CN114740827A - Second-order filter-based control loop performance index measurement method - Google Patents

Abstract

The invention discloses a method for measuring performance indexes of a control loop based on a second-order filter, which adopts the idea of dynamic frequency searching, combines a second-order band-pass filter B(s), a second-order high-pass filter H(s) and a PI regulator, has the measuring time far shorter than that of the traditional sine frequency scanning method, has high detection speed and high accuracy, and can be suitable for an alternating current power grid with rich background harmonics. The performance index measuring method can measure the cut-off frequency and the phase angle margin of the control loop, and provides valuable reference information for stability analysis, closed-loop parameter design and online self-adaptive adjustment of the control system.

Description

A Measurement Method of Control Loop Performance Index Based on Second-Order Filter

technical field

The invention belongs to the technical field of automatic control systems, and mainly realizes continuous and rapid measurement of the cut-off frequency and phase angle margin of a control loop, in particular to a method for measuring the performance index of a control loop based on a second-order filter.

Background technique

In automatic control theory, control loop performance indicators (including cutoff frequency and phase margin) can characterize the dynamic 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, the control loop performance index has a very wide range of applications, such as online dynamic performance monitoring of server/spacecraft power supplies, stability analysis of cascaded power converters, new energy grid-connected stability analysis, and adaptive online controller parameters. adjustment etc.

Usually, the acquisition of control loop performance indicators is mostly based on the small-signal linearization model of the control system, which is obtained by theoretically deriving the transfer function between the controlled variable and the controlled variable. 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 welders, saturated transformers, motors, etc.) and switching devices (such as op amps) in the electrical system , switch tubes, etc.), the linearized models of these strongly nonlinear and strongly coupled systems cannot fully and equivalently represent the actual system; 2) Affected by the compound effects of load changes, state changes, temperature drift, aging and other factors, the system Parameter changes on short time scale/long time scale. Therefore, fast and accurate measurement of the actual performance index information of the control loop is of great significance for the closed-loop optimization design of the regulator, the guarantee of the dynamic and static performance of the control system, and the adaptive control of the strongly time-varying system.

The existing measurement methods are generally implemented based on the small signal injection method, and there are mainly two types of widely used methods: 1) a sine frequency sweep method; 2) a broadband measurement method. Among them, the sine frequency sweep method not only needs to inject signals of different frequencies successively, but also often requires Fourier decomposition processing to obtain accurate results, so the measurement time is as long as several seconds. In the broadband measurement method, in order to shorten the measurement time, different broadband small signals (such as pseudo-random binary sequences, PRBS) are used as disturbance signals, and only one injection is used to measure the loop gain, and the measurement time is successfully shortened to 100 milliseconds (measurement spectrum: 10Hz-100kHz). However, in weak 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 grids.

SUMMARY OF THE INVENTION

In view of the deficiencies of the prior art, in order to further shorten the measurement time and better meet the situation of the microgrid, where the loop gain changes rapidly due to the influence of impedance, the present invention aims to propose a control loop performance based on a second-order filter. The index measurement method is used to realize the measurement of the cut-off frequency and phase angle margin of the control loop within a few milliseconds, and to provide important information support for the closed-loop optimization design of the control system regulator, so as to ensure the dynamic and static performance. At the same time, it provides the additional advantage of satisfying harmonic attenuation, which is valuable in AC microgrid applications with rich background harmonics.

The technical solution of the present invention to solve the technical problem is: designing a method for measuring the performance index of a control loop based on a second-order filter, and the method includes the following steps:

(1) inject small signal

其中，A为正弦波小信号(x_p)的幅值，

为正弦波小信号(x_p)的角频率；A small sine wave signal (x _p ) with variable angular frequency is injected into the control loop under test, and its expression is

where A is the amplitude of the sine wave small signal (x _p ),

is the angular frequency of the sine wave small signal (x _p );

(2) Extract the detection signal

与右侧检测信号

左侧检测信号

与右侧检测信号

均分别通过二阶带通滤波器B(s)和二阶高通滤波器H(s)进行处理，分别得到此时检测信号在当前角频率

下的左侧正弦信号(x_in)与右侧正弦信号(x_out)的实部和虚部，

表示左侧正弦信号(x_in)的实部与虚部，

表示右侧正弦信号(x_out)的实部与虚部；利用

得到左侧待测信号(x_in)与右侧待测信号(x_out)的幅值与相角；There are detection signal interfaces on the left and right sides of the signal injection point of the control loop, which are respectively used for real-time detection of the detection signal on the left side of the signal injection point.

with right side heartbeat

Left detection signal

with right side heartbeat

Both are processed by the second-order band-pass filter B(s) and the second-order high-pass filter H(s), respectively, to obtain the detection signal at the current corner frequency.

The real and imaginary parts of the left sinusoidal signal (x _in ) and the right sinusoidal signal (x _out ) below,

represents the real and imaginary parts of the left sinusoidal signal (x _in ),

represents the real and imaginary parts of the right-hand sinusoidal signal (x _out ); using

Obtain the amplitude and phase angle of the signal to be measured on the left (x _in ) and the signal to be measured on the right (x _out );

(3) Dynamic frequency seeking

即在角频率

下，满足|T_m|＝|x_out|/|x_in|；令e_|x|＝|x_out|-|x_in|，将步骤(2)中得到左侧待测信号(x_in)与右侧待测信号(x_out)的幅值代入到该公式中，即可依据e_|x|与0的大小关系来判断此时注入频率

与截止频率的大小关系；The intersection (ω _c ) of the open-loop transfer function (T _m ) of the control loop under test and the abscissa is the desired cut-off frequency; since

i.e. at angular frequency

, satisfy |T _m |=|x _out |/|x _in |; let e _|x| =|x _out |-|x _{in |} Substitute the amplitