A control loop performance index measurement method based on second-order filter

Abstract

The present invention discloses a control loop performance index measurement method based on a second-order filter. The method adopts the idea of ​​dynamic frequency search, combines a second-order bandpass filter B(s) with a second-order high-pass filter H(s) and a PI regulator, and the measurement time is much shorter than the traditional sine frequency sweep method. The detection speed is fast, the accuracy is high, and the method can be applied to AC power grids with rich background harmonics. The performance index measurement method can measure the cutoff frequency and phase margin of the control loop, and provides valuable reference information for stability analysis, closed-loop parameter design, and online adaptive adjustment of the control system.

Description

Technical Field

[0001] The invention belongs to the technical field of automatic control systems, and mainly realizes continuous and rapid measurement of a control loop cutoff frequency and a phase margin, and is specifically a control loop performance index measurement method based on a second-order filter. Background Art

[0002] In automatic control theory, control loop performance indicators (including cutoff frequency and phase margin) can characterize the dynamic performance and steady-state performance of the control system. In the design stage of the control system, the designer needs to adjust it by scientifically and rationally designing the parameters of the controller so that the control system can obtain satisfactory static and dynamic performance. Therefore, control loop performance indicators have very wide applications, such as online dynamic performance monitoring of server / spacecraft power supplies, stability analysis of cascade power converters, stability analysis of new energy grid-connected power supplies, and adaptive online adjustment of controller parameters.

[0003] Usually, the acquisition of control loop performance indicators is based on the small signal linearization model of the control system, and is obtained by theoretically deriving the transfer function between the controlled variable and the control quantity. However, there are errors between the theoretically derived results and the actual values ​​due to the following two reasons: 1) There are a large number of nonlinear devices (such as arc welding machines, saturated transformers, motors, etc.) and switching devices (such as op amps, switch tubes, etc.) in the electrical system. The linearization models of these strongly nonlinear and strongly coupled systems cannot completely represent the actual system equivalently; 2) Due to the combined influence of multiple factors such as load changes, state changes, temperature drift, and aging, the system parameters will change on short time scales / long time scales. Therefore, quickly and accurately measuring the actual performance indicator information of the control loop is extremely important for the closed-loop optimization design of the regulator, the dynamic and static performance guarantee of the control system, and the adaptive control of the strongly time-varying system.

[0004] Existing measurement methods are generally based on small signal injection methods, and there are two main types of methods that are widely used: 1) Sine frequency sweep method; 2) Wideband measurement method. Among them, the sine frequency sweep method not only requires the injection of signals of different frequencies one by one, but also often requires Fourier decomposition processing to obtain accurate results, so the measurement time is as long as several seconds. In order to shorten the measurement time, the wideband measurement method uses different broadband small signals (such as pseudo-random binary sequence, PRBS) as disturbance signals, and only uses one injection for loop gain measurement, and the measurement time is successfully shortened to 100 milliseconds (measurement spectrum: 10Hz-100kHz). However, in weak power grids, the loop gain should be measured as soon as possible, and the existing methods still cannot meet the needs of adaptive control of power converters in weak power grids. Summary of the invention

[0005] In view of the shortcomings of the existing technology, in order to further shorten the measurement time and better meet the scenario of microgrids where the loop gain changes rapidly due to impedance, the present invention aims to propose a control loop performance index measurement method based on a second-order filter, so as to achieve the measurement of the control loop cutoff frequency and phase margin within a few milliseconds, and provide important information support for the closed-loop optimization design of the control system regulator, thereby ensuring the dynamic and static performance of the control system under parameter disturbance. At the same time, it also provides the additional advantage of meeting the harmonic attenuation, which is very valuable in AC microgrid applications with rich background harmonics.

[0006] The technical solution of the present invention to solve the technical problem is: designing a control loop performance index measurement method based on a second-order filter, the method comprising the following steps:

[0007] (1) Injecting a small signal

[0008] Inject a small sinusoidal signal (x) with a variable angular frequency into the control loop under test. p ), whose expression is Where A is a small sine wave signal (x p ), is a small sine wave signal (x p )’s angular frequency;

[0009] (2) Extracting detection signals

[0010] There are detection signal interfaces on the left and right sides of the signal injection point of the control loop, which are used to detect the detection signal on the left side of the signal injection point in real time. With the right detection signal Left detection signal With the right detection signal They are processed by a second-order band-pass filter B(s) and a second-order high-pass filter H(s) respectively, and the detection signal at the current angular frequency is obtained. The left sine signal (x in ) and the right side sinusoidal signal (x out ), Represents the left sine signal (x in ), Represents the right side sinusoidal signal (x out )'s real and imaginary parts; using Get the left side signal to be tested (x in ) and the signal to be measured on the right (x out )’s amplitude and phase angle;

[0011] (3) Dynamic frequency search

[0012] The open-loop transfer function of the control loop to be tested (T m ) and the abscissa (ω c ) is the desired cutoff frequency; since That is, at the angular frequency Under, satisfy |T m |=|x out | / |x in |; Let e |x| =|x out |-|x in |, the left test signal (x in ) and the signal to be measured on the right (x out ) is substituted into the formula, and the value of e |x| The relationship between the size of 0 and the injection frequency at this time is determined Relationship with cutoff frequency;

