A task index-based servo system bandwidth parameter fast acquisition method

Abstract

The application discloses a kind of based on task index's servo system bandwidth parameter fast acquisition method, belongs to motion control technical field, comprising the following steps: S1: set core motion task set value and performance constraint set value;S2: select servo system to three equal-time trapezoidal curve as motion trajectory, establish dynamic model and correct, select critical damping state to obtain the open-loop gain of servo system in dynamic model;S3: in dynamic model, the absolute value of steady-state error of uniform speed section in motion trajectory and the maximum dynamic error absolute value of uniform acceleration section and uniform deceleration section are calculated;S4: based on the actual application of servo system, obtain minimum closed-loop bandwidth;By the above mode, the servo control system design in prior art is overcome Experience trial and error, lack the precise theory mapping from task index to bandwidth parameter, provide the bandwidth fast acquisition method of servo control system based on time-position-precision constraint.

Description

Technical Field

[0001] This invention relates to the field of motion control technology, and more specifically to a method for rapidly obtaining bandwidth parameters of a servo system based on task indicators. Background Technology

[0002] In the engineering design of position servo systems, bandwidth is a core performance parameter that determines the system's dynamic response speed and trajectory tracking accuracy: too low bandwidth will lead to severe trajectory tracking lag or tracking errors exceeding the allowable range; too high bandwidth will introduce high-frequency noise, increase system energy consumption and control difficulty, and may even cause system oscillation and instability.

[0003] In existing technologies, determining system bandwidth typically relies on rules of thumb, trial-and-error methods, design methods based on frequency domain metrics, and optimization design methods based on modern control theory. Rules of thumb and trial-and-error methods initially set parameters based on similar equipment or experience, then approximate the target through repeated experiments and adjustments. This lacks theoretical foresight, results in long development cycles, and often leads to performance redundancy or inadequacy. Designing based on frequency domain metrics such as system phase margin, gain margin, and disturbance suppression bandwidth, while theoretically rigorous, lacks an explicit mathematical relationship with the time-domain metrics and time-domain tracking accuracy of the motion task, causing a disconnect between the design process and the final motion performance. Optimization design based on modern control theory can optimize the controller under specific performance metrics. However, it is computationally complex, requires accurate system models, and the physical relationship between the optimized bandwidth and the top-level task metrics is not intuitive, hindering rapid design and decision-making by engineers.

[0004] To address the aforementioned issues, existing technologies lack a simple, intuitive, and quantitative method that can directly link motion constraints, full trajectory error constraints, and bandwidth parameters in a quantitative design process. This method would enable a single design to meet time, accuracy, and stability requirements without repeated iterations, reducing redundant and complex processes. Consequently, it would provide a clear theoretical basis for control system selection and controller design, avoiding design blindness and improving design efficiency and reliability. Summary of the Invention

[0005] The technical problem to be solved by this invention is to overcome the shortcomings of existing servo control system designs that rely on trial and error based on experience and lack precise theoretical mapping from task indicators to bandwidth parameters, and to provide a method for rapidly obtaining the bandwidth of a servo control system based on time-position-precision constraints.

[0006] The technical solution adopted by this invention to solve the technical problem is as follows: a method for quickly obtaining the bandwidth parameters of a servo system based on task indicators, comprising the following steps:

[0007] S1: Set the core motion task settings and performance constraint settings;

[0008] The core motion task settings include the target total displacement. and total exercise time ;

[0009] The performance constraint settings include the maximum allowable tracking error. ;

[0010] (1)

[0011] in, The relative error coefficient;

[0012] S2: Selecting a three-segment isochronous trapezoidal curve as the motion trajectory for the servo system, and combining the core motion task settings and performance constraint settings, establish a dynamic model of the servo system. Then, calibrate the dynamic model, selecting a critical damping state to constrain the calibrated dynamic model, and obtain the open-loop gain of the servo system in the dynamic model. ;

[0013] S3: Based on the maximum acceleration in the three isochronous trapezoidal curves. Maximum speed Total target displacement Total exercise time and open-loop gain The relationship between the two factors is used to calculate the absolute value of the steady-state error of the uniform segment within the motion trajectory in the dynamic model. And the maximum absolute value of dynamic error in the uniform acceleration and uniform deceleration segments. ;

[0014] (2)

[0015] (3)

[0016] (4)

[0017] (5)

[0018] (6)

[0019] in, It is the undamped natural frequency;

[0020] S4: Based on the maximum allowable tracking error The maximum bandwidth of the servo system in actual application must meet the following requirements:

[0021] (7)

[0022] The relative error coefficient in the practical application of the servo system The minimum closed-loop bandwidth of the servo system is obtained. ;

[0023] (8).

