CN105182800A - Amplitude frequency characteristic curve drafting method - Google Patents

Abstract

The invention provides an amplitude frequency characteristic curve drafting method, comprising inputting once synthesized excitation source signals and detected output signals to obtain an amplitude frequency characteristic curve through calculation; the measurement time of the amplitude frequency characteristic curve is equivalent to the measurement time of a smallest frequency sinusoidal signal (single) in a traditional frequency sweep method test; in other words, the time of a whole detection process is greatly shortened, and the test efficiency is substantially increased; in addition, the method can realize digital automatic estimation, and have high real engineering application values.

Description

A kind of method for drafting of amplitude-versus-frequency curve

Technical field

The present invention relates to automatic control technology field, is specifically the method for drafting of a kind of amplitude-versus-frequency curve for automatic control system.

Background technology

The frequency response characteristic of automatic control system is one of the rapidity of analytic system and the important means of stability, is also the core analysis method in classical control theory.Frequency response characteristic comprises amplitude response and phase response, is reflected on curve, is exactly amplitude-frequency curve and phase frequency curve.Amplitude-frequency curve is also referred to as amplitude-versus-frequency curve.

The general all following several scheme of amplitude-versus-frequency curve of automatic control system is drawn: scheme (1) obtains system transter by mathematical modeling and analyzes in prior art, this scheme is generally used for analyzing the amplitude versus frequency characte of ideally system when system, but in Practical Project, the model of system and transport function are difficult to accurately obtain, and therefore the program is not suitable for practical engineering application; Scheme (2) buys expensive sweep generator equipment, and obtained the amplitude-versus-frequency curve of system by the mode of frequency sweep, adopt this scheme, the sweep generator on market is expensive, bulky, operation inconvenience; Scheme (3) is similar to the amplitude versus frequency characte of the system of recording by the mode of sinusoidal wave Frequency sweep experiments, this test needs interface support, and need frequency frequency ground to carry out inputting then recording output, waste time and energy, be difficult to promote in practical engineering application.

Summary of the invention

The technical problem to be solved in the present invention is, overcomes the defect of prior art, provide a kind of test duration greatly to shorten, and process is simple, realizes the method for drafting of lower-cost a kind of amplitude-versus-frequency curve.

For solving the problems of the technologies described above, the invention provides a kind of method for drafting of amplitude-versus-frequency curve, it is characterized in that: it comprises the following steps:

Step 1: choose the sinusoidal signal under k different frequency, namely i=1,2 ... k, wherein A _irepresent amplitude, represent phase place;

Step 2: utilize the different frequency signals component in step 1, synthesis excitation source signal x (t), namely

Step 3: by the input source of excitation source signal x (t) of synthesis as automatic control system H (s), and record and output signal y (t) accordingly, when surveying excitation source signal x (t) and output signal y (t), the sample frequency choosing signal is F _s, the data count of sampling is N;

Step 4: utilize discrete fourier formula to try to achieve excitation source signal x (t) and output signal y (t) at different frequency f _i, i=1,2 ... k, sinusoidal component amplitude, namely

$SinX\left(i\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}x\left(n\right)\sin \left(2{\mathrm{\πf}}_{i}n/N\right),CosX\left(i\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}x\left(n\right)\cos \left(2{\mathrm{\πf}}_{i}n/N\right),$

$SinY\left(i\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}y\left(n\right)\sin \left(2{\mathrm{\πf}}_{i}n/N\right),CosY\left(i\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}y\left(n\right)\cos \left(2{\mathrm{\πf}}_{i}n/N\right),$

$A_i=\sqrt{SinX{\left(i\right)}^2+CosX{\left(i\right)}^2},B_i=\sqrt{SinY{\left(i\right)}^2+CosY{\left(i\right)}^2}$

Wherein SinX (i), CosX (i), SinY (i), CosY (i) are the intermediate variable calculated, A _ifor frequency f _iunder the amplitude of driving source component, B _ifor frequency f _ithe amplitude of lower output signal component;

Step 5: with log ₁₀(2 π f _i) be horizontal ordinate, 20log ₁₀(B _i/ A _i) be ordinate, i=1,2 ..., k, the amplitude frequency curve figure of drawing system H (s).

After adopting said method, only need the excitation source signal once inputting synthesis, and the output signal recorded, just can by calculating amplitude-versus-frequency curve, amplitude frequency curve record the time equivalence time that minimum frequency sinusoidal signal (single) records in the test of traditional frequency sweeping method, in other words, the time of whole testing process will significantly shorten, and substantially increase testing efficiency.On the other hand, the method of testing that the present invention proposes can realize in all-digital signal, namely in engineer applied, can in the upper software program programming increasing part of original hardware platform (such as single-chip microcomputer or DSP process chip), the driving source synthesized by input and detection system export the amplitude-versus-frequency curve that just can be recorded system by software, do not need to increase extra hardware cost or equipment cost, in other words, script cost is high and the amplitude-versus-frequency curve of wasting time and energy estimation can realize digital robotization estimation by the inventive method, practical engineering application is worth very high.

