WO2021115150A1 - 一种伺服机构简化模型建模方法、存储介质及服务器 - Google Patents

一种伺服机构简化模型建模方法、存储介质及服务器 Download PDF

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WO2021115150A1
WO2021115150A1 PCT/CN2020/132799 CN2020132799W WO2021115150A1 WO 2021115150 A1 WO2021115150 A1 WO 2021115150A1 CN 2020132799 W CN2020132799 W CN 2020132799W WO 2021115150 A1 WO2021115150 A1 WO 2021115150A1
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servo mechanism
simplified model
phase
amplitude
frequency
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PCT/CN2020/132799
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French (fr)
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朱凯
赵向楠
钟友武
赵卫娟
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蓝箭航天空间科技股份有限公司
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Priority to AU2020400213A priority Critical patent/AU2020400213B2/en
Publication of WO2021115150A1 publication Critical patent/WO2021115150A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD

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  • the invention relates to the field of aerospace, in particular to aircraft control and simulation technology, specifically a modeling method, storage medium and server for a simplified model of an aircraft servo mechanism.
  • the servo mechanism In the attitude control system of the large aircraft represented by the launch vehicle, the servo mechanism is the actuating device that controls the actuator. It receives the command signal given by the attitude control law and drives the swing engine to swing, thereby correcting the deviation of the flight trajectory and attitude.
  • the electric servo mechanism is a high-order system that contains non-linear characteristics such as dead zone, gap, saturation, etc.
  • the electric servo mechanism is usually simplified to A second-order oscillation link.
  • the stability analysis model of a large-scale launch vehicle is a rigid body -Elastic-sloshing coupled rocket body, control law and servo mechanism dynamic characteristics of a high-level system
  • the attitude control system of large liquid rockets usually needs to take into account the amplitude and phase stability margin indexes in the low-frequency rigid body section.
  • the first-order liquid sloshing frequency and the first-order elastic frequency are low, and it is difficult to achieve amplitude stability, and phase stability is usually adopted.
  • a stable amplitude method is usually used for elastic frequencies above the second order.
  • the correctness of the simplified model of the servo mechanism directly affects the correctness of the results of the stability analysis of the attitude control system. Therefore, in order to ensure the accuracy of the stability analysis results, we must pay attention to the amplitude-frequency and phase-frequency characteristics of the servo mechanism model in the low-frequency rigid body section, the first-order sloshing and the phase-frequency characteristics near the first-order elastic vibration frequency, and the high-frequency (second-order elastic) (Vibration frequency and above), such as key frequency characteristics such as amplitude-frequency characteristics.
  • the purpose of the present invention is to solve the problem that the second-order oscillation link is used as the simplified model of the servo mechanism, and it is difficult to meet the requirements of the amplitude-frequency and phase-frequency characteristics of the servo mechanism at multiple frequency points at the same time, and to provide a more complete servo mechanism.
  • One aspect of the present invention provides a modeling method for a simplified model of a servo mechanism, which includes the following steps:
  • the servo mechanism is preliminarily simplified and modeled with the traditional second-order oscillation link, and the error between the amplitude, phase and frequency characteristics of the model at the critical frequency point and the expected value is analyzed. If the amplitude and phase errors are both less than the set value Threshold value, the simplified model of the servo mechanism is determined to be the second-order oscillation link, otherwise a system consisting of the second-order oscillation link and the amplitude-phase correction link in series is adopted as the simplified model of the servo mechanism;
  • the characteristic parameters of the model are determined by the optimization control algorithm.
  • the item that needs to be corrected in the amplitude-phase-frequency characteristic is taken as the optimization target, and the other item As an optimization constraint;
  • the threshold value of the amplitude error is taken as 1 dB.
  • the threshold value of the phase error is taken as 2 degrees.
  • the amplitude and phase correction link includes but is not limited to a lag-lead link and a time lag link, wherein the lag-lead link is used to correct amplitude or phase errors, and the time lag link is used to increase the lag of the phase.
  • the number of the lag-lead link or the time lag link connected in series in the simplified model of the servo mechanism is not limited to one.
  • the problem of solving characteristic parameters is transformed into an optimization problem, with the minimum error of the item that needs to be corrected in the amplitude, phase and frequency characteristics relative to the expected value as the optimization goal, and the other item that satisfies the expected value as the optimization constraint;
  • the obtained optimal solution is substituted into the transfer function to obtain the characteristic parameters of the simplified model of the servo mechanism.
  • ⁇ n , ⁇ n , a, ⁇ 11 , and ⁇ 21 are the characteristic parameters of the simplified model of the servo mechanism to be solved.