[0024] As a preferred embodiment of the present invention, step S2, which involves correcting the dynamic model, specifically includes:

[0025] In the dynamic model, the servo system is corrected to be a typical second-order system.

[0026] As a preferred embodiment of the present invention, the closed-loop transfer function of the typical second-order system... The standardized formula is as follows:

[0027] (9)

[0028] in, For the damping ratio, It is the undamped natural frequency.

[0029] As a preferred technical solution of the present invention, the open-loop transfer function of the typical second-order system The formula is as follows:

[0030] (10).

[0031] As a preferred embodiment of the present invention, the step S2 of selecting the critical damping state to limit the corrected dynamic model specifically includes:

[0032] The corrected dynamic model is constrained by selecting a critical damping state, wherein the critical damping state is... The open-loop transfer function The simplified formula is as follows:

[0033] (11).

[0034] As a preferred embodiment of the present invention, the open-loop gain of the servo system in the dynamic model is obtained in step S2. Specifically, it includes:

[0035] According to the simplified formula, the servo system in the dynamic model is a Type I system, and the open-loop gain of the servo system in the dynamic model is obtained based on the Type I system. .

[0036] As a preferred embodiment of the present invention, in the three segments of the isochronous trapezoidal curve, the uniform acceleration segment, the uniform velocity segment, and the uniform deceleration segment each occupy the same time, and the time is... The formula is as follows:

[0037] (12)

[0038] in, This represents the total displacement time.

[0039] As a preferred embodiment of the present invention, the sum of the displacements of the uniformly accelerated segment, the uniformly velocity segment, and the uniformly decelerated segment in the three isochronous trapezoidal curves is... Then, combining the following formulas:

[0040] (13)

[0041] Based on formulas (11) and (13), formulas (3) and (4) can be obtained.

[0042] As a preferred embodiment of the present invention, step S4 incorporates the relative error coefficient in the practical application of the servo system. The minimum closed-loop bandwidth of the servo system is obtained. Specifically, it includes:

[0043] Combining formulas (1), (5), and (7), if the absolute value of the steady-state error... If the maximum error source of the servo system is determined, then:

[0044] (14)

[0045] Combining formulas (1), (6), and (7), if the absolute value of the maximum dynamic error is... If the maximum error source of the servo system is determined, then:

[0046] (15).

[0047] As a preferred technical solution of the present invention, if the absolute value of the steady-state error Given the maximum error source of the servo system, according to formula (7), the following constraint formula exists:

[0048] (16)

[0049] Combining formulas (1), (5), and (16), formula (14) can be obtained.

[0050] If the absolute value of the maximum dynamic error Given the maximum error source of the servo system, according to formula (7), the following constraint formula exists:

[0051] (17)

[0052] Combining formulas (1), (6) and (17), formula (15) can be obtained.

[0053] The beneficial effects of this invention are reflected in:

[0054] 1. This invention theoretically clarifies the "minimum performance boundary for meeting task requirements," effectively avoiding cost waste and high-frequency noise introduction caused by over-designing to reserve margins. Under the premise of ensuring that the system meets the requirements of time, accuracy, and stability, it establishes an analytical and quantitative relationship between the "time-position-accuracy" task indicators and the system's core parameter "bandwidth," thereby directly calculating the required minimum bandwidth lower limit based on task requirements. This provides a quantitative basis for controller design, actuator selection, and performance verification, achieving accurate, efficient, and optimal forward design, and ultimately achieving the optimal balance between economy and reliability, improving overall efficiency and reliability.

