CN109858170B - Frequency characteristic estimation system and method of strong nonlinear Modelica system model - Google Patents
Frequency characteristic estimation system and method of strong nonlinear Modelica system model Download PDFInfo
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Abstract
The invention discloses a frequency characteristic estimation system and a method of a strong nonlinear Modelica system model, wherein the system comprises a system model construction module, a frequency estimation input module, a frequency test signal creation module, a system model solving module, a frequency characteristic calculation module and a frequency response map drawing module; the method comprises the steps of constructing a system model, defining an IO interface and a frequency range of frequency estimation, creating a test signal, compiling and solving the system model according to the test signal, calculating frequency characteristics and drawing a frequency response graph. The invention mainly adopts Modelica modeling analysis technology to realize the estimation of the system frequency characteristic, solves the problem of model development of a large-scale complex heterogeneous system, effectively solves the problem of frequency characteristic of a strong nonlinear Modelica model acquisition system by a sweep frequency analysis method and principle, and provides an effective and convenient design method for the control loop design of an industrial system.
Description
Technical Field
The invention belongs to the field of system modeling simulation, and particularly relates to a frequency characteristic estimation system and method of a strong nonlinear Modelica system model based on a sweep frequency analysis method and principle, which are particularly suitable for a common Modelica multi-domain model, an FMU model and an operable black box model.
Background
The controlled object of the industrial system generally has the characteristics of multiple fields, high rigidity and strong nonlinearity, and the adoption of block diagram modeling or procedural language modeling requires artificial decoupling and linearization processing, so that an accurate system model is difficult to construct. The Modelica language has natural advantages in the aspect of building a physical model, can build the physical model according to a system physical topological structure, and is particularly suitable for modeling and simulation analysis of a large-scale complex heterogeneous system.
Besides time domain analysis, engineers in different fields need to perform more types of analysis on the system, and the frequency domain analysis plays an important role in the system design process as a supplement to the time domain analysis. Two important control loop design methods are introduced in the classical control theory: the root trace method and the frequency response method. The frequency response method is popular in practical engineering, and can provide good design effect when the controlled object model has uncertainty (such as a black box model) or is unknown. The control loop design based on the frequency domain analysis method is widely applied due to the strong convenience and applicability, and the premise of designing based on the method is to obtain the frequency characteristic of the system. However, when the control system is designed, because the controlled system generally has non-linearity and is difficult to linearize, it is more difficult to derive the transfer function, so that the frequency characteristic of the system cannot be obtained.
Disclosure of Invention
In order to solve the defects in the prior art, the invention aims to provide a frequency characteristic estimation system and a frequency characteristic estimation method for a multi-field, high-rigidity and strong nonlinear Modelica system model.
In order to achieve the technical purpose and achieve the technical effect, the invention is realized by the following technical scheme:
a frequency characteristic estimation system of a strong nonlinear Modelica system model comprises a Modelica system model building module, a frequency estimation input module, a frequency test signal creating module, a Modelica system model solving module, a frequency characteristic calculating module and a frequency response map drawing module;
the Modelica system model building module has the function of building a Modelica system model corresponding to a real system according to the structure and principle of the finished real system;
the frequency estimation input module has the functions of defining an input interface and an output interface for frequency estimation and a frequency estimation range for a Modelica system model of the SIMO according to the finished working scene of the real system;
the frequency test signal creating module is used for creating a test signal SineStream for frequency characteristic calculation according to the definition of the frequency estimation input module, transmitting the test signal SineStream to a Modelica system model to be tested through an input interface and using the Modelica system model for solving calculation;
the Modelica system model solving module has the functions of compiling and solving the Modelica system model by using a compiler and a solver of simulation software according to a test signal SineStream of the frequency test signal creating module, segmenting an output signal according to different frequency components after solving is finished, and obtaining IO simulation data of the Modelica system model;
the frequency characteristic calculation module has the functions of filtering the obtained IO simulation data by using a stability criterion according to the Modelica system model IO simulation data obtained by the Modelica system model solving module to obtain stable data containing complete main frequency components, and finally calculating the amplitude-frequency characteristic and the phase-frequency characteristic of the Modelica system model frequency through discrete Fourier transform (FFT);
the frequency response graph drawing module is used for drawing a typical frequency response graph, such as a Bode graph, according to the results of the amplitude-frequency characteristic and the phase-frequency characteristic calculated by the frequency characteristic calculating module, and realizing the visualization of the frequency estimation result.