  • the optimization target is taken as:
  • the key frequency points include the key frequency points corresponding to the first-order rigid body segment, the first-order liquid sloshing frequency, and the first-order elastic oscillation frequency.
  • the optimization goal is to minimize the phase error relative to the expected value at these key frequency points.
  • the optimization constraint is the amplitude requirement of the frequency point corresponding to the second-order and above oscillation frequency, and the characteristic parameters of the servo simplified model are obtained by solving the optimization objective.
  • the optimized control algorithm adopts the SQP algorithm.
  • Another aspect of the present invention provides a memory, which stores an executable program, and when the executable program is called, executes the above-mentioned servo mechanism simplified model modeling method.
  • Another aspect of the present invention provides a server including a memory and a processor, the memory stores an executable program, and the processor is configured to call the executable program to execute the above-mentioned servo mechanism simplified model modeling method.
  • the simplified model modeling method of the servo mechanism improves the simplified model structure of the servo mechanism commonly used at present, and introduces the amplitude and phase correction link to ensure that the simplified model has higher modeling accuracy in multiple frequency bands; ,
  • the characteristic parameter fitting problem of the simplified model of the servo structure is transformed into an optimal control problem, which avoids the trial and error process of characteristic parameters and significantly improves the efficiency of the solution.
  • Fig. 1 is a flow chart of a method for modeling a simplified model of a servo mechanism according to an exemplary embodiment
  • Fig. 2 is a bode diagram of a simplified model of a servo mechanism obtained by a method for modeling a simplified model of a servo mechanism according to an exemplary embodiment.
  • Fig. 1 shows a flow chart of a method for modeling a simplified model of a servo mechanism according to an exemplary embodiment. As shown in Figure 1, the method includes the following steps:
  • the amplitude-frequency and phase-frequency characteristics that the simplified model of the servo mechanism needs to meet are based on the actual measured value or index value of the amplitude-frequency and phase-frequency characteristics of the servo mechanism, combined with the rigid body cut-off frequency of the aircraft, the first-order liquid sloshing frequency, the lateral first-order, and the second-order And the third-order elastic vibration frequency is determined comprehensively.
  • the first-order liquid sloshing frequency and first-order elastic frequency of this kind of aircraft are relatively low, and the phase stabilization method is required, while the low-frequency rigid body section needs to consider both the amplitude stability margin and the phase stability margin.
  • the frequency relationship usually satisfies: cut-off frequency of rigid body ⁇ first-order liquid sloshing frequency ⁇ first-order elastic mode frequency. Therefore, for the actual measured values or index values of the amplitude and phase characteristics of the servo mechanism that are lower than the first-order elastic vibration frequency of the rocket, the simplified servo mechanism model is required to have both high amplitude accuracy and phase accuracy; for the second-order and The third-order elastic vibration needs to adopt a stable amplitude method.
  • the simplified servo mechanism model is required to have higher amplitude accuracy; and for the actual measured value or index value of the servo mechanism
  • the frequency point higher than the third-order elastic vibration frequency requires the simplified servo mechanism model to have appropriate amplitude accuracy.
  • the amplitude and phase correction link is used to adjust the amplitude and phase characteristics of the simplified model of the servo mechanism composed of only the traditional second-order oscillation link and the expected value error, so that it is close to the amplitude and phase characteristics that need to be met.
  • the amplitude and phase correction link can adopt a lag-lead link or a time lag link, where the lag-lead link is used to correct amplitude or phase errors, and the time lag link is used to increase the lag of the phase.
  • the lag-lead link is used to correct amplitude or phase errors
  • the time lag link is used to increase the lag of the phase.
  • those skilled in the art can also use all other existing links that can adjust the system's amplitude-frequency or phase-frequency characteristics according to specific needs.
  • the threshold value of the amplitude error is 1 dB
  • the threshold value of the phase error is 2 degrees.
  • the number of lag-lead links or time lag links connected in series in the simplified model of the servo mechanism is not limited to one. Preferred examples are:
  • the characteristic parameters of the model are determined by the optimization control algorithm. Among them, the item that needs to be corrected in the amplitude-phase-frequency characteristic is taken as the optimization target. The other is used as an optimization constraint.
  • the characteristic parameters of the model are estimated as mature technology, which can usually be estimated based on empirical values.
  • the present invention transforms the characteristic parameter fitting problem of this type of model into an optimization problem, and the simplified model of the servo mechanism obtained in step 1 Determine the optimization index and optimization constraint conditions at the expected value of the amplitude and phase of the key frequency points.