[0055] 2. This invention provides a "one-click" bandwidth design formula with clear physical meaning and simple form. It can quickly complete performance estimation and feasibility judgment without the need for complex model identification and iterative debugging, which significantly reduces the design threshold for engineers and improves decision-making efficiency.

[0056] 3. This invention establishes a direct and rigorous analytical mapping relationship from top-level task indicators (time, distance, accuracy) to the core parameters of the system (bandwidth), which completely changes the traditional design mode that relies on experience-based trial and error, frequency domain indicators are disconnected, or complex optimization calculations, and realizes a qualitative change in the design process from "qualitative experience estimation" to "quantitative analytical calculation". Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the steps of the present invention;

[0058] Figure 2 The trajectory planning curve defined in this invention;

[0059] Figure 3 The position servo system control block diagram established for this invention;

[0060] Figure 4 This is an embodiment of the present invention. System response curve;

[0061] Figure 5 This is an embodiment of the present invention. System response curve. Detailed Implementation

[0062] The invention will now be described in further detail with reference to the accompanying drawings.

[0063] like Figure 1As shown, a method for quickly obtaining servo system bandwidth parameters based on task metrics includes the following steps:

[0064] S1: Set the core motion task settings and performance constraint settings;

[0065] The core motion task settings include the target total displacement. and total exercise time ;

[0066] The performance constraint settings include the maximum allowable tracking error. ;

[0067] (1)

[0068] in, The relative error coefficient;

[0069] S2: Select a three-segment isochronous trapezoidal curve as the motion trajectory for the servo system, wherein the motion trajectory includes a uniform acceleration segment, a uniform velocity segment, and a uniform deceleration segment, and the acceleration of the uniform acceleration segment is the maximum acceleration. The constant speed segment speed is the maximum speed. The initial acceleration value of the uniform deceleration section is the maximum acceleration. The initial acceleration of the uniformly decelerated section is... Wherein, the negative sign represents the deceleration process. Based on the three isochronous trapezoidal curves, combined with the core motion task settings and performance constraint settings, a dynamic model of the servo system is established to analyze the system's response to the above instructions and to correct the dynamic model. Preferably, based on... A dynamic model is established for subsequent simulation analysis. Specifically, the servo system in the dynamic model is corrected to be a typical second-order system, and the closed-loop transfer function of the typical second-order system is... The standardized formula is as follows:

[0070] (9)

[0071] in, For the damping ratio, For the undamped natural frequency, further, Approximately the closed-loop bandwidth;

[0072] The open-loop transfer function of the typical second-order system The formula is as follows:

[0073] (10);

[0074] To balance response speed and overshoot-free characteristics, a critical damping state is selected to constrain the corrected dynamic model, thereby obtaining the open-loop gain of the servo system in the dynamic model. ;

[0075] Specifically:

[0076] The corrected dynamic model is constrained by selecting a critical damping state, wherein the critical damping state is... The open-loop transfer function The simplified formula is as follows:

[0077] (11)

[0078] According to the simplified formula, the servo system in the dynamic model is: Type system, according to the The system obtains the open-loop gain of the servo system in the dynamic model. ;

[0079] S3: Based on the maximum acceleration in the three isochronous trapezoidal curves. Maximum speed Total target displacement Total exercise time and open-loop gain The relationship between the two factors is used to calculate the absolute value of the steady-state error of the uniform segment within the motion trajectory in the dynamic model. And the maximum absolute value of dynamic error in the uniform acceleration and uniform deceleration segments. :

[0080] (2)

[0081] (3)

[0082] (4)

[0083] (5)

[0084] (6)

[0085] in, It is the undamped natural frequency;

[0086] Specifically, in the three isochronous trapezoidal curves, the uniform acceleration segment, the uniform velocity segment, and the uniform deceleration segment each occupy the same time, and the time is... The formula is as follows:

[0087] (12)

[0088] in, This represents the total displacement time.

[0089] The sum of the displacements of the uniformly accelerated segment, the uniformly velocity segment, and the uniformly decelerated segment in the three isochronous trapezoidal curves is: Based on kinematic relationships, the following formulas can be combined:

[0090] (13)

[0091] Based on formulas (12) and (13), formulas (3) and (4) can be obtained.

