CN111159851A - Servo mechanism simplified model modeling method, storage medium and server - Google Patents
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Abstract
The invention provides a modeling method of a simplified model of a servo mechanism, a storage medium and a server. The modeling method comprises the following steps: determining an expected value of amplitude-phase-frequency characteristics of the simplified model of the servo mechanism; analyzing and determining a model structure; and solving the characteristic parameters of the model by adopting an optimization control algorithm, and verifying the amplitude-phase-frequency characteristics of the model. The method improves the structure of a servo mechanism simplified model which is usually adopted at present, introduces a phase-amplitude correction link, and ensures that the simplified model has higher modeling precision in a plurality of frequency bands; meanwhile, the characteristic parameter fitting problem of the servo structure simplified model is converted into the optimal control problem, the trial and error process of the characteristic parameters is avoided, and the solving efficiency is obviously improved.
Description
Technical Field
The invention relates to the field of aerospace, in particular to an aircraft control and simulation technology, and specifically relates to a modeling method, a storage medium and a server for a simplified model of an aircraft servo mechanism.
Background
In an attitude control system of a large aircraft represented by a carrier rocket, a servo mechanism is an actuating device for controlling an actuating mechanism, receives command signals given by an attitude control law, and drives a swing engine to swing so as to correct deviation of flight trajectories and attitudes. The electric servo mechanism is a high-order system with nonlinear characteristics such as dead zones, gaps, saturation and the like, and is generally simplified into a second-order oscillation link from the viewpoint of convenience of modeling work when small deviation stability analysis of a rocket control system is performed.
For a large carrier rocket taking liquid fuel as propellant, when analyzing attitude stability of the large carrier rocket, the influence of propellant shaking and elastic vibration on the stability of a rocket attitude system needs to be considered, so that a stability analysis model of the large carrier rocket is a high-order system consisting of a rigid body-elasticity-shaking coupled rocket body, a control law and the dynamic characteristics of a servo mechanism, and the attitude control system of the large liquid rocket generally needs to consider amplitude and phase stability margin indexes at a low-frequency rigid body section. The first-order liquid shaking frequency and the first-order elastic frequency are low, amplitude stability is difficult to achieve, and a phase stability mode is usually adopted. For elastic frequencies above the second order, an amplitude-stabilized approach is usually employed.
The correctness of the simplified model of the servo mechanism directly influences the correctness of the stability analysis result of the attitude control system. Therefore, in order to ensure the accuracy of the stability analysis result, attention must be paid to key frequency characteristics of the servo model, such as amplitude-frequency and phase-frequency characteristics in the low-frequency rigid body section, phase-frequency characteristics in the vicinity of the first-order vibration and first-order elastic vibration frequencies, and amplitude-frequency characteristics in the high-frequency section (second-order elastic vibration frequency and higher). However, the traditional servo mechanism simplified model described by only one second-order vibration link is difficult to meet the high-precision servo mechanism modeling requirements of multiple key frequency points such as the rigid body, the shaking and the elastic vibration.
Disclosure of Invention
The invention aims to provide a more complete simplified model modeling method for a servo mechanism, which aims to solve the problem that the amplitude-frequency and phase-frequency characteristic requirements of the servo mechanism at a plurality of frequency points are difficult to meet by adopting a second-order oscillation link as a simplified model of the servo mechanism, and comprises the steps of determining a model structure and rapidly solving the characteristic parameters of the model.
One aspect of the present invention provides a modeling method of a simplified servo mechanism model, comprising the steps of:
determining amplitude-phase-frequency characteristics required to be met by a simplified servo mechanism model, wherein the amplitude-phase-frequency characteristics comprise expected values of amplitude and phase at a series of key frequency points;
adopting a traditional second-order oscillation link to carry out preliminary simplified modeling on the servo mechanism, analyzing the error between the amplitude-phase-frequency characteristic of the model at the key frequency point and the expected value, if the amplitude and the phase error are both smaller than a set threshold value, determining that the simplified model of the servo mechanism is a second-order oscillation link, otherwise, adopting a system formed by connecting the second-order oscillation link and an amplitude-phase correction link in series as the simplified model of the servo mechanism;
determining characteristic parameters of a serial structure simplified model consisting of the second-order oscillation link and the amplitude-phase correction link by using an optimization control algorithm, wherein an item needing to be corrected in amplitude-phase frequency characteristics is used as an optimization target, and the other item is used as an optimization constraint condition;
and verifying whether the error between the amplitude-phase-frequency characteristic of the simplified servo mechanism model at the key frequency point and the expected value meets the requirement.
