CN102999037A - Loop bandwidth virtual testing method - Google Patents

Abstract

The invention belongs to the technical field of photoelectric tracking, and relates to a loop bandwidth virtual testing method which includes steps of outputting sine command signals with specific frequency, sending the sine command signals to a control loop of a to-be-tested digital control system to generate loop response signals, performing correlation operation to the loop response signals and the sine command signals; determining the maximum correlation amplitude and corresponding time thereof in the frequency according to the maximum value obtained from the correlation operation, and determining the amplitude and phase of the loop control signals in the frequency; changing frequency of the sine command signals and repeating the above steps, recording and saving the amplitude and phase changes of the loop response signals, and accordingly, drawing curves of amplitude frequency and phase frequency so as to determine loop bandwidth. By the loop bandwidth virtual testing method, the technical problem that testing efficiency is reduced due to difficulty in matching between a physical instrument and the digital control system in the process of testing the loop bandwidth of the digital control system by the physical instrument is solved, energy is saved and efficiency is improved by means of virtual testing.

Description

A kind of loop bandwidth virtual measuring method

Technical field

The invention belongs to the photoelectric tracking technical field, be specifically related to a kind of loop bandwidth virtual measuring method.

Background technology

In the prior art, test control loop bandwidth method generally adopts dynamic signal analyzer, and most of dynamic signal analyzer is analog signal interface, when treating that tested system is digital control system, can't test.Even dynamic signal analyzer is provided with digital interface, also often can't mate with tested digital control system digital interface, need to carry out for particular system the conversion of interface, increased unnecessary testing procedure, reduced testing efficiency.

Summary of the invention

The technical problem to be solved in the present invention is: the digital control system loop bandwidth is carried out that physical apparatus and digital control system interface are difficult to coupling in the test process by physical apparatus, reduced testing efficiency.

Technical scheme of the present invention is as described below: this method may further comprise the steps:

The sinusoidal command signal of step (1) software sinusoidal signal generator output characteristic frequency, it sends to the control loop of digital control system to be measured as command signal, control loop produces the loop response signal, and this loop response signal and described sinusoidal command signal are carried out related operation;

Step (2) is determined maximal correlation amplitude and the corresponding moment of amplitude under this frequency by the related operation maximal value, thereby determines amplitude response and the phase response of loop control signal under this frequency;

Step (3) changes the frequency of sinusoidal command signal, repeat above-mentioned steps, determine amplitude response and the phase response of corresponding loop response signal under the different frequency, record and amplitude response and the phase response variation of preserving the loop response signal, thereby draw out amplitude-frequency, phase frequency curve, determine loop bandwidth.

In the step (1), loop response signal and sinusoidal command signal are carried out related operation according to formula (1):

$R\left(\mathrm{\τ}\right)={\∫}_0^{T}X(t-\mathrm{\τ})Y\left(t\right)\mathrm{dt}---\left(1\right),$

In the formula (1), X (t) is sinusoidal command signal, and Y (t) is the loop response signal, and T is sine wave period, and R (τ) is related function;

Formula (1) is carried out discretize obtains formula (2):

$R\left(\mathrm{\τ}\right)=\underset{n=1}{\overset{1/f{T}_s}{\mathrm{\Σ}}}X(n-\mathrm{\τ})Y\left(n\right)---\left(2\right),$

In the formula (2), X (n) is the sinusoidal command signal of discrete form, and Y (n) is the loop response signal of discrete form, and f is sine wave freuqency, T _sBe signal sampling period, R (τ) is related function.

In the step (1), loop response signal Y (t) is expressed as Ae ^{J θ}, A is loop gain, and θ is loop phase, and namely loop response signal Y (t) is than sinusoidal command signal X (t) phase place hysteresis θ;

Formula (1) can be expressed as:

$R\left(\mathrm{\τ}\right)={\∫}_0^T\cos (\mathrm{m\ωt}-\mathrm{m\ω\τ})A\cos (\mathrm{n\ωt}-\mathrm{\θ})\mathrm{dt},m\≥1,n\≥1---\left(3\right)$

In the formula (3), ω=2 π f;

Wherein, the two is uncorrelated in sinusoidal command signal X (t) situation different from loop response signal Y (t) frequency, shown in (4):

$R\left(\mathrm{\τ}\right)=\left\{\begin{array}{cc}\mathrm{A\π}\cos (\mathrm{m\ω\τ}-\mathrm{\θ})& m=n\\ 0& m\≠n\end{array}\right.---\left(4\right).$

In the step (2), according to the amplitude maximal value of related function R (τ), determine maximal correlation amplitude A π and corresponding constantly τ, thereby determine amplitude A and the phase theta of loop control signal under this frequency f, θ=ω τ.