  • the specific steps for determining the characteristic parameters of the model by using the optimized control algorithm are as follows:
  • ⁇ n , ⁇ n , a, ⁇ 11 , and ⁇ 21 are the characteristic parameters of the simplified model of the servo mechanism to be solved.
  • the phase is generally used as the optimization index, and the amplitude is used as the optimization constraint.
  • the optimization target is taken as:
  • the key frequency points include the key frequency points corresponding to the first-order rigid body segment, the first-order liquid sloshing frequency, and the first-order elastic oscillation frequency.
  • the optimization goal is to minimize the phase error relative to the expected value at these key frequency points.
  • the optimization constraint is the amplitude requirement of the frequency point corresponding to the second-order and above oscillation frequency, and the characteristic parameters of the servo simplified model are obtained by solving the optimization objective.
  • the optimized control algorithm adopts the sequential quadratic programming method, that is, the SQP algorithm. It can be realized by the fmincon function of matlab.
  • the first-order liquid sloshing frequency is in the range of 0.2Hz ⁇ 1Hz
  • the first-order elastic vibration frequency is in the range of 1.8Hz ⁇ 3.1Hz
  • the second-order elastic vibration frequency is in the range of 5.4Hz ⁇
  • the third-order elastic vibration frequency is in the range of 8.4 Hz to 12.1 Hz.
  • the modeling process of the simplified model of the servo mechanism includes the following steps:
  • the amplitude-frequency and phase-frequency characteristics of the simplified model of the servo mechanism are obtained.
  • the expected value at key frequency points is: in the range of 0.16Hz ⁇ 12Hz, the amplitude is about 0dB; at 15Hz, the amplitude is about -2dB; at 0.16Hz, 1Hz, 2Hz, and 3Hz, the phase is about -6°,- 12°, -19°, -28°.
  • the second-order oscillation link has a 3dB amplitude attenuation at its bandwidth and a phase lag of 90°.
  • the servo mechanism is simplified as:
  • the model of the servo mechanism is approximated as a second-order oscillation link, its amplitude can meet the index requirements of the servo mechanism, but the phase lag should be significantly smaller than the index requirement. If the second-order oscillation link is used as a simplified model of the servo mechanism for the system For stability analysis, the phase margin obtained for the low-frequency rigid body section and the first-order liquid sloshing may be greater than the actual situation, making the stability analysis results inaccurate.
  • ⁇ n , ⁇ n , a, ⁇ 11 , and ⁇ 21 are the characteristic parameters of the servo mechanism to be confirmed.
  • the characteristic parameter fitting problem of the simplified model of the servo structure is transformed into an optimization problem. Since the amplitude-frequency characteristic requirements are easily met by reasonably selecting the characteristic parameters of the second-order oscillation link, the lag-lead link is mainly used to improve the phase-frequency characteristics of the simplified model of the servo mechanism and make it closer to the index requirements of the servo mechanism. Therefore, according to the expected value of the phase-frequency characteristic of the simplified model of the servo mechanism obtained in step 1, the optimization index is taken as:
  • the above optimization indicators ensure the phase accuracy of the simplified model of the servo mechanism at the low-frequency rigid body section, the first-order liquid sloshing frequency, and the first-order elastic vibration frequency. Regarding the amplitude requirements of 5Hz ⁇ 15Hz and other frequency points in the frequency characteristic index, it is regarded as the optimization constraint.
  • the problem of determining the characteristic parameters of the simplified model of the servo mechanism is transformed into the following optimization problem:
  • ⁇ 5 5 Hz
  • ⁇ 6 8 Hz
  • ⁇ 7 10 Hz
  • ⁇ 8 12 Hz
  • ⁇ 9 15 Hz.
  • the amplitude-frequency characteristic of the simplified model of the servo mechanism meets the index requirements, and the error between the phase characteristic and the index value at the critical frequency point is less than 2 degrees.
  • the simplified model of the servo mechanism has higher phase accuracy at the key frequency points concerned in the stability analysis of the control system. The resulting simplified model of the servo mechanism is reasonable.
  • the embodiment of the present application may also represent the program code for executing the above method in a digital signal processor (DSP).
  • DSP digital signal processor
  • This application may also involve multiple functions performed by a computer processor, a digital signal processor, a microprocessor, or a field programmable gate array (Field Programmable Gate Array, FPGA).
  • the above-mentioned processor can be configured to perform a specific task according to the present application, which is completed by executing machine-readable software code or firmware code that defines the specific method disclosed in the present application.
  • the software code or firmware code can be developed to express different programming languages and different formats or forms. It can also mean that the software code is compiled for different target platforms. However, the different code styles, types and languages of the software code for performing tasks according to this application and other types of configuration codes do not depart from the spirit and scope of this application.