Further, the threshold value of the amplitude error is taken to be 1 dB.
Further, the threshold value of the phase error is taken to be 2 degrees.
Further, the phase-amplitude correction element includes, but is not limited to, a lag-lead element for correcting an error in amplitude or phase, and a time-lag element for increasing a lag in phase.
Further, the number of the lag-lead elements or the lag elements connected in series in the servo simplified model is not limited to 1.
Furthermore, 2 lagging links are connected in series on the basis of a second-order oscillation link to correct the phase characteristics of the second-order oscillation link, and the series system is used as a simplified model of a servo mechanism.
Further, the specific steps of determining the model characteristic parameters by using the optimization control algorithm are as follows:
determining a transfer function of the simplified model of the servo mechanism according to the structure of the model;
converting the characteristic parameter solving problem into an optimization problem, taking the minimum error of an item needing to be corrected in the amplitude-phase-frequency characteristic relative to an expected value as an optimization target, and taking another item meeting the expected value as an optimization constraint condition;
solving the problem by an optimization control method aiming at the nonlinear constraint optimization problem;
and substituting the obtained optimal solution into the transfer function to obtain the characteristic parameters of the simplified model of the servo mechanism.
Further, the simplified model transfer function of the servo mechanism consisting of the second-order oscillation link connected with 2 hysteresis links in series is as follows:
in the formula, ωn、ξn、a、τ11、τ21Model characteristic parameters are simplified for the servomechanism to be solved.
Further, when the term to be corrected is a phase-frequency characteristic, the optimization target is taken as:
min J
wherein the content of the first and second substances,
in the formula, n is the number of key frequency points related to the phase frequency characteristics needing to be corrected; omega is a key frequency point related to the phase frequency characteristic needing to be corrected; p (omega)i) Simplifying the phase values of the model at the involved key frequency points for the servomechanism; pref(ωi) Is the phase expectation at the key frequency point of interest; w is aiAre weighted values.
Further, the key frequency points comprise key frequency points corresponding to a first-order rigid body segment, a first-order liquid shaking frequency and a first-order elastic oscillation frequency, the optimization target is the minimization of the phase relative to the expected value error at the key frequency points, the optimization constraint is the amplitude requirement of the frequency points corresponding to the second-order oscillation frequency and the above oscillation frequency, and the characteristic parameters of the servo simplified model are obtained by solving the optimization target.
Further, the optimization control algorithm adopts an SQP algorithm.
Another aspect of the present invention provides a memory storing an executable program that executes the above-described servo mechanism simplified model modeling method when the executable program is called.
Yet another aspect of the present invention provides a server comprising a memory storing an executable program and a processor for calling the executable program to execute the above-mentioned servo mechanism simplified model modeling method.
Therefore, the servo mechanism simplified model modeling method provided by the invention improves the structure of the servo mechanism simplified model which is usually adopted at present, introduces a phase-amplitude correction link, and ensures that the simplified model has higher modeling precision in a plurality of frequency bands; meanwhile, the characteristic parameter fitting problem of the servo structure simplified model is converted into the optimal control problem, the trial and error process of the characteristic parameters is avoided, and the solving efficiency is obviously improved.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a flow diagram of a servo simplified model modeling method according to an exemplary embodiment;
FIG. 2 is a simplified servo model bode diagram resulting from a simplified servo model modeling method according to an exemplary embodiment.
Detailed Description
Reference will now be made in detail to exemplary embodiments of the present invention, examples of which are not to be construed as limiting the invention but are to be construed as more particularly describing certain aspects, features and embodiments of the invention, which are susceptible to various modifications and alternative forms by those skilled in the art without departing from the scope or spirit of the invention.
A flow diagram of a simplified modeling method for a servomechanism according to an exemplary embodiment is given in fig. 1. As shown in fig. 1, the method comprises the steps of:
(1) and determining amplitude-phase-frequency characteristics required to be met by the simplified servo mechanism model, wherein the amplitude-phase-frequency characteristics comprise expected values of amplitude and phase at a series of key frequency points.