Accompanying drawing explanation

The schematic diagram of Fig. 1 frequency spectrum estimation of the present invention principle;

Fig. 2 is the Simulink realistic model figure of the embodiment of the present invention;

Fig. 3 is by amplitude frequency curve figure that the inventive method obtains in embodiment;

Fig. 4 is by amplitude frequency curve figure that mathematical modeling obtains in embodiment.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention will be further described in detail:

As shown in the figure, Fig. 1 is the basic thought of the inventive method, and automatic control system is H (s), x (t) is given injected system H (s) driving source, it by i=1,2 ... k, the sinusoidal signal synthesis altogether under k different frequency, signal syntheses refers to these Signal averaging; The output signal that y (t) is system H (s), after Fourier transform, decomposable asymmetric choice net goes out the output component under a corresponding k different frequency, namely i=1,2 ... k; Therefore, at different frequency f _iunder, utilize driving source sinusoidal component amplitude A _iwith output signal sinusoidal component amplitude B _itry to achieve the amplitude-versus-frequency curve of system, namely with log ₁₀f _ifor horizontal ordinate, 20log ₁₀(B ₁/ A ₁) be ordinate drafting amplitude-versus-frequency curve.

In practical engineering application, such as, in the digital processing chip such as single-chip microcomputer or DSP, the Fourier transform in patent of the present invention needs the form adopting discretize, and concrete implementation step is as follows:

Step 1: choose the sinusoidal signal under k different frequency, namely i=1,2 ... k, wherein A _irepresent amplitude, ω _i=2 π f _irepresent in frequency f _icorresponding angular frequency, represent phase place, signal amplitude and phase place can be arranged arbitrarily, frequency selection purposes also can be chosen arbitrarily, if need you should pay special attention to the amplitude versus frequency characte (such as there is resonant frequency point etc.) in a certain region in real work, can choose multiple frequency signals in this region.

Step 2: utilize the different frequency signals component in step 1, synthesis excitation source signal x (t), namely

Step 3: by the input source of excitation source signal x (t) of synthesis as system H (s), and record and output signal y (t) accordingly, in Practical Project, the numerical value of excitation source signal x (t) and output signal y (t) is through sample frequency F _sunder preserve, i.e. x (n), y (n), n=1,2 ..., N, wherein x (n) and y (n) represents that excitation source signal x (t) and output signal y (t) are in sampling instant numerical value, F _srepresent the sample frequency of signal, N represents the data count of sampling, and in order to ensure estimation precision, the data count N of sampling will get greatly as far as possible, and ensures i=1,2 ... k is integer.

Step 4: utilize discrete fourier formula to try to achieve signal at different frequency f _i, i=1,2 ... k, sinusoidal component amplitude, namely

$SinX\left(i\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}x\left(n\right)\sin \left(2{\mathrm{\πf}}_{i}n/N\right),CosX\left(i\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}x\left(n\right)\cos \left(2{\mathrm{\πf}}_{i}n/N\right),$

$SinY\left(i\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}y\left(n\right)\sin \left(2{\mathrm{\πf}}_{i}n/N\right),CosY\left(i\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}y\left(n\right)\cos \left(2{\mathrm{\πf}}_{i}n/N\right),$

$A_i=\sqrt{SinX{\left(i\right)}^2+CosX{\left(i\right)}^2},B_i=\sqrt{SinY{\left(i\right)}^2+CosY{\left(i\right)}^2}$

Wherein SinX (i), CosX (i), SinY (i), CosY (i) are the intermediate variable calculated, A _ifor frequency f _iunder the amplitude of driving source component, B _ifor frequency f _ithe amplitude of lower output signal component.

Step 5: with log ₁₀(2 π f _i) be horizontal ordinate, 20log ₁₀(B _i/ A _i) be ordinate, i=1,2 ..., k, the amplitude frequency diagram of drawing system H (s).

Enumerate an embodiment below to verify the precision that this method amplitude-frequency is estimated:

Quote servo control system mathematical model $H\left(s\right)=\frac{\frac{1}{{110}^2}{s}^2+\frac{0.02}{110}s+1}{\frac{1}{{68}^2}{s}^2+\frac{0.07}{68}s+1}\×\frac{1}{\frac{1}{{130}^2}{s}^2+\frac{0.1}{130}s+1},$ For the amplitude-frequency evaluation method that checking the application proposes, we will utilize the Simulink emulation tool in Matlab, set up the realistic model of this embodiment as shown in Figure 2:

Step 1: the sinusoidal signal choosing k=24 different frequency, amplitude is 100, and phase place is by the random function stochastic generation in Matlab, routine $x_{f_1}\left(t\right)=100sin(1t+0.7669),...,x_{f_{24}}\left(t\right)=100sin(600t-1.623),$ Frequency selection purposes 2 π f _i∈ { 10,20,30,40,50,55,60,65,70,80,90,95,100,110,120,125,130,135,140,170,200,300,400,600}.