A frequency characteristic estimation method of a strong nonlinear Modelica system model comprises the following steps:
step 0) developing a corresponding Modelica system model by adopting a Modelica language according to the structure and the principle of the finished real system;
step 1) according to the working scene of the system, performing frequency estimation input by setting input and output interfaces of a Modelica system model and a frequency range of frequency estimation;
step 2) establishing a test signal SineStream with estimated frequency according to the frequency estimation input, and transmitting the test signal SineStream to a Modelica system model through an input interface;
step 3) according to the created test signal SineStream, compiling and solving the Modelica system model by using a compiler and a solver of simulation software to obtain IO simulation data of the Modelica system model;
step 4) filtering the obtained IO simulation data by using a stability criterion to obtain steady state data containing complete main frequency components, and then calculating by using discrete Fourier transform (FFT) to obtain the amplitude-frequency characteristic and the phase-frequency characteristic of the model frequency of the Modelica system;
and 5) drawing a typical frequency response graph according to the amplitude-frequency characteristic and the phase-frequency characteristic obtained by calculation, so as to realize the visualization of the frequency estimation result.
Further, in step 2), the specific implementation steps of creating the test signal SineStream are as follows:
the frequency estimated test signal SineStream is a segmented signal and has the principle formula:
according to the method, firstly, according to frequency estimation input, signal attributes including a frequency estimation range, estimation points in the frequency range, a system steady-state working point, and amplitude, period and sampling points of a corresponding sinusoidal signal under each specific frequency are defined, then according to the defined signal attributes of a test signal Sinemelow, the test signal Sinemelow is created by using a Modelica language, and the test signal Sinemelow is used as an excitation signal obtained by Modelica system model IO simulation data.
Further, in step 3), the concrete implementation steps of compiling and solving the Modelica system model are as follows:
after a test signal Sinestream is loaded to a Modelica system model to be tested, performing time domain simulation on the Modelica system model, and setting a corresponding cycle number for each frequency in the test signal Sinestream to ensure that the Modelica system model can enter a stable state under the excitation of sinusoidal signals of each frequency;
after the time domain simulation is completed, obtaining an output signal of a Modelica system model linearization output point, and dividing the output signal into m sections according to the duration time of different frequency components to ensure the accuracy of an estimation result, wherein m represents the number of different frequency points contained in a set frequency range, and m is a positive integer; the output signal is IO simulation data of the Modelica system model and is used as an original signal for next frequency characteristic estimation.
Further, in step 4), the specific implementation steps for obtaining the steady-state data are as follows:
setting the periodicity of the obtained IO simulation data to ensure that the IO simulation data for frequency estimation enters a steady state, then carrying out data slicing on the IO simulation data entering the steady state, ensuring that each section of data only contains one main frequency component, and finally carrying out equal-step-length sampling on each section of data to obtain the steady-state data.
Furthermore, when each segment of data is sampled in equal step length, the sampling frequency and the number of sampling points need to satisfy the following conditions:
1) According to the sampling theorem, the sampling frequency is required to be ensured to be more than 2 times of the signal frequency;
2) In order to ensure the calculation speed of discrete Fourier transform, the number of sampling points is an integral power of 2.
Further, in the step 4), the specific implementation steps of calculating the amplitude-frequency characteristic and the phase-frequency characteristic of the model frequency of the Modelica system are as follows:
performing discrete Fourier transform (FFT) on each section of steady-state data obtained after processing, and assuming that one section of steady-state data is
The length of which is n, and discrete fourier transform is performed on it:
wherein the content of the first and second substances,
the frequency spectrum of the steady-state data obtained after discrete Fourier transform is used for calculating the amplitude-frequency characteristic and the phase-frequency characteristic of each frequency point through the frequency spectrum of the Modelica system model, and finally the frequency characteristic of the Modelica system model is obtained.