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Abstract

一种伺服机构简化模型的建模方法、存储介质及服务器，该建模方法包括步骤：伺服机构简化模型幅相频特性期望值的确定；模型结构的分析确定；采用优化控制算法进行模型特征参数求解，以及模型幅相频特性的验证。该方法对目前通常采用的伺服机构简化模型的结构进行了改进，引入了幅相校正环节，保证简化模型在多个频段具有较高的建模精度；同时，将伺服结构简化模型的特征参数拟合问题转化为最优控制问题，避免了特征参数的试凑过程，显著提高了求解效率。

Description

一种伺服机构简化模型建模方法、存储介质及服务器 技术领域
本发明涉及航空航天领域，尤其涉及飞行器控制与仿真技术，具体为飞行器伺服机构简化模型的建模方法、存储介质及服务器。
背景技术
以运载火箭为代表的大型飞行器的姿控系统中，伺服机构是控制执行机构的作动装置，接受姿态控制律给出的指令信号，驱动摇摆发动机摆动，从而纠正飞行轨迹和姿态的偏差。电动伺服机构是一个包含死区、间隙、饱和等非线性特性的高阶系统，在进行火箭控制系统的小偏差稳定性分析时，从建模工作的便利性考虑，通常将电动伺服机构简化为一个二阶振荡环节。
对于以液体燃料做推进剂的大型运载火箭，在分析其姿态稳定性时，需要考虑推进剂晃动和弹性振动对火箭姿态系统稳定性的影响，因此大型运载火箭的稳定性分析模型是一个由刚体-弹性-晃动耦合的火箭本体、控制律以及伺服机构动态特性组成的高阶系统，大型液体火箭的姿态控制系统在低频刚体段通常需要兼顾幅值和相位稳定裕度指标。一阶液体晃动频率和一阶弹性频率较低，难以实现幅值稳定，通常采用相位稳定的方式。对于二阶以上弹性频率，通常采用幅值稳定的方式。
伺服机构简化模型的正确性直接影响着姿控系统稳定性分析结果的正确性。因此，为了保证稳定性分析结果的正确性，必须关注伺服机构模型在低频刚体段的幅频和相频特性、一阶晃动和一阶弹性振动频率附近的相频特性、高频段(二阶弹性振动频率及以上)的幅频特性等关键频率特性。然而，仅用一个二阶振动环节描述的传统伺服 机构简化模型，难以同时满足上述刚体、晃动以及弹性振动等多个关键频点的高精度伺服机构建模需求。
发明内容
本发明的目的在于针对采用二阶振荡环节作为伺服机构的简化模型，难以同时满足伺服机构在多个频点的幅频和相频特性要求这一问题，给出了一种更加完善的伺服机构简化模型建模方法，包括模型结构的确定，以及可快速求解模型特征参数的方法。
本发明的一个方面提供了一种伺服机构简化模型的建模方法，包括以下步骤：
确定伺服机构简化模型需要满足的幅相频特性，包括在一系列关键频点处幅度和相位的期望值；
采用传统二阶振荡环节对伺服机构进行初步简化建模，分析该模型在所述关键频点处的幅相频特性与所述期望值之间的误差，如果幅值和相位误差均小于设定的门限值，则确定伺服机构的简化模型为二阶振荡环节，否则采用由二阶振荡环节和幅相校正环节串联而成的系统作为伺服机构的简化模型；
对于由所述二阶振荡环节和幅相校正环节组成的串联结构简化模型，利用优化控制算法确定模型的特征参数，其中，将幅相频特性中需要校正的项作为优化目标，将另一项作为优化约束条件；
验证伺服机构简化模型在关键频点处的幅相频特性与所述期望值的误差是否满足要求。
进一步地，所述幅值误差的门限值取为1dB。
进一步地，所述相位误差的门限值取为2度。
进一步地，所述幅相校正环节包括但不限于滞后-超前环节和时滞环节，其中滞后-超前环节用于校正幅值或相位的误差，所述时滞 环节用于增加相位的滞后。
进一步地，伺服机构简化模型中串联的所述滞后-超前环节或时滞环节的数量不限于1个。
进一步地，在二阶振荡环节的基础上串联2个滞后环节以校正其相位特性，将该串联系统作为伺服机构的简化模型。
进一步地，所述利用优化控制算法确定模型特征参数的具体步骤为：
根据伺服机构简化模型的结构，确定其传递函数；
将特征参数求解问题转化为优化问题，以幅相频特性中需要校正的项相对于期望值的误差最小作为优化目标，以另一项满足期望值作为优化约束条件；
用针对非线性约束最优化问题的优化控制方法求解该问题；
将得到的最优解代入所述传递函数，得到所述伺服机构简化模型特征参数。