[0013] When e |x| = 0, that is When the current angular frequency This is the cutoff frequency of the control loop (ω c ); cut-off frequency (ω c ) is the bandwidth of the control loop;

[0014] When e |x| ≠1, then at the current angular frequency Next, minus The obtained value is input into a PI regulator, and the output of the PI regulator is added to the current angular frequency The injected signal (x p )'s new angular frequency Then the injected signal (x p ) Adjust to Continue to perform the process of extracting the detection signal in step (2) and set the new angular frequency The left sine signal (x in ) and the right side sinusoidal signal (x out ) into e |x| =|x out |-|x in |, if it is still e |x| ≠1, repeat the above process and adjust the angular frequency continuously until e |x| =0, to achieve dynamic frequency search;

[0015] (4) Phase margin calculation

[0016] According to the cutoff frequency (ω) obtained in step (3) c), the left sine signal (x in ) and the right side sinusoidal signal (x out ) is substituted into the formula PM = ∠x out -∠x in , and obtain the phase margin of the control loop under test.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: the control loop performance index measurement method proposed by the present invention adopts the idea of ​​dynamic frequency search, combines the second-order high-pass filter H(s) and the second-order band-pass filter B(s) and the PI regulator, and the measurement time (within 10ms) is much shorter than the traditional sine frequency sweep method, with fast detection speed and high accuracy, and can be applied to AC power grids with rich background harmonics. The performance index measurement method can measure the cutoff frequency and phase margin of the control loop, and provides valuable reference information for stability analysis, closed-loop parameter design, and online adaptive adjustment of the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The control loop structure diagram is a control loop performance indicator measurement method based on a second-order filter according to an embodiment of the present invention.

[0019] Figure 2 The present invention is a schematic diagram of the bandwidth measurement principle of a control loop performance indicator measurement method based on a second-order filter.

[0020] Figure 3 The present invention is a measurement principle block diagram of an embodiment of a control loop performance indicator measurement method based on a second-order filter.

[0021] Figure 4 In order to use the control loop performance index measurement method based on the second-order filter of the present invention to Figure 1 The control loop in G The loop changes the grid impedance Z of the single-phase grid-connected inverter (containing 5% background harmonics) multiple times G The measurement result diagram when .

[0022] Figure 5 for Figure 4 A partial enlarged view of . Specific embodiments

[0023] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0024] In this embodiment, the control loop under test adopts a relatively common single-phase full-bridge inverter circuit, and the filter is an LCL filter. Figure 1 As shown, the control loop performance index measurement method provided by the present invention (ie Figure 1In order to demonstrate its anti-noise and dynamic performance, a 5% background harmonic is introduced into the power grid, and the grid impedance Z is changed several times. G Change the performance indicators of the system. Now in this scenario, the outermost loop, i G The cutoff frequency and phase margin of the loop (which can be regarded as a current closed loop system).

[0025] The present invention provides a control loop performance index measurement method based on a second-order filter, the method comprising the following steps:

[0026] (1) Injecting a small signal

[0027] Inject a small sinusoidal signal x with variable angular frequency into the control loop under test p , whose expression is Where A is a small sinusoidal signal x p The amplitude of is a small sine wave signal x p t is time, the same below; in this embodiment, an amplitude A of 0.5 and an initial angular frequency value are injected into the control loop. It is a small sine wave signal of 1000Hz.

[0028] (2) Extracting detection signals

[0029] There are detection signal interfaces on the left and right sides of the signal injection point of the control loop, which are used to detect the detection signal on the left side of the signal injection point in real time. (j is an imaginary unit, the same below) and the detection signal on the right Left detection signal With the right detection signal They are processed by a second-order band-pass filter B(s) and a second-order high-pass filter H(s) respectively, and the detection signal at the current angular frequency is obtained. The left side sinusoidal signal x in With the right side sinusoidal signal x out The real and imaginary parts of Represents the left side sinusoidal signal x in The real and imaginary parts of Represents the right side sinusoidal signal x out The real and imaginary parts of . k pB and k pH are the constant parameters of the two filters respectively, and the constant parameters in the two filters may be the same or different; s represents the complex frequency in the S domain (complex frequency domain), which is obtained by Laplace transform.

[0030] use Get the left side signal xin and the signal x to be measured on the right out Amplitude and phase angle.

[0031] In this example, the constant parameter k in the second-order bandpass filter B(s) and the second-order high-pass filter H(s) is pB and k pH The value of is 0.2.

[0032] (3) Dynamic frequency search

[0033] The open-loop transfer function of the control loop to be tested is T m The intersection point with the horizontal axis ω c is the desired cutoff frequency; since That is, at the angular frequency Under, satisfy |T m |=|x out | / |x in |. Let e |x| =|x out |-|x in |, the left side signal x obtained in step (2) in and the signal x to be measured on the right out Substituting the amplitude of into the formula, we can get |x| The relationship between the size of 0 and the injection frequency at this time is determined Relationship with cutoff frequency;

[0034] When e |x| = 0, that is When the current angular frequency This is the cutoff frequency of the control loop. c ; Cut-off frequency ω c This is the bandwidth of the control loop.