Further, in step 5), the frequency response graph is plotted as Bode graph.
The invention has the beneficial effects that:
the method mainly adopts a Modelica modeling analysis technology to realize the estimation of the frequency characteristic of the system, solves the problem of model development of a large-scale complex heterogeneous system by means of the characteristics of Modelica language, such as multiple fields, non-causal property and the like, improves the model development efficiency, effectively solves the problem of frequency characteristic acquisition of a strong nonlinear Modelica model system by means of a sweep frequency analysis method and principle, and provides an effective and convenient design method for the design of a control loop of an industrial system.
The foregoing is a summary of the present invention, and in order to provide a clear understanding of the technical means of the present invention and to be implemented in accordance with the present specification, the following is a detailed description of the preferred embodiments of the present invention with reference to the accompanying drawings. The detailed description of the present invention is given in detail by the following examples and the accompanying drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention without limiting the invention. In the drawings:
fig. 1 is a flow chart showing the operation of functional blocks of the frequency characteristic estimation system of the present invention;
FIG. 2 is a schematic diagram illustrating the steps of the frequency characteristic estimation method according to the present invention;
FIG. 3 is a diagram of a test signal SineStream and its properties according to the present invention;
FIG. 4 is a schematic diagram of the system output signal of a single frequency point according to the present invention;
FIG. 5 is a system model diagram of a hydraulic steering engine of an aircraft flight control system in the embodiment of the invention;
FIG. 6 is a schematic diagram of a test signal SineStream of a hydraulic steering engine system model of an aircraft flight control system in the embodiment of the invention;
FIG. 7 is a schematic diagram of a frequency calculation result of a hydraulic steering engine system model of an aircraft flight control system in the embodiment of the invention;
fig. 8 is a Bode diagram of the frequency response of a hydraulic steering engine system model of an aircraft flight control system in the embodiment of the invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Referring to fig. 1, the frequency characteristic estimation system of the strong nonlinear Modelica system model includes a Modelica system model building module 1, a frequency estimation input module 2, a frequency test signal creating module 3, a Modelica system model solving module 4, a frequency characteristic calculating module 5 and a frequency response map drawing module 6;
the Modelica system model building module 1 has the function of building a Modelica system model corresponding to a real system according to the structure and principle of the finished real system;
the frequency estimation input module 2 has the functions of defining an input interface and an output interface for frequency estimation and a frequency estimation range for a Modelica system model of a single-input multi-output SIMO according to the finished working scene of a real system;
the frequency test signal creation module 3 has the functions of creating a test signal SineStream for frequency characteristic calculation according to the definition of the frequency estimation input module 2, transmitting the test signal SineStream to a Modelica system model to be tested through an input interface, and performing Modelica solution operation;
the Modelica system model solving module 4 has the functions of compiling and solving the Modelica system model by using a compiler and a solver of MWorks Sysplorer simulation software according to the test signal SineStream created by the frequency test signal creating module 3, and segmenting output signals according to different frequency components after solving is finished to obtain IO simulation data of the Modelica system model;
the frequency characteristic calculation module 5 has the functions of filtering the obtained IO simulation data according to the IO simulation data of the Modelica system model obtained by the Modelica system model solving module 4 by using a stabilization criterion to obtain stable data containing complete main frequency components, and finally calculating the amplitude-frequency characteristic and the phase-frequency characteristic of the Modelica system model frequency through discrete Fourier transform (FFT);
the function of the frequency response map drawing module 6 is to draw a typical frequency response map, such as a Bode map, according to the results of the amplitude-frequency characteristic and the phase-frequency characteristic calculated by the frequency characteristic calculation module 5, thereby realizing the visualization of the frequency estimation result.