The servo mechanism simplifies the amplitude-frequency and phase-frequency characteristics required to be met by the model, and the amplitude-frequency and phase-frequency characteristics are comprehensively determined according to the measured values or index values of the amplitude-frequency and phase-frequency characteristics of the servo mechanism and by combining the rigid body cut-off frequency, the first-order liquid shaking frequency, the transverse first-order, second-order and third-order elastic vibration frequencies and the like of the aircraft.
Taking a large liquid carrier rocket as an example, the first-order liquid sloshing frequency and the first-order elastic frequency of the aircraft are lower, a phase stabilization mode needs to be adopted, while the amplitude stability margin and the phase stability margin need to be considered at the same time in the low-frequency rigid body section, and the frequency relation generally meets the following requirements: rigid body cutoff frequency < first order liquid sloshing frequency < first order elastic modal frequency. Therefore, for frequency points which are lower than the first-order elastic vibration frequency of the rocket in the measured value or the index value of the amplitude-phase characteristic of the servo mechanism, a simplified servo mechanism model is required to have higher amplitude precision and phase precision at the same time; the second-order and third-order elastic vibration needs to adopt a stable amplitude mode, so that a simplified servo mechanism model is required to have higher amplitude precision within the frequency range of the second-order and third-order elastic vibration; for the frequency points with a frequency higher than the third order elastic vibration frequency in the actual measured values or index values of the servo mechanism, the simplified servo mechanism model is required to have proper amplitude precision.
(2) And performing preliminary simplified modeling on the servo mechanism by adopting a traditional second-order oscillation link, analyzing the error between the amplitude-phase-frequency characteristic of the model at the key frequency point and the expected value, if the amplitude and the phase error are both smaller than a set threshold value, determining that the simplified model of the servo mechanism is the second-order oscillation link, and otherwise, adopting a system formed by connecting the second-order oscillation link and the amplitude-phase correction link in series as the simplified model of the servo mechanism.
The amplitude-phase correction link is used for adjusting the amplitude-phase characteristic of a servo mechanism simplified model which is only composed of the traditional second-order oscillation link and has a large error with an expected value, so that the amplitude-phase characteristic is close to the amplitude-phase characteristic required to be met.
Preferably, the amplitude-phase correction element may adopt a lag-lead element or a time-lag element, wherein the lag-lead element is used for correcting the amplitude or phase error, and the time-lag element is used for increasing the lag of the phase. Of course, those skilled in the art may also adopt any other existing links capable of adjusting the amplitude-frequency or phase-frequency characteristics of the system according to specific requirements.
As a preferred example, the threshold value of the amplitude error is 1dB, and the threshold value of the phase error is 2 degrees.
In addition, the number of lag-lead elements or time-lag elements connected in series in the servo simplified model is not limited to 1. Preferred examples are:
2 lagging links are connected in series on the basis of a second-order oscillation link to correct the phase characteristics of the second-order oscillation link, and the series system is used as a simplified model of a servo mechanism.
(3) And determining characteristic parameters of a serial structure simplified model consisting of the second-order oscillation link and the amplitude-phase correction link by using an optimization control algorithm, wherein an item needing to be corrected in the amplitude-phase frequency characteristic is used as an optimization target, and the other item is used as an optimization constraint condition.
For a servo mechanism simplified model only consisting of order oscillation links, the characteristic parameters of the model are estimated as mature technology and can be generally estimated according to empirical values.
For the serial structure simplified model composed of the second-order oscillation link and the amplitude and phase correction link, the characteristic parameter fitting problem of the model is converted into an optimization problem, and an optimization index and an optimization constraint condition are determined according to the amplitude value and phase expected value of the servo mechanism simplified model obtained in the step 1 at the key frequency point.
As a preferred scheme, the specific steps of determining the characteristic parameters of the model by using an optimization control algorithm are as follows:
① determining the transfer function of the simplified model according to the servo mechanism;
②, converting the characteristic parameter solving problem into an optimization problem, taking the minimum error of the item needing to be corrected in the amplitude-phase-frequency characteristic relative to the expected value as an optimization target, and taking the other item meeting the expected value as an optimization constraint condition;
③ solving the problem with an optimization control method for a nonlinear constrained optimization problem;
④, substituting the obtained optimal solution into the transfer function to obtain the characteristic parameters of the simplified model of the servo mechanism.