[0035] When e |x| ≠1, then at the current angular frequency Next, minus The obtained value is input into a PI regulator (i.e. proportional integral regulator, symbol G in the figure) PI (s), this embodiment uses G PI (s) = 11660 + 2668000 / s, s represents the complex frequency in the S domain), add the output of the PI regulator to the current angular frequency The injected signal x can be obtained p The new angular frequency Then the injected signal x p In Adjust to Continue to perform the process of extracting the detection signal in step (2) and set the new angular frequency The left side sinusoidal signal x in With the right side sinusoidal signal x out Substitute the amplitude of e into |x| =|x out |-|x in |, if it is still e |x| ≠1, repeat the above process and adjust the angular frequency continuously until e |x| =0, to achieve dynamic frequency search;

[0036] (4) Phase margin calculation

[0037] According to the cutoff frequency ω obtained in step (3) c , the left sine signal x at this angular frequency in With the right side sinusoidal signal x out Substitute the phase angle into the formula PM = ∠x out -∠x in , and obtain the phase margin of the control loop under test.

[0038] In this example, the grid impedance Z of the single-phase grid-connected inverter (containing 5% background harmonics) is changed multiple times. G To change the control bandwidth and phase margin of the control system, where the grid impedance Z G The change is: 0.5Ω+0.5mH(Case1)→0.5Ω+1mH(Case2)→0.5Ω+1.5mH(Case3)→0.5Ω+1mH(Case2)→0.5Ω+0.5mH(Case1, i G * Set to 10A).

[0039] From the attached Figure 4 It can be seen that the phase margin (PM) can be measured in about 0.2s to be 60°→52°→47°, and the control bandwidth (BW, i.e., the cutoff frequency) is 1kHz→813Hz→692Hz. In the process of multiple changes, the measurement results are stable. G =10A. And, from the enlarged view Figure 5 As can be seen in Figure 1, the measurement results for one scenario can be obtained within 10ms.

[0040] The control loop in this embodiment is theoretically calculated to have a grid impedance Z G is 0.5Ω+0.5mH, its cut-off frequency is 1kHz, and the phase margin is 60°; the grid impedance Z G is 0.5Ω+1mH, its cut-off frequency is 813Hz, the phase margin is 53°, and the grid impedance is Z GIt is 0.5Ω+1.5mH, its cut-off frequency is 692Hz, and the phase margin is 47°. From the measurement results, the theoretical value of the control loop performance index is consistent with the result obtained by the control loop performance index measurement method of the present invention, so the measurement result is accurate within the allowable error range.

[0041] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A control loop performance index measurement method based on a second-order filter, characterized in that: The method comprises the following steps: (1) Injecting a small signal Inject a small sinusoidal signal (x) with a variable angular frequency into the control loop under test. p ), whose expression is Where A is a small sine wave signal (x p ), is a small sine wave signal (x p )’s angular frequency; (2) Extracting detection signals There are detection signal interfaces on the left and right sides of the signal injection point of the control loop, which are used to detect the detection signal on the left side of the signal injection point in real time. With the right detection signal Left detection signal With the right detection signal They are processed by a second-order band-pass filter B(s) and a second-order high-pass filter H(s) respectively, and the detection signal at the current angular frequency is obtained. The left sine signal (x in ) and the right side sinusoidal signal (x out ), Represents the left sine signal (x in ), Represents the right side sinusoidal signal (x out )'s real and imaginary parts; using Get the left side sinusoidal signal (x in ) and the right side sinusoidal signal (x out )’s amplitude and phase angle; (3) Dynamic frequency search The open-loop transfer function of the control loop to be tested (T m ) and the abscissa (ω c ) is the desired cutoff frequency; since That is, at the angular frequency Under, satisfy |T m |=|x out | / |x in |; Let e |x| =|x out |-|x in |, the left test signal (x in ) and the signal to be measured on the right (x out ) is substituted into the formula, and the value of e |x| The relationship between the size of 0 and the injection frequency at this time is determined Relationship with cutoff frequency; When e |x| = 0, that is When the current angular frequency This is the cutoff frequency of the control loop (ω c ); cut-off frequency (ω c ) is the bandwidth of the control loop; When e |x| ≠1, then at the current angular frequency Next, minus The obtained value is input into a PI regulator, and the output of the PI regulator is added to the current angular frequency The injected signal (x p )'s new angular frequency Then the injected signal (x p ) Adjust to Continue to perform the process of extracting the detection signal in step (2) and set the new angular frequency The left sine signal (x in ) and the right side sinusoidal signal (x out ) into e |x| =|x out |-|x in |, if it is still e |x| ≠1, repeat the above process and adjust the angular frequency continuously until e |x| =0, to achieve dynamic frequency search; (4) Phase margin calculation According to the cutoff frequency (ω) obtained in step (3) c ), the left sine signal (x in ) and the right side sinusoidal signal (x out ) into the formula PM = ∠x out -∠x in , and obtain the phase margin of the control loop under test.

Images