[0092] Based on the set values ​​planned in S1, the trajectory command of the servo system is: The position response output is The trajectory tracking error is The formula is as follows:

[0093] (18)

[0094] in, For time;

[0095] Preferred trajectory instructions If the input is a position ramp during the uniform velocity segment, then the absolute value of the steady-state error during the uniform velocity segment within the motion trajectory is... As shown in formula (5);

[0096] Preferred trajectory instructions Given a parabolic input with finite time intervals for both the uniform acceleration and uniform deceleration phases, the maximum absolute value of the dynamic error is... As shown in formula (6), specifically, the trajectory instruction During the finite-time phases of uniform acceleration and uniform deceleration, the core of the parabolic input curve has a constant maximum acceleration. The position servo system is a type I second-order system, and its steady-state error for parabolic input tends to infinity, but the actual acceleration / deceleration phase is finite in time. That is, formula (12), the error is a dynamic error and has a peak value;

[0097] Through the Laplace transform, the critically damped second-order system in a finite-time... Under parabolic input, the peak dynamic error occurs at the end of this segment ( or Maximum dynamic error absolute value The approximate formula is:

[0098] (19)

[0099] Furthermore, Substituting and simplifying the expression yields : (20);

[0100] S4: Based on the maximum allowable tracking error The maximum bandwidth of the servo system in actual application must meet the following requirements:

[0101] (7)

[0102] Combining formulas (1), (5), and (7), if the absolute value of the steady-state error... If the maximum error source of the servo system is denoted as , then the following relationship exists:

[0103] (14)

[0104] Specifically:

[0105] If the absolute value of steady-state error Given the maximum error source of the servo system, according to formula (7), the following constraint formula exists:

[0106] (16)

[0107] Combining formulas (1), (5), and (16), formula (14) can be obtained.

[0108] Combining formulas (1), (6), and (7), if the absolute value of the maximum dynamic error is... If the maximum error source of the servo system is denoted as , then the following relationship exists:

[0109] (15)

[0110] Specifically:

[0111] If the absolute value of the maximum dynamic error Given the maximum error source of the servo system, according to formula (7), the following constraint formula exists:

[0112] (17)

[0113] Combining formulas (1), (6), and (17), formula (15) can be obtained.

[0114] The relative error coefficient in the practical application of the servo system The minimum closed-loop bandwidth of the servo system is obtained. ;

[0115] (8);

[0116] Specifically, compare the absolute value of the steady-state error. The maximum error source and the absolute value of the maximum dynamic error of the servo system are... This refers to the case where the servo system has the largest error source.

[0117] When relative error coefficient Then the following relationship holds:

[0118] (twenty one)

[0119] At this point, formula (14) is used to limit the minimum closed-loop bandwidth in the actual application of the servo system to obtain the bandwidth parameter of the servo system. The minimum closed-loop bandwidth is... The formula is shown in formula (8);

[0120] When relative error coefficient Then the following relationship holds:

[0121] (twenty two)

[0122] At this point, formula (15) is used to limit the minimum closed-loop bandwidth in the actual application of the servo system to obtain the bandwidth parameter of the servo system. The minimum closed-loop bandwidth is... The formula is as follows:

[0123] (twenty three)

[0124] Based on practical applications, the relative error coefficient Much less than 0.5, therefore the minimum closed-loop bandwidth is The formula is shown in formula (8);

[0125] Furthermore, formula (8) can be converted into a form more commonly used in engineering. unit system bandwidth Then we have the following formula:

[0126] (twenty four).

[0127] After achieving the minimum closed-loop bandwidth of Once determined, a complete set of deterministic design parameters for the servo system that meets the given task specifications can be output. This parameter package includes core frequency domain performance indicators and key time domain motion parameters.

[0128] The core frequency domain performance metric is the minimum closed-loop bandwidth required by the system. (or Its value is calculated according to formula (8) and serves as a quantitative design target for the dynamic performance of the system.

[0129] The key time-domain motion parameter is the maximum motion velocity generated by trajectory planning. And the maximum motion acceleration generated by trajectory planning ;

[0130] Applying the above design parameter package to the specific design phase of the servo control system: When designing the controller, the goal should be to achieve a closed-loop bandwidth greater than or equal to... Design and tune controller parameters for the target;

[0131] When selecting actuators, the response bandwidth of the chosen actuator and drive unit should be higher than [the specified value]. Furthermore, its speed and torque / thrust output capabilities must meet the following requirements. and Requirements.