Step 2: synthesis excitation source signal $x\left(t\right)=x_{f_1}\left(t\right)+x_{f_2}\left(t\right)+...+x_{f_{24}}\left(t\right)=\underset{i=1}{\overset{24}{\Σ}}{x}_{f_i}\left(t\right).$

Step 3: composite signal x (t) is emulated as the signal source in Simulink Fig. 2, and record and output signal y (t) accordingly, wherein sample frequency F _s=4096Hz, data length chooses N=8192.

Step 4: utilize discrete fourier formula to ask signal at different frequency f _i, i=1,2 ... 24, sinusoidal component amplitude, namely

$SinX\left(i\right)=\underset{n=1}{\overset{8192}{\mathrm{\Σ}}}x\left(n\right)\sin \left(2{\mathrm{\πf}}_{i}n/8192\right),CosX\left(i\right)=\underset{n=1}{\overset{8192}{\mathrm{\Σ}}}x\left(n\right)\cos \left(2{\mathrm{\πf}}_{i}n/8192\right),$

$SinY\left(i\right)=\underset{n=1}{\overset{8192}{\mathrm{\Σ}}}y\left(n\right)\sin \left(2{\mathrm{\πf}}_{i}n/8192\right),CosY\left(i\right)=\underset{n=1}{\overset{8192}{\mathrm{\Σ}}}y\left(n\right)\cos \left(2{\mathrm{\πf}}_{i}n/8192\right),$

$A_i=\sqrt{SinX{\left(i\right)}^2+CosX{\left(i\right)}^2},B_i=\sqrt{SinY{\left(i\right)}^2+CosY{\left(i\right)}^2}$

Wherein SinX (i), CosX (i), SinY (i), CosY (i) are the intermediate variable calculated, A _ifor frequency f _iunder the amplitude of driving source component, B _ifor frequency f _ithe amplitude of lower output signal component.

Step 5: with log ₁₀(2 π f _i) be horizontal ordinate, 20log ₁₀(B _i/ A _i) be ordinate, i=1,2 ..., k, the amplitude-frequency of drawing system H (s), as shown in Figure 3.

For the accuracy of checking estimation amplitude-frequency, we draw Bode diagram by the Bode () in Matlab and Margin () function to the transport function of system H (s), as shown in Figure 4, can find out amplitude frequency curve in Fig. 4 and estimation result curve Fig. 3 of the present invention very close.

Claims (1)

1. a method for drafting for amplitude-versus-frequency curve, is characterized in that: it comprises the following steps:

Step 1: choose the sinusoidal signal under k different frequency, namely i=1,2 ... k, wherein A _irepresent amplitude, represent phase place;

Step 2: utilize the different frequency signals component in step 1, synthesis excitation source signal x (t), namely

Step 3: by the input source of excitation source signal x (t) of synthesis as automatic control system H (s), and record and output signal y (t) accordingly, when surveying excitation source signal x (t) and output signal y (t), the sample frequency choosing signal is F _s, the data count of sampling is N;

Step 4: utilize discrete fourier formula to try to achieve excitation source signal x (t) and output signal y (t) at different frequency f _i, i=1,2 ... k, sinusoidal component amplitude, namely

$SinX\left(i\right)=\underset{n=1}{\overset{N}{\Σ}}x\left(n\right)\sin (2{\mathrm{\πf}}_{i}n/N),CosX\left(i\right)=\underset{n=1}{\overset{N}{\Σ}}x\left(n\right)\cos (2{\mathrm{\πf}}_{i}n/N),$

$SinY\left(i\right)=\underset{n=1}{\overset{N}{\Σ}}y\left(n\right)sin(2{\mathrm{\πf}}_{i}n/N),CosY\left(i\right)=\underset{n=1}{\overset{N}{\Σ}}y\left(n\right)cos(2{\mathrm{\πf}}_{i}n/N),$

$A_i=\sqrt{SinX{\left(i\right)}^2+CosX{\left(i\right)}^2},B_i=\sqrt{SinY{\left(i\right)}^2+CosY{\left(i\right)}^2}$

Wherein SinX (i), CosX (i), SinY (i), CosY (i) are the intermediate variable calculated, A _ifor frequency f _iunder the amplitude of driving source component, B _ifor frequency f _ithe amplitude of lower output signal component;

Step 5: with log ₁₀(2 π f _i) be horizontal ordinate, 20log ₁₀(B _i/ A _i) be ordinate, i=1,2 ..., k, the amplitude frequency curve figure of drawing system H (s).