Beneficial effect of the present invention is: the present invention is directed to digital control system, utilize the internal system resource, adopt the related algorithm computing, processing obtains the various achievement datas of loop characteristic, thereby replace the actual physics instrument, do not exist interface problem can finish virtual test during to difference system testing to be measured, saved the energy, improved efficient.

Description of drawings

Fig. 1 is a kind of loop bandwidth virtual measuring method process flow diagram of the present invention;

Fig. 2 is amplitude frequency curve;

Fig. 3 is phase frequency curve.

Embodiment

Below in conjunction with drawings and Examples a kind of loop bandwidth virtual measuring method of the present invention is described in detail.

As shown in Figure 1, loop bandwidth virtual measuring method of the present invention mainly may further comprise the steps:

The sinusoidal command signal of step (1) software sinusoidal signal generator output characteristic frequency, it sends to the control loop of digital control system to be measured as command signal, control loop produces the loop response signal, and this loop response signal and described sinusoidal command signal are carried out related operation;

Step (2) is determined maximal correlation amplitude and the corresponding moment of amplitude under this frequency by the related operation maximal value, thereby determines amplitude response and the phase response of loop control signal under this frequency;

Step (3) changes the frequency of sinusoidal command signal, repeat above-mentioned steps, determine amplitude response and the phase response of corresponding loop response signal under the different frequency, record and amplitude response and the phase response variation of preserving the loop response signal, thereby draw out amplitude-frequency, phase frequency curve, determine loop bandwidth.

In the step (1), loop response signal and sinusoidal command signal are carried out related operation according to formula (1):

$R\left(\mathrm{\τ}\right)={\∫}_0^{T}X(t-\mathrm{\τ})Y\left(t\right)\mathrm{dt}---\left(1\right),$

In the formula (1), X (t) is sinusoidal command signal, and Y (t) is the loop response signal, and T is sine wave period, and R (τ) is related function.

Formula (1) is carried out discretize obtains formula (2):

$R\left(\mathrm{\τ}\right)=\underset{n=1}{\overset{1/f{T}_s}{\mathrm{\Σ}}}X(n-\mathrm{\τ})Y\left(n\right)---\left(2\right),$

In the formula (2), X (n) is the sinusoidal command signal of discrete form, and Y (n) is the loop response signal of discrete form, and f is sine wave freuqency, T _sBe signal sampling period, R (τ) is related function.

According to the control loop characteristic of digital control system to be measured, loop response signal Y (t) is identical with sinusoidal command signal X (t) cycle.By fourier series knowledge as can be known, periodic signal can be decomposed into DC component, fundamental frequency signal and frequency-doubled signal thereof.And amplitude-frequency and phase-frequency characteristic curve are only paid close attention to the variation of fundamental frequency signal for linear system, and ignore other frequencies, therefore loop response signal Y (t) can be reduced to Ae ^{J θ}, A is loop gain, and θ is loop phase, and namely loop response signal Y (t) is than sinusoidal command signal X (t) phase place hysteresis θ.

Since sinusoidal signal complete cycle signal related operation, formula (1) can be expressed as:

$R\left(\mathrm{\τ}\right)={\∫}_0^T\cos (\mathrm{m\ωt}-\mathrm{m\ω\τ})A\cos (\mathrm{n\ωt}-\mathrm{\θ})\mathrm{dt},m\≥1,n\≥1---\left(3\right)$

In the formula (3), ω=2 π f.

Wherein, the two is uncorrelated in sinusoidal command signal X (t) situation different from loop response signal Y (t) frequency, shown in (4):

$R\left(\mathrm{\τ}\right)=\left\{\begin{array}{cc}\mathrm{A\π}\cos (\mathrm{m\ω\τ}-\mathrm{\θ})& m=n\\ 0& m\≠n\end{array}\right.---\left(4\right).$

By formula (4) as can be known, except fundamental frequency signal, frequency-doubled signal is inoperative in the related operation, so related operation can be determined amplitude and the phase propetry of fundamental frequency signal.