[0132] With the target total displacement Total exercise time The positioning accuracy is required to be no more than 1% of the total displacement, i.e., the relative error coefficient. For example:

[0133] S1: Set the core motion task settings and performance constraint settings;

[0134] The core motion task settings include the target total displacement. and total exercise time ;

[0135] The performance constraint settings include the maximum allowable tracking error. ;

[0136] (1)

[0137] in, The relative error coefficient;

[0138] S2: Select the servo system to use a three-segment isochronous trapezoidal curve as the motion trajectory, such as... Figure 2 As shown, the motion trajectory includes a uniform acceleration segment, a uniform velocity segment, and a uniform deceleration segment, wherein the acceleration during the uniform acceleration segment is the maximum acceleration. The constant speed segment speed is the maximum speed. Preferred, maximum acceleration For constant acceleration, maximum speed For a constant velocity, the initial acceleration value of the uniform deceleration segment is the maximum acceleration. The initial acceleration of the uniformly decelerated section is... In this context, the negative sign represents the deceleration process. Based on the three isochronous trapezoidal curves, and combined with the core motion task settings and performance constraint settings, a dynamic model of the servo system is established, such as... Figure 3 The diagram shown is a control diagram of the position servo system, used to analyze the system's response to the aforementioned commands and to correct the dynamic model. Preferably, it is based on... A dynamic model is established for subsequent simulation analysis. Specifically, the servo system in the dynamic model is calibrated to be a typical second-order system. Ideally, in engineering applications, the position servo system can be controlled by proportional control or... The control correction is a typical second-order system, and the closed-loop transfer function of the typical second-order system is... The standardized formula is as follows:

[0139] (9)

[0140] in, For the damping ratio, For the undamped natural frequency, further, Approximately the closed-loop bandwidth;

[0141] The open-loop transfer function of the typical second-order system The formula is as follows:

[0142] (10);

[0143] To balance response speed and overshoot-free characteristics, a critical damping state is selected to constrain the corrected dynamic model, thereby obtaining the open-loop gain of the servo system in the dynamic model. ;

[0144] Specifically:

[0145] The corrected dynamic model is constrained by selecting a critical damping state, wherein the critical damping state is... The open-loop transfer function The simplified formula is as follows:

[0146] (11)

[0147] According to the simplified formula, the servo system in the dynamic model is: Type system, according to the The system obtains the open-loop gain of the servo system in the dynamic model. ;

[0148] S3: Based on the maximum acceleration in the three isochronous trapezoidal curves. Maximum speed Total target displacement Total exercise time and open-loop gain The relationship between the two factors is used to calculate the absolute value of the steady-state error of the uniform segment within the motion trajectory in the dynamic model. And the maximum absolute value of dynamic error in the uniform acceleration and uniform deceleration segments. :

[0149] (2)

[0150] (3)

[0151] (4)

[0152] (5)

[0153] (6)

[0154] in, It is the undamped natural frequency;

[0155] Specifically, in the three isochronous trapezoidal curves, the uniform acceleration segment, the uniform velocity segment, and the uniform deceleration segment each occupy the same amount of time, and the time is... The formula is as follows:

[0156] (12)

[0157] in, This represents the total displacement time.

[0158] The sum of the displacements of the uniformly accelerated segment, the uniformly velocity segment, and the uniformly decelerated segment in the three isochronous trapezoidal curves is: Based on kinematic relationships, the following formulas can be combined:

[0159] (13)

[0160] Based on formulas (12) and (13), formulas (3) and (4) can be obtained.