Taking the simplified servo mechanism model formed by connecting 2 hysteresis links in series with the second-order oscillation link as an example, the transfer function is as follows:
in the formula, ωn、ξn、a、τ11、τ21Model characteristic parameters are simplified for the servomechanism to be solved.
When determining the terms to be corrected in the amplitude-phase-frequency characteristics, the requirement of the amplitude-frequency characteristics is easily met by reasonably selecting the characteristic parameters of a second-order oscillation link, so that the phase is generally used as an optimization index, and the amplitude is used as optimization constraint.
Preferably, when the term to be corrected is a phase-frequency characteristic, the optimization target is:
min J
wherein the content of the first and second substances,
in the formula, n is the number of key frequency points related to the phase frequency characteristics needing to be corrected; omega is a key frequency point related to the phase frequency characteristic needing to be corrected; p (omega)i) Simplifying the phase values of the model at the involved key frequency points for the servomechanism; pref(ωi) Is the phase expectation at the key frequency point of interest; w is aiAre weighted values.
Further, the key frequency points comprise key frequency points corresponding to a first-order rigid body segment, a first-order liquid shaking frequency and a first-order elastic oscillation frequency, the optimization target is the minimization of the phase relative to the expected value error at the key frequency points, the optimization constraint is the amplitude requirement of the frequency points corresponding to the second-order oscillation frequency and the above oscillation frequency, and the characteristic parameters of the servo simplified model are obtained by solving the optimization target.
As a preferred scheme, the optimization control algorithm adopts a sequence quadratic programming method, namely an SQP algorithm. Implementation can be done using the fmincon function of matlab.
(4) And verifying whether the error between the amplitude-phase-frequency characteristic of the simplified servo mechanism model at the key frequency point and the expected value meets the requirement. If the requirements are not met, the former model structure is adjusted, and the amplitude-phase characteristics are further corrected.
Examples of the applications
According to the analysis result of the elastic characteristic and the shaking characteristic of a certain carrier rocket, the first-order liquid shaking frequency is within the range of 0.2Hz to 1Hz, the first-order elastic vibration frequency is within the range of 1.8Hz to 3.1Hz, the second-order elastic vibration frequency is within the range of 5.4Hz to 9.0Hz, and the third-order elastic vibration frequency is within the range of 8.4Hz to 12.1 Hz.
The index requirements of the servomechanism are shown in table 1.
TABLE 1 Servo frequency characteristic requirement
The modeling process of the simplified servo mechanism model comprises the following steps:
(1) determination of expected value of amplitude-phase-frequency characteristic
By analyzing the shaking and elastic frequency of the liquid rocket and the index requirements of the servo mechanism and considering that a certain margin is reserved for the theoretical analysis result of the stability margin compared with the actual situation, the expected values of the amplitude-frequency and phase-frequency characteristics of the simplified model of the servo mechanism at the key frequency point are obtained as follows: the amplitude is about 0dB within the range of 0.16Hz to 12 Hz; at 15Hz, the amplitude is about-2 dB; the phases at 0.16Hz, 1Hz, 2Hz and 3Hz are about-6 DEG, -12 DEG, -19 DEG and-28 DEG, respectively.
(2) Structure for analyzing and determining simplified model of servo mechanism
The second-order oscillation link has the characteristics of 3dB amplitude attenuation and 90 DEG phase lag at the bandwidth. The servo mechanism is simplified to be:
in the formula, ξn＝0.707，ωn＝17Hz。
TABLE 2 frequency characteristics of second order oscillation elements
Therefore, if the model of the servo mechanism is approximated to a second-order oscillation link, the amplitude of the servo mechanism can meet the index requirement of the servo mechanism, but the phase lag is obviously smaller than the index requirement, and if the second-order oscillation link is adopted as the simplified model of the servo mechanism to carry out system stability analysis, the phase margin obtained by shaking the low-frequency rigid body section and the first-order liquid is possibly larger than the actual condition, so that the obtained stability analysis result is inaccurate.