进一步地，所述由二阶振荡环节串联2个滞后环节组成的伺服机构简化模型传递函数为：
Figure PCTCN2020132799-appb-000001
式中，ω n、ξ n、a、τ 11、τ 21为待求解的伺服机构简化模型特征参数。
进一步地，当所述需要校正的项为相频特性时，所述优化目标取为：
min J
其中，
Figure PCTCN2020132799-appb-000002
式中，n为需要校正的相频特性涉及的关键频点数量；ω为需要校正的相频特性涉及的关键频点；P(ω i)为伺服机构简化模型在 所涉及的关键频点处的相位值；P ref(ω i)为在所涉及的关键频点处的相位期望值；w i为加权值。
进一步地，所述关键频点包括一阶刚体段、一阶液体晃动频率和一阶弹性振荡频率所对应的关键频点，优化目标为这些关键频点处的相位相对于期望值误差的最小化，优化约束为二阶及以上振荡频率对应的频点的幅值要求，通过对优化目标求解获得伺服简化模型的特征参数。
进一步地，所述优化控制算法采用SQP算法。
本发明的另一个方面提供了一种存储器，其存储有可执行程序，在可执行程序被调用时，执行上述伺服机构简化模型建模方法。
本发明的再一个方面提供了一种服务器包括存储器和处理器，所述存储器存储有可执行程序，所述处理器用于调用所述可执行程序，以执行上述伺服机构简化模型建模方法。
可见，本发明提供的伺服机构简化模型建模方法对目前通常采用的伺服机构简化模型结构进行了改进，引入了幅相校正环节，保证简化模型在多个频段具有较高的建模精度；同时，将伺服结构简化模型的特征参数拟合问题转化为最优控制问题，避免了特征参数的试凑过程，显著提高了求解效率。
应了解的是，上述一般描述及以下具体实施方式仅为示例性及阐释性的，其并不能限制本发明所欲主张的范围。
附图说明
下面的附图是本发明的说明书的一部分，其绘示了本发明的示例实施例，所附附图与说明书的描述一起用来说明本发明的原理。
图1为根据示例性实施例的伺服机构简化模型建模方法流程图；
图2为根据示例性实施例的伺服机构简化模型建模方法得到的伺服机构简化模型bode图。
具体实施方式
下面将参照附图详细说明本发明的示例性实施方式，各种实施例不应认为是对本发明的限制，而应理解为是对本发明的某些方面、特性和实施方案的更详细的描述，在不背离本发明的范围或精神的情况下，本领域技术人员可对本发明说明书的具体实施方式做多种改进和变化。
附图1中给出了根据示例性实施例的伺服机构简化模型建模方法流程图。如图1所示，该方法包括以下步骤：
(1)确定伺服机构简化模型需要满足的幅相频特性，包括在一系列关键频点处幅度和相位的期望值。
伺服机构简化模型需要满足的幅频和相频特性，根据伺服机构的幅频、相频特性实测值或指标值，并结合飞行器的刚体截止频率、一阶液体晃动频率、横向一阶、二阶和三阶弹性振动频率等综合确定。
以大型液体运载火箭为例，这种飞行器的一阶液体晃动频率和一阶弹性频率较低，需要采用相位稳定的方式，而低频刚体段需要同时考虑幅值稳定裕度和相位稳定裕度，并且频率关系通常满足：刚体截止频率<一阶液体晃动频率<一阶弹性模态频率。因此，对于伺服机构幅相特性的实测值或指标值中低于火箭一阶弹性振动频率的频点，要求简化的伺服机构模型能够同时具有较高的幅值精度和相位精度；对于二阶和三阶弹性振动需要采用幅值稳定的方式，因此，在二阶和三阶弹性振动频率范围内，要求简化的伺服机构模型具有较高的幅值精 度；而对于伺服机构实测值或指标值中频率高于第三阶弹性振动频率的频点，要求简化的伺服机构模型具有适当的幅值精度。
(2)采用传统二阶振荡环节对伺服机构进行初步简化建模，分析该模型在所述关键频点处的幅相频特性与所述期望值之间的误差，如果幅值和相位误差均小于设定的门限值，则确定伺服机构的简化模型为二阶振荡环节，否则采用由二阶振荡环节和幅相校正环节串联而成的系统作为伺服机构简化模型。
其中的幅相校正环节用于调整仅由传统二阶振荡环节组成的伺服机构简化模型与期望值误差较大的幅相特性，使其向需要满足的幅相特性接近。
作为优选方案，幅相校正环节可以采用滞后-超前环节或时滞环节，其中滞后-超前环节用于校正幅值或相位的误差，所述时滞环节用于增加相位的滞后。当然，本领域技术人员也可以根据具体需求采用现有其它一切能够调整系统幅频或相频特性的环节。