[0161] Based on the set values ​​planned in S1, the trajectory command of the servo system is: The position response output is The trajectory tracking error is The formula is as follows:

[0162] (18)

[0163] in, For time;

[0164] Preferred trajectory instructions If the input is a position ramp during the uniform velocity segment, then the absolute value of the steady-state error during the uniform velocity segment within the motion trajectory is... As shown in formula (5);

[0165] Preferred trajectory instructions Given a parabolic input with finite time intervals for both the uniform acceleration and uniform deceleration phases, the maximum absolute value of the dynamic error is... As shown in formula (6), specifically, the trajectory instruction During the finite-time phases of uniform acceleration and uniform deceleration, the core of the parabolic input curve has a constant maximum acceleration. The position servo system is a type I second-order system, and its steady-state error for parabolic input tends to infinity, but the actual acceleration / deceleration phase is finite in time. That is, formula (12), the error is a dynamic error and has a peak value;

[0166] Through the Laplace transform, the critically damped second-order system in a finite-time... Under parabolic input, the peak dynamic error occurs at the end of this segment ( or Maximum dynamic error absolute value The approximate formula is:

[0167] (19)

[0168] Furthermore, Substituting the expression and simplifying it yields : (20);

[0169] S4: Based on the maximum allowable tracking error The maximum bandwidth of the servo system in actual application must meet the following formula:

[0170] (7)

[0171] in, To find the function with the maximum value;

[0172] Combining formulas (1), (5), and (7), if the absolute value of the steady-state error... If the maximum error source of the servo system is denoted as , then the following relationship exists:

[0173] (14)

[0174] Specifically:

[0175] If the absolute value of steady-state error Given the maximum error source of the servo system, according to formula (7), the following constraint formula exists:

[0176] (16)

[0177] Combining formulas (1), (5), and (16), formula (14) can be obtained.

[0178] Combining formulas (1), (6), and (7), if the absolute value of the maximum dynamic error is... If the maximum error source of the servo system is denoted as , then the following relationship exists:

[0179] (15)

[0180] Specifically:

[0181] If the absolute value of the maximum dynamic error is the maximum error source of the servo system, then according to formula (7), the following constraint formula exists:

[0182] (17)

[0183] Combining formulas (1), (6), and (17), formula (15) can be obtained.

[0184] The relative error coefficient in the practical application of the servo system The minimum closed-loop bandwidth of the servo system is obtained. ;

[0185] (8);

[0186] Calculations show that ;

[0187] Specifically, compare the absolute value of the steady-state error. The maximum error source and the absolute value of the maximum dynamic error of the servo system are... This refers to the case where the servo system has the largest error source.

[0188] When relative error coefficient Then the following relationship holds:

[0189] (twenty one)

[0190] At this point, formula (14) is used to limit the minimum closed-loop bandwidth in the actual application of the servo system to obtain the bandwidth parameter of the servo system. The minimum closed-loop bandwidth is... The formula is shown in formula (8);

[0191] When relative error coefficient Then the following relationship holds:

[0192] (twenty two)

[0193] At this point, formula (15) is used to limit the minimum closed-loop bandwidth in the actual application of the servo system to obtain the bandwidth parameter of the servo system. The minimum closed-loop bandwidth is... The formula is as follows:

[0194] (twenty three)

[0195] Based on practical applications, the relative error coefficient Much less than 0.5, therefore the minimum closed-loop bandwidth is The formula is shown in formula (8);

[0196] Furthermore, formula (8) can be converted into a form more commonly used in engineering. unit system bandwidth Then we have the following formula:

[0197] (twenty four)

[0198] Calculations show that .

[0199] After achieving the minimum closed-loop bandwidth of Once determined, a complete set of deterministic design parameters for the servo system that meets the given task specifications can be output. This parameter package includes core frequency domain performance indicators and key time domain motion parameters.

[0200] Specifically:

[0201] The closed-loop bandwidth of the position loop in a high-precision CNC machine tool linear axis positioning system must be no less than (correspond The maximum motion speed generated by trajectory planning The maximum acceleration generated by trajectory planning ;

[0202] Applying the above design parameter package to the specific design phase of the servo control system: This machine tool's X-axis servo control system

[0203] Location ring bandwidth not less than (correspond After the drive motor and transmission mechanism work together, they should be able to provide continuous speed under load. Continuous acceleration athletic ability;

[0204] The combined response bandwidth of the motor, driver, and mechanical structure should be significantly higher than that of the standard motor. This is to ensure that it does not become a bottleneck in the system's dynamic performance.

