-band constraint boundary for the servo system according to user constraints on stability and anti-interference of the servo system; A determination module is configured to make the real and imaginary parts of the coordinates of the open-loop transfer function and the coordinates of the full-band constraint boundary equal, make the slopes of the open-loop transfer function and the full-band constraint boundary at the intersection point equal, and determine the full-rank equation group; The solution module is configured to solve the full-rank equation group to obtain a target solution set of controller parameters, and select target controller parameters from the target solution set according to a maximum bandwidth criterion.

9. A device for setting controller parameters in a servo system, comprising a processor and a memory storing program instructions, characterized in that: The processor is configured to execute the method for tuning controller parameters in a servo system according to any one of claims 1 to 7.

10. A computing device, characterized in that include: Equipment body; The device for setting controller parameters in a servo system as claimed in claim 9 is arranged on the device body.

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