作为优选示例，所述幅值误差的门限值取1dB，所述相位误差的门限值取2度。
另外，串联在伺服机构简化模型中的滞后-超前环节或时滞环节的数量不限于1个。优选示例为：
在二阶振荡环节的基础上串联2个滞后环节以校正其相位特性，将该串联系统作为伺服机构的简化模型。
(3)对于由所述二阶振荡环节和幅相校正环节组成的串联结构简化模型，利用优化控制算法确定模型的特征参数，其中，将幅相频特性中需要校正的项作为优化目标，将另一项作为优化约束条件。
对于仅由阶振荡环节组成的伺服机构简化模型，模型的特征参数估计为成熟技术，通常可以根据经验值进行估计。
而对于由所述二阶振荡环节和幅相校正环节组成的串联结构简 化模型，本发明中将该类模型的特征参数拟合问题转化为优化问题，并根据步骤1所得到的伺服机构简化模型在关键频点的幅值和相位期望值，确定优化指标以及优化约束条件。
作为优选方案，利用优化控制算法确定模型特征参数的具体步骤为：
①根据伺服机构简化模型的结构，确定其传递函数；
②将特征参数求解问题转化为优化问题，以幅相频特性中需要校正的项相对于期望值的误差最小作为优化目标，以另一项满足期望值作为优化约束条件；
③用针对非线性约束最优化问题的优化控制方法求解该问题；
④将得到的最优解代入所述传递函数，得到所述伺服机构简化模型特征参数。
以前述由二阶振荡环节串联2个滞后环节组成的伺服机构简化模型为例，其传递函数为：
Figure PCTCN2020132799-appb-000003
式中，ω n、ξ n、a、τ 11、τ 21为待求解的伺服机构简化模型特征参数。
在确定幅相频特性中需要校正的项时，由于幅频特性要求容易通过合理地选择二阶振荡环节特征参数来满足，因而一般会将相位作为优化指标，将幅值作为优化约束。
作为优选方案，当所述需要校正的项为相频特性时，所述优化目标取为：
min J
其中，
Figure PCTCN2020132799-appb-000004
式中，n为需要校正的相频特性涉及的关键频点数量；ω为需 要校正的相频特性涉及的关键频点；P(ω i)为伺服机构简化模型在所涉及的关键频点处的相位值；P ref(ω i)为在所涉及的关键频点处的相位期望值；w i为加权值。
进一步地，所述关键频点包括一阶刚体段、一阶液体晃动频率和一阶弹性振荡频率所对应的关键频点，优化目标为这些关键频点处的相位相对于期望值误差的最小化，优化约束为二阶及以上振荡频率对应的频点的幅值要求，通过对优化目标求解获得伺服简化模型的特征参数。
作为优选方案，所述优化控制算法采用序列二次规划法，即SQP算法。可利用matlab的fmincon函数实现。
(4)验证伺服机构简化模型在关键频点处的幅相频特性与所述期望值的误差是否满足要求。如果不满足要求，则对前面的模型结构进行调整，对幅相特性进一步修正。
应用举例
根据某运载火箭的弹性特性及晃动特性分析结果，其一阶液体晃动频率在0.2Hz～1Hz范围内，一阶弹性振动频率在1.8Hz～3.1Hz范围内，二阶弹性振动频率在5.4Hz～9.0Hz范围内，三阶弹性振动频率在8.4Hz～12.1Hz范围内。
伺服机构的指标要求如表1所示。
表1伺服机构频率特性要求
频率(Hz) 幅值(dB) 相位(°)
0.16 ≤0.3 ≥-6
1 ≤0.3 ≥-12
2 ≤0.3 ≥-19
3 ≤0.3 ≥-28
5 ≤0.3 ≥-42
8 ≤0.3 ≥-56
10 ≤0.3 ≥-66
12 ≤0.3 ≥-75
15 ≤-2.0 ≥-90
该伺服机构简化模型的建模过程包括如下步骤：
(1)幅相频特性期望值的确定
通过分析液体火箭的晃动和弹性频率以及伺服机构的指标要求，并考虑到稳定裕度的理论分析结果应较实际情况留有一定的余量，得出伺服机构简化模型的幅频和相频特性在关键频率点的期望值为：在0.16Hz～12Hz范围内，幅值约为0dB；在15Hz，幅值约为-2dB；在0.16Hz、1Hz、2Hz、3Hz相位分别约为-6°、-12°、-19°、-28°。
(2)分析确定伺服机构简化模型的结构
二阶振荡环节在其带宽处具有幅值衰减3dB，相位滞后90°的特性。根据表1中的幅值指标将伺服机构简化为：
Figure PCTCN2020132799-appb-000005