Referring to fig. 1 and 2, a method for estimating frequency characteristics of a model of a strongly nonlinear Modelica system includes the following steps:
step 0) developing a corresponding Modelica system model by adopting a Modelica language according to the structure and the principle of the finished real system;
step 1) according to the working scene of the system, performing frequency estimation input by setting input and output interfaces of a Modelica system model and a frequency range of frequency estimation;
step 2) establishing a test signal SineStream with estimated frequency according to the estimated frequency input, and transmitting the test signal SineStream to the Modelica system model through an input interface; the specific implementation steps for creating the test signal SineStream are as follows:
the frequency estimated test signal SineStream is a segmented signal and has the principle formula:
firstly, according to frequency estimation input, referring to fig. 3, defining signal attributes including a frequency estimation range, estimation points in the frequency range, a system steady-state operating point, and amplitudes, periods and sampling points of corresponding sinusoidal signals under each specific frequency, then creating a test signal Sinemelow by using a Modelica language according to the defined signal attributes of the test signal Sinemelow, and using the test signal Sinemelow as an excitation signal obtained by Modelica system model IO simulation data;
and 3) according to the created test signal SineStream, compiling and solving the Modelica system model by using a compiler and a solver of MWorks Sysplorer simulation software to obtain IO simulation data of the Modelica system model, wherein the specific implementation steps are as follows:
after a test signal Sinestream is loaded to a Modelica system model to be tested, performing time domain simulation on the Modelica system model, and setting a corresponding cycle number for each frequency in the test signal Sinestream to ensure that the Modelica system model can enter a stable state under the excitation of sinusoidal signals of each frequency;
after the time domain simulation is completed, referring to fig. 4, obtaining an output signal of a Modelica system model linearization output point, and dividing the output signal into m segments according to the duration of different frequency components to ensure the accuracy of the estimation result, wherein m represents the number of different frequency points included in a set frequency range, and m is a positive integer;
the output signal is IO simulation data of a Modelica system model and is used as an original signal for carrying out next frequency characteristic estimation;
step 4) filtering the obtained IO simulation data by using a stability criterion to obtain steady state data containing complete main frequency components, and then calculating by using discrete Fourier transform (FFT) to obtain the amplitude-frequency characteristic and the phase-frequency characteristic of the model frequency of the Modelica system; the specific implementation steps for obtaining the steady-state data are as follows:
setting the periodicity of the obtained IO simulation data to ensure that the IO simulation data for frequency estimation enters a steady state, then carrying out data slicing on the IO simulation data entering the steady state, ensuring that each section of data only contains one main frequency component, and finally carrying out equal-step-length sampling on each section of data to obtain steady-state data;
and, when each segment of data is sampled in equal step length, the sampling frequency and the number of sampling points need to satisfy the following conditions:
1) According to the sampling theorem, the sampling frequency is required to be ensured to be more than 2 times of the signal frequency;
2) In order to ensure the calculation speed of discrete Fourier transform, the number of sampling points is an integral power of 2;
the specific implementation steps for calculating the amplitude-frequency characteristic and the phase-frequency characteristic of the Modelica system model frequency are as follows:
performing discrete Fourier transform (FFT) on each section of steady-state data obtained after processing, and assuming that one section of steady-state data is
The length of which is n, and discrete fourier transform is performed on it:
wherein the content of the first and second substances,
the frequency spectrum of the steady-state data after discrete Fourier transform is obtained, the amplitude-frequency characteristic and the phase-frequency characteristic of each frequency point are calculated through the frequency spectrum of the Modelica system model, and the frequency characteristic of the Modelica system model is finally obtained;
and 5) drawing a typical frequency response graph, such as a Bode graph, according to the amplitude-frequency characteristic and the phase-frequency characteristic obtained by calculation, and realizing visualization of a frequency estimation result.