In the step (2), by seeking the amplitude maximal value of related function R (τ), record maximal correlation amplitude A π and corresponding constantly τ, thereby determine amplitude A and phase theta under this frequency f, θ=ω τ.

In the step (3), change the frequency of sinusoidal command signal, repeat above-mentioned steps, determine amplitude response and the phase response of corresponding loop response signal under the different frequency, record and amplitude response and the phase response variation of preserving the loop response signal, thereby draw out amplitude-frequency, phase frequency curve, determine loop bandwidth.

For instance, if the transport function of the control loop of digital control system to be measured suc as formula shown in (5):

$H=\frac{24s^2+960s+9600}{0.1s^3+24.65s^2+961.4s+9601}---\left(5\right),$

Then change the frequency of sinusoidal command signal, can access data shown in the following table:

According to data shown in the upper table, can draw out amplitude frequency curve shown in Figure 2 and phase frequency curve shown in Figure 3.By Fig. 2 amplitude frequency curve as can be known, control loop-three dB bandwidth is 42Hz, and is very approaching with theoretical value 43Hz, verified the validity of virtual measuring method of the present invention.

Claims (4)

1. loop bandwidth virtual measuring method, it is characterized in that: this method may further comprise the steps:

The sinusoidal command signal of step (1) software sinusoidal signal generator output characteristic frequency, it sends to the control loop of digital control system to be measured as command signal, control loop produces the loop response signal, and this loop response signal and described sinusoidal command signal are carried out related operation;

Step (2) is determined maximal correlation amplitude and the corresponding moment of amplitude under this frequency by the related operation maximal value, thereby determines amplitude response and the phase response of loop control signal under this frequency;

Step (3) changes the frequency of sinusoidal command signal, repeat above-mentioned steps, determine amplitude response and the phase response of corresponding loop response signal under the different frequency, record and amplitude response and the phase response variation of preserving the loop response signal, thereby draw out amplitude-frequency, phase frequency curve, determine loop bandwidth.

2. a kind of loop bandwidth virtual measuring method according to claim 1 is characterized in that:

In the step (1), loop response signal and sinusoidal command signal are carried out related operation according to formula (1):

$R\left(\mathrm{\τ}\right)={\∫}_0^{T}X(t-\mathrm{\τ})Y\left(t\right)\mathrm{dt}---\left(1\right),$

In the formula (1), X (t) is sinusoidal command signal, and Y (t) is the loop response signal, and T is sine wave period, and R (τ) is related function;

Formula (1) is carried out discretize obtains formula (2):

$R\left(\mathrm{\τ}\right)=\underset{n=1}{\overset{1/f{T}_s}{\mathrm{\Σ}}}X(n-\mathrm{\τ})Y\left(n\right)---\left(2\right),$

In the formula (2), X (n) is the sinusoidal command signal of discrete form, and Y (n) is the loop response signal of discrete form, and f is sine wave freuqency, T _sBe signal sampling period, R (τ) is related function.

3. a kind of loop bandwidth virtual measuring method according to claim 2 is characterized in that:

In the step (1), loop response signal Y (t) is expressed as Ae ^{J θ}, A is loop gain, and θ is loop phase, and namely loop response signal Y (t) is than sinusoidal command signal X (t) phase place hysteresis θ;

Formula (1) can be expressed as:

$R\left(\mathrm{\τ}\right)={\∫}_0^T\cos (\mathrm{m\ωt}-\mathrm{m\ω\τ})A\cos (\mathrm{n\ωt}-\mathrm{\θ})\mathrm{dt},m\≥1,n\≥1---\left(3\right)$

In the formula (3), ω=2 π f;

Wherein, the two is uncorrelated in sinusoidal command signal X (t) situation different from loop response signal Y (t) frequency, shown in (4):

$R\left(\mathrm{\τ}\right)=\left\{\begin{array}{cc}\mathrm{A\π}\cos (\mathrm{m\ω\τ}-\mathrm{\θ})& m=n\\ 0& m\≠n\end{array}\right.---\left(4\right).$

4. a kind of loop bandwidth virtual measuring method according to claim 3 is characterized in that:

In the step (2), according to the amplitude maximal value of related function R (τ), determine maximal correlation amplitude A π and corresponding constantly τ, thereby determine amplitude A and the phase theta of loop control signal under this frequency f, θ=ω τ.

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