[0205] The bandwidth design method described in this invention is simulated using Simulink. The position trajectory command designed in step S2 is input into the position servo system whose bandwidth is calculated in step S4, as shown in the attached figure. Figure 4 As shown trajectory instructions With system position response Curve. (See attached image) Figure 5 As shown trajectory instructions With system position response curve.

[0206] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for rapidly obtaining servo system bandwidth parameters based on task indicators, characterized in that: Includes the following steps: S1: Set the core motion task settings and performance constraint settings; The core motion task settings include the target total displacement. and total exercise time ; The performance constraint settings include the maximum allowable tracking error. ; （1） in, The relative error coefficient; S2: Selecting a three-segment isochronous trapezoidal curve as the motion trajectory for the servo system, and combining the core motion task settings and performance constraint settings, establish a dynamic model of the servo system. Then, calibrate the dynamic model, selecting a critical damping state to constrain the calibrated dynamic model, and obtain the open-loop gain of the servo system in the dynamic model. ; S3: Based on the maximum acceleration in the three isochronous trapezoidal curves. Maximum speed Total target displacement Total exercise time and open-loop gain The relationship between the two factors is used to calculate the absolute value of the steady-state error of the uniform segment within the motion trajectory in the dynamic model. And the maximum absolute value of dynamic error in the uniform acceleration and uniform deceleration segments. ; （2） （3） （4） （5） （6） in, It is the undamped natural frequency; S4: Based on the maximum allowable tracking error The maximum bandwidth of the servo system in actual application must meet the following requirements: （7） The relative error coefficient in the practical application of the servo system The minimum closed-loop bandwidth of the servo system is obtained. ; （8）。 2. The method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 1, characterized in that: The S2 step of correcting the dynamic model specifically includes: In the dynamic model, the servo system is corrected to be a typical second-order system.

3. The method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 2, characterized in that: The closed-loop transfer function of the typical second-order system The standardized formula is as follows: （9） in, For the damping ratio, It is the undamped natural frequency.

4. The method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 3, characterized in that: The open-loop transfer function of the typical second-order system The formula is as follows: （10）。 5. The method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 4, characterized in that: The selection of the critical damping state in S2 to constrain the corrected dynamic model specifically includes: The corrected dynamic model is constrained by selecting a critical damping state, wherein the critical damping state is... The open-loop transfer function The simplified formula is as follows: （11）。 6. The method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 5, characterized in that: In step S2, the open-loop gain of the servo system in the dynamic model is obtained. Specifically, it includes: According to the simplified formula, the servo system in the dynamic model is a Type I system, and the open-loop gain of the servo system in the dynamic model is obtained based on the Type I system. .

7. The method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 1, characterized in that: In the three isochronous trapezoidal curves, the uniform acceleration segment, the uniform velocity segment, and the uniform deceleration segment each occupy the same time, and the time is... The formula is as follows: （12） in, This represents the total displacement time.

8. The method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 7, characterized in that: The sum of the displacements of the uniformly accelerated segment, the uniformly velocity segment, and the uniformly decelerated segment in the three isochronous trapezoidal curves is: Then, combining the following formulas: （13） Based on formulas (11) and (13), formulas (3) and (4) can be obtained.

9. The method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 1, characterized in that: The relative error coefficient in S4 is combined with the actual application of the servo system. The minimum closed-loop bandwidth of the servo system is obtained. Specifically, it includes: Combining formulas (1), (5), and (7), if the absolute value of the steady-state error... If the maximum error source of the servo system is determined, then: （14） Combining formulas (1), (6), and (7), if the absolute value of the maximum dynamic error is... If the maximum error source of the servo system is determined, then: （15）。 10. A method for quickly obtaining servo system bandwidth parameters based on task indicators according to claim 9, characterized in that: If the absolute value of steady-state error Given the maximum error source of the servo system, according to formula (7), the following constraint formula exists: （16） Combining formulas (1), (5), and (16), formula (14) can be obtained. If the absolute value of the maximum dynamic error Given the maximum error source of the servo system, according to formula (7), the following constraint formula exists: （17） Combining formulas (1), (6) and (17), formula (15) can be obtained.

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