式中，ξ n＝0.707，ω n＝17Hz。
表2二阶振荡环节的频率特性
频率(Hz) 幅值(dB) 相位(°)
0.16 0 -0.8
1 0 -4.7
2 0 -9.5
3 0 -14.3
5 0 -24.3
8 -0.2 -40.2
10 -0.4 -51.5
12 -0.9 -63.0
15 -2.0 -79.8
可见，如果将伺服机构的模型近似为一个二阶振荡环节，其幅值可以满足伺服机构的指标要求，但相位滞后要明显小于指标要求，如果采用该二阶振荡环节作为伺服机构简化模型进行系统稳定性分析，则对于低频刚体段、一阶液体晃动所得的相位裕度可能大于实际情况，使得到的稳定性分析结果不准确。
为了解决这一问题，在二阶振荡环节的基础上串联两个滞后环节来改进简化模型的相位特性，将该串联系统作为伺服机构的简化模型。伺服机构简化模型的传递函数为：
Figure PCTCN2020132799-appb-000006
式中，ω n、ξ n、a、τ 11、τ 21为待确认的伺服机构特征参数。
(3)特征参数求解
在步骤2所确定的伺服机构简化模型的基础上，将伺服结构简化模型的特征参数拟合问题转化为优化问题。由于幅频特性要求容易通过合理地选择二阶振荡环节特征参数来满足，滞后-超前环节主要用于改善伺服机构简化模型的相频特性，使其更接近于伺服机构的指标要求。因此，根据步骤1所得的伺服机构简化模型的相频特性期望值，优化指标取为：
Figure PCTCN2020132799-appb-000007
式中，n＝4；ω 1＝0.16Hz、ω 2＝1Hz、ω 3＝2Hz、ω 4＝3Hz；P(ω i)为简化的伺服机构模型在各关键频点的相位值；P ref(ω i)为伺服机构在各关键频点的期望相位值，根据步骤1的分析，P ref(ω 1)＝-6°、P ref(ω 2)＝-12°、P ref(ω 3)＝-19°、P ref(ω 4)＝-28°；w i为加权值。
上述优化指标保证了伺服机构简化模型在低频刚体段、一阶液体晃动频率、一阶弹性振动频率等频点的相位精度。对于频率特性指标中5Hz～15Hz等频点的幅值要求，将其作为优化约束。将伺服机构简化模型的特征参数确定问题转化为如下优化问题：
min J
Figure PCTCN2020132799-appb-000008
式中，ω 5＝5Hz、ω 6＝8Hz、ω 7＝10Hz、ω 8＝12Hz、ω 9＝15Hz。
利用matlab的fmincon函数求解上述最优问题，将最优解
Figure PCTCN2020132799-appb-000009
a *＝0.899代入式(1)，得到伺服机构的简化模型。
(4)模型验证
检验上述伺服机构简化模型在关键频点的幅频和相频特性与指标值的误差是否满足要求。
绘制伺服机构简化模型的bode图，如附图2所示。该简化模型在步骤1给出的关键频点的频率特性如表3所示。
表3伺服机构简化模型的关键频率特性
Figure PCTCN2020132799-appb-000010
Figure PCTCN2020132799-appb-000011
可见，该伺服机构的简化模型的幅频特性满足指标要求，在关键频点的相位特性与指标值的误差小于2度。该伺服机构的简化模型较传统的二阶简化模型，在控制系统稳定性分析所关心的关键频点具有更高的相位精度，所得的伺服机构简化模型是合理的。
上述的本申请实施例可在各种硬件、软件编码或两者组合中进行实施。例如，本申请的实施例也可表示在数据信号处理器(Digital Signal Processor，DSP)中执行上述方法的程序代码。本申请也可涉及计算机处理器、数字信号处理器、微处理器或现场可编程门阵列(Field Programmable Gate Array，FPGA)执行的多种功能。可根据本申请配置上述处理器执行特定任务，其通过执行定义了本申请揭示的特定方法的机器可读软件代码或固件代码来完成。可将软件代码或固件代码发展表示不同的程序语言与不同的格式或形式。也可表示不同的目标平台编译软件代码。然而，根据本申请执行任务的软件代码与其他类型配置代码的不同代码样式、类型与语言不脱离本申请的精神与范围。