By taking a hydraulic steering engine of an airplane flight control system as an embodiment, the frequency characteristic estimation method of the strong nonlinear Modelica system model comprises the following specific steps:
step 0) as shown in fig. 5, according to the structure and principle of a hydraulic steering engine of an airplane flight control system, a hydraulic steering engine system model corresponding to a real system is constructed by adopting a Modelica language;
step 1) setting an electro-hydraulic servo valve input of a hydraulic steering engine as an input interface of a hydraulic steering engine system model, setting a deflection angle of the hydraulic steering engine as an output interface of the hydraulic steering engine system model and setting an estimation frequency range f = [0.1-30Hz ] according to a working scene of the hydraulic steering engine of an airplane flight control system;
step 2) referring to fig. 6, a test signal linestream for frequency estimation is created according to the set input interface, output interface and estimated frequency range f = [0.1-30Hz ], and the Modelica main code of the test signal linestream is as follows:
transmitting the test signal SineStream to a hydraulic steering engine system model through an input interface for Modelica solution operation;
step 3) compiling and solving a hydraulic steering engine system model according to the created test signal SineStream to obtain IO simulation data of the hydraulic steering engine system model;
simulating a hydraulic steering engine system model by using MWorks Sysplorer simulation software, compiling and solving the Modelica system model by using a compiler and a solver of the simulation software, and after the simulation is finished, performing data slicing on an obtained output signal of a linearized output point of the hydraulic steering engine system model to obtain IO simulation data of the hydraulic steering engine system model;
step 4) filtering IO simulation data of the hydraulic steering engine system model by using a stability criterion algorithm to obtain steady state data of the simulation of the hydraulic steering engine system of the airplane flight control system, and calculating by using an FFT algorithm to obtain the amplitude-frequency characteristic and the phase-frequency characteristic of the hydraulic steering engine system of the airplane flight control system as shown in figure 7;
and 5) drawing a Bode diagram according to the amplitude-frequency characteristic and the phase-frequency characteristic of the hydraulic steering engine system of the airplane flight control system obtained through calculation and referring to fig. 8, and realizing visualization of the frequency estimation result of the hydraulic steering engine system of the airplane flight control system.
The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention accordingly, and not to limit the protection scope of the present invention accordingly. All equivalent changes or modifications made in accordance with the spirit of the present disclosure are intended to be covered by the scope of the present disclosure.
Claims (6)
1. A frequency characteristic estimation method of a strong nonlinear Modelica system model is realized by a frequency characteristic estimation system of the strong nonlinear Modelica system model, and the system comprises a Modelica system model building module (1), a frequency estimation input module (2), a frequency test signal creating module (3), a Modelica system model solving module (4), a frequency characteristic calculating module (5) and a frequency response map drawing module (6);
the Modelica system model building module (1) has the function of building a Modelica system model corresponding to a real system according to the structure and the principle of the finished real system;
the frequency estimation input module (2) has the function of defining an input interface and an output interface for estimating the frequency of a Modelica system model of the SIMO according to the finished working scene of the real system and the frequency estimation range;
the frequency test signal creating module (3) has the function of creating a test signal SineStream for frequency characteristic calculation according to the definition of the frequency estimation input module (2), transmitting the test signal SineStream to a Modelica system model to be tested through an input interface, and using the test signal SineStream for the solving operation of Modelica;
the Modelica system model solving module (4) has the functions of compiling and solving the Modelica system model by using a compiler and a solver of simulation software according to the test signal SineStream created by the frequency test signal creating module (3), segmenting an output signal according to different frequency components after solving is finished, and obtaining IO simulation data of the Modelica system model;
the frequency characteristic calculation module (5) has the functions of filtering the obtained IO simulation data by using a stability criterion according to the IO simulation data of the system model obtained by the Modelica system model solving module (4) to obtain stable data containing complete main frequency components, and finally calculating the amplitude-frequency characteristic and the phase-frequency characteristic of the Modelica system model frequency through discrete Fourier transform;
the frequency response graph drawing module (6) is used for drawing a typical frequency response graph according to the results of the amplitude-frequency characteristic and the phase-frequency characteristic calculated by the frequency characteristic calculating module (5) so as to realize the visualization of a frequency estimation result;