In order to solve the problem, two hysteresis links are connected in series on the basis of a second-order oscillation link to improve the phase characteristic of a simplified model, and the series system is used as the simplified model of a servo mechanism. The transfer function of the simplified model of the servomechanism is:
in the formula, ωn、ξn、a、τ11、τ21Is the characteristic parameter of the servo mechanism to be confirmed.
(3) Solution of characteristic parameters
And (3) on the basis of the servo mechanism simplified model determined in the step (2), converting the characteristic parameter fitting problem of the servo mechanism simplified model into an optimization problem. The amplitude-frequency characteristic requirement is easily met by reasonably selecting the characteristic parameters of the second-order oscillation link, and the lag-lead link is mainly used for improving the phase-frequency characteristic of the simplified model of the servo mechanism and enabling the phase-frequency characteristic to be closer to the index requirement of the servo mechanism. Therefore, according to the expected value of the phase-frequency characteristic of the simplified servo mechanism model obtained in the step 1, the optimization index is:
wherein n is 4; omega1＝0.16Hz、ω2＝1Hz、ω3＝2Hz、ω4＝3Hz；P(ωi) Phase values of the simplified servo mechanism model at each key frequency point; pref(ωi) For the expected phase value of the servo mechanism at each key frequency point, according to the analysis of step 1, Pref(ω1)＝-6°、Pref(ω2)＝-12°、Pref(ω3)＝-19°、Pref(ω4)＝-28°；wiAre weighted values.
The optimization indexes ensure the phase precision of the servo mechanism simplified model at frequency points such as a low-frequency rigid body section, a first-order liquid shaking frequency, a first-order elastic vibration frequency and the like. And regarding the amplitude requirement of 5 Hz-15 Hz equal frequency points in the frequency characteristic index as optimization constraint. The characteristic parameter determination problem of the simplified model of the servo mechanism is converted into the following optimization problem:
min J
in the formula, ω5＝5Hz、ω6＝8Hz、ω7＝10Hz、ω8＝12Hz、ω9＝15Hz。
Solving the optimal problem by using the fmincon function of matlab, and solving the optimal solution
A simplified model of the servomechanism is obtained by substituting equation (1).
(4) Model validation
And checking whether the error of the amplitude-frequency and phase-frequency characteristics and the index value of the simplified model of the servo mechanism at the key frequency point meets the requirement or not.
A bode plot of the simplified servo model is drawn as shown in fig. 2. The frequency characteristics of the key frequency points given by the simplified model in step 1 are shown in table 3.
TABLE 3 Key frequency characteristics of the Servo simplified model
Therefore, the amplitude-frequency characteristic of the simplified model of the servo mechanism meets the index requirement, and the error between the phase characteristic of the key frequency point and the index value is less than 2 degrees. Compared with the traditional second-order simplified model, the simplified model of the servo mechanism has higher phase precision at the key frequency point concerned by the stability analysis of the control system, and the obtained simplified model of the servo mechanism is reasonable.
The embodiments of the present application described above may be implemented in various hardware, software code, or a combination of both. For example, the embodiments of the present application may also represent program codes for executing the above-described methods in a Digital Signal Processor (DSP). The present application may also relate to a variety of functions performed by a computer processor, digital signal processor, microprocessor, or Field Programmable Gate Array (FPGA). The processor described above may be configured in accordance with the present application to perform certain tasks by executing machine-readable software code or firmware code that defines certain methods disclosed herein. Software code or firmware code may be developed to represent different programming languages and different formats or forms. Different target platforms may also be represented to compile the software code. However, different code styles, types, and languages of software code and other types of configuration code for performing tasks according to the present application do not depart from the spirit and scope of the present application.
The foregoing is merely an illustrative embodiment of the present invention, and any equivalent changes and modifications made by those skilled in the art without departing from the spirit and principle of the present invention should fall within the protection scope of the present invention.