以上所述仅为本发明示意性的具体实施方式，在不脱离本发明的构思和原则的前提下，任何本领域的技术人员所做出的等同变化与修改，均应属于本发明保护的范围。

Claims (13)

  1. 一种伺服机构简化模型建模方法，其特征在于，包括以下步骤：
    确定伺服机构简化模型需要满足的幅相频特性，包括在一系列关键频点处幅值和相位的期望值；
    采用二阶振荡环节对伺服机构进行初步简化建模，分析该模型在所述关键频点处的幅相频特性与所述期望值之间的误差，如果幅值和相位误差均小于设定的门限值，则确定伺服机构的简化模型为二阶振荡环节，否则采用由二阶振荡环节和幅相校正环节串联而成的系统作为伺服机构的简化模型；
    对于由所述二阶振荡环节和幅相校正环节组成的串联结构简化模型，利用优化控制算法确定模型的特征参数，其中，将幅相频特性中需要校正的项作为优化目标，将另一项作为优化约束条件；
    验证伺服机构简化模型在关键频点处的幅相频特性与所述期望值的误差是否满足要求。
  2. 根据权利要求1所述的伺服机构简化模型建模方法，其特征在于，所述幅值误差的门限值取为1dB。
  3. 根据权利要求1所述的伺服机构简化模型建模方法，其特征在于，所述相位误差的门限值取为2度。
  4. 根据权利要求1所述的伺服机构简化模型建模方法，其特征在于，所述幅相校正环节包括但不限于滞后-超前环节和时滞环节，其中滞后-超前环节用于校正幅值或相位的误差，所述时滞环节用于增加相位的滞后。
  5. 根据权利要求4所述的伺服机构简化模型建模方法，其特征在于，伺服机构简化模型中串联的所述滞后-超前环节或时滞环节的数量不限于1个。
  6. 根据权利要求5所述的伺服机构简化模型建模方法，其特征在 于，在二阶振荡环节的基础上串联2个滞后环节以校正其相位特性，将该串联系统作为伺服机构的简化模型。
  7. 根据权利要求1所述的伺服机构简化模型建模方法，其特征在于，所述利用优化控制算法确定模型特征参数的具体步骤为：
    根据伺服机构简化模型的结构，确定其传递函数；
    将特征参数求解问题转化为优化问题，以幅相频特性中需要校正的项相对于期望值的误差最小作为优化目标，以另一项满足期望值作为优化约束条件；
    用针对非线性约束最优化问题的优化控制方法求解该问题；
    将得到的最优解代入所述传递函数，得到所述伺服机构简化模型特征参数。
  8. 根据权利要求7所述的伺服机构简化模型建模方法，其特征在于，所述由二阶振荡环节串联2个滞后环节组成的伺服机构简化模型传递函数为：
    Figure PCTCN2020132799-appb-100001
    式中，ω n、ξ n、a、τ 11、τ 21为待求解的伺服机构简化模型特征参数。
  9. 根据权利要求1或7所述的伺服机构简化模型建模方法，其特征在于，当所述需要校正的项为相频特性时，所述优化目标取为：
    min J
    其中，
    Figure PCTCN2020132799-appb-100002
    式中，n为需要校正的相频特性涉及的关键频点数量；ω为需要校正的相频特性涉及的关键频点；P(ω i)为伺服机构简化模型在所涉及的关键频点处的相位值；P ref(ω i)为在所涉及的关键频点处 的相位期望值；w i为加权值。
  10. 根据权利要求9所述的伺服机构简化模型建模方法，其特征在于，所述关键频点包括一阶刚体段、一阶液体晃动频率和一阶弹性振荡频率所对应的关键频点，优化目标为这些关键频点处的相位相对于期望值误差的最小化，优化约束为二阶及以上振荡频率对应的频点的幅值要求，通过对优化目标求解获得伺服简化模型的特征参数。
  11. 根据权利要求1或7所述的伺服机构简化模型建模方法，其特征在于，所述优化控制算法采用SQP算法。
  12. 一种存储介质，其特征在于，其上存储有可执行程序，在可执行程序被调用时，执行如权利要求1-11任一项所述的伺服机构简化模型建模方法。
  13. 一种服务器，其特征在于，包括存储器和处理器，所述存储器存储有可执行程序，所述处理器用于调用所述可执行程序，以执行如权利要求1-11任一项所述的伺服机构简化模型建模方法。
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