the method is characterized by comprising the following steps:
step 0) developing a corresponding Modelica system model by adopting a Modelica language according to the structure and the principle of the finished real system;
step 1) according to the working scene of the system, performing frequency estimation input by setting input and output interfaces of a Modelica system model and a frequency range of frequency estimation;
step 2) establishing a test signal SineStream with estimated frequency according to the frequency estimation input, and transmitting the test signal SineStream to a Modelica system model through an input interface;
step 3) according to the created test signal SineStream, a compiler and a solver of simulation software are used for compiling and solving the Modelica system model to obtain IO simulation data of the Modelica system model;
the concrete implementation steps of compiling and solving the Modelica system model are as follows:
after a test signal Sinestream is loaded to a Modelica system model to be tested, performing time domain simulation on the Modelica system model, and setting a corresponding cycle number for each frequency in the test signal Sinestream to ensure that the Modelica system model can enter a stable state under the excitation of sinusoidal signals of each frequency;
after the time domain simulation is completed, obtaining an output signal of a Modelica system model linearization output point, and dividing the output signal into m sections according to the duration time of different frequency components to ensure the accuracy of an estimation result, wherein m represents the number of different frequency points contained in a set frequency range, and m is a positive integer; the output signal is IO simulation data of the Modelica system model and is used as an original signal for next frequency characteristic estimation;
step 4) filtering the obtained IO simulation data by using a stability criterion to obtain steady state data containing complete main frequency components, and then calculating by using discrete Fourier transform to obtain the amplitude-frequency characteristic and the phase-frequency characteristic of the Modelica system model frequency;
and 5) drawing a typical frequency response graph according to the amplitude-frequency characteristic and the phase-frequency characteristic obtained by calculation, so as to realize the visualization of the frequency estimation result.
2. The method for estimating frequency characteristics of a robust nonlinear Modelica system model according to claim 1, wherein the step 2) of creating the test signal honeystream is implemented by the following steps:
firstly, according to frequency estimation input, defining signal attributes including a frequency estimation range, an estimation point number in the frequency range, a system steady-state working point, and an amplitude value, a period and a sampling point number of a corresponding sinusoidal signal under each specific frequency, then according to the defined signal attributes of a test signal Sinestream, creating the test signal Sinestream by using a Modelica language, and using the test signal Sinestream as an excitation signal obtained by Modelica system model IO simulation data.
3. The method for estimating the frequency characteristic of the robust nonlinear Modelica system model according to claim 1, wherein the step 4) of obtaining the steady-state data comprises the following steps:
setting the periodicity of the obtained IO simulation data to ensure that the IO simulation data for frequency estimation enters a steady state, then carrying out data slicing on the IO simulation data entering the steady state, ensuring that each section of data only contains one main frequency component, and finally carrying out equal-step-length sampling on each section of data to obtain the steady-state data.
4. The method for estimating the frequency characteristics of the strong nonlinear Modelica system model according to claim 3, wherein when each segment of data is sampled at equal step length, the sampling frequency and the number of sampling points need to satisfy the following conditions:
according to the sampling theorem, the sampling frequency is required to be ensured to be more than 2 times of the signal frequency;
to ensure the computation speed of discrete Fourier transform, the number of sampling points is an integral power of 2.
5. The method for estimating the frequency characteristic of the strong nonlinear Modelica system model according to claim 1, wherein the step 4) of calculating the amplitude-frequency characteristic and the phase-frequency characteristic of the Modelica system model frequency is implemented by the following steps:
performing discrete Fourier transform (FFT) on each section of steady-state data obtained after processing, and assuming that one section of steady-state data is
The length is n, and discrete Fourier transform is performed on the length:
and Y (k) is a frequency spectrum obtained after the steady-state data is subjected to discrete Fourier transform, and the amplitude-frequency characteristic and the phase-frequency characteristic of each frequency point are calculated through the frequency spectrum of the Modelica system model, so that the frequency characteristic of the Modelica system model is finally obtained.
6. The method for estimating frequency characteristics of a robust nonlinear Modelica system model according to claim 1, wherein the frequency response map drawn in step 5) is a Bode map.
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