Claims (13)
1. A modeling method of a simplified model of a servo mechanism is characterized by comprising the following steps:
determining amplitude-phase-frequency characteristics required to be met by a simplified servo mechanism model, wherein the amplitude-phase-frequency characteristics comprise expected values of amplitude and phase at a series of key frequency points;
adopting a traditional second-order oscillation link to carry out preliminary simplified modeling on the servo mechanism, analyzing the error between the amplitude-phase-frequency characteristic of the model at the key frequency point and the expected value, if the amplitude and the phase error are both smaller than a set threshold value, determining that the simplified model of the servo mechanism is a second-order oscillation link, otherwise, adopting a system formed by connecting the second-order oscillation link and an amplitude-phase correction link in series as the simplified model of the servo mechanism;
determining characteristic parameters of a serial structure simplified model consisting of the second-order oscillation link and the amplitude-phase correction link by using an optimization control algorithm, wherein an item needing to be corrected in amplitude-phase frequency characteristics is used as an optimization target, and the other item is used as an optimization constraint condition;
and verifying whether the error between the amplitude-phase-frequency characteristic of the simplified servo mechanism model at the key frequency point and the expected value meets the requirement.
2. The servo simplified model modeling method of claim 1, wherein the threshold value of the amplitude error is 1 dB.
3. The servo simplified model modeling method of claim 1, wherein the threshold value of the phase error is taken to be 2 degrees.
4. The servo simplified modeling method as claimed in claim 1, wherein the amplitude-phase correction element includes but is not limited to lag-lead element for correcting amplitude or phase errors and lag element for increasing phase lag.
5. The modeling method of a servo simplified model according to claim 4, wherein the number of lag-lead elements or lag elements connected in series in the servo simplified model is not limited to 1.
6. The modeling method of simplified servo mechanism model according to claim 5, wherein 2 hysteresis loops are connected in series on the basis of the second order oscillation loop to correct the phase characteristics thereof, and the series system is used as the simplified servo mechanism model.
7. The servo mechanism simplified model modeling method according to claim 1, wherein the specific steps of determining the model characteristic parameters by using the optimization control algorithm are as follows:
determining a transfer function of the simplified model of the servo mechanism according to the structure of the model;
converting the characteristic parameter solving problem into an optimization problem, taking the minimum error of an item needing to be corrected in the amplitude-phase-frequency characteristic relative to an expected value as an optimization target, and taking another item meeting the expected value as an optimization constraint condition;
solving the problem by an optimization control method aiming at the nonlinear constraint optimization problem;
and substituting the obtained optimal solution into the transfer function to obtain the characteristic parameters of the simplified model of the servo mechanism.
8. The modeling method of simplified servo mechanism model according to claim 7, wherein the transfer function of simplified servo mechanism model composed of a second order oscillating element connected in series with 2 hysteresis elements is:
in the formula, ωn、ξn、a、τ11、τ21Model characteristic parameters are simplified for the servomechanism to be solved.
9. The servo simplified model modeling method according to claim 1 or 7, wherein when the term to be corrected is a phase frequency characteristic, the optimization objective is taken as:
min J
wherein the content of the first and second substances,
in the formula, n is the number of key frequency points related to the phase frequency characteristics needing to be corrected; omega is a key frequency point related to the phase frequency characteristic needing to be corrected; p (omega)i) Simplifying the phase values of the model at the involved key frequency points for the servomechanism; pref(ωi) Is the phase expectation at the key frequency point of interest; w is aiAre weighted values.
10. The modeling method of the simplified servo mechanism model according to claim 9, wherein the key frequency points include key frequency points corresponding to a first-order rigid body segment, a first-order liquid shaking frequency, and a first-order elastic oscillation frequency, the optimization objective is minimization of errors of phases at the key frequency points relative to an expected value, the optimization constraint is amplitude requirements of frequency points corresponding to the second-order oscillation frequency and above, and the characteristic parameters of the simplified servo mechanism model are obtained by solving the optimization objective.
11. The servo mechanism simplified model modeling method according to claim 1 or 7, characterized in that the optimization control algorithm employs SQP algorithm.
12. A storage medium having stored thereon an executable program which, when invoked, performs a servomechanism simplified model modeling method as set forth in any one of claims 1-11.
13. A server comprising a memory storing an executable program and a processor for invoking the executable program to perform the servomechanism simplified model modeling method of any of claims 1-11.
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| WO2021115150A1 (en) | 2021-06-17 |
| CN111159851B (en) | 2020-12-11 |
| AU2020400213B2 (en) | 2023-05-18 |
| AU2020400213A1 (en) | 2022-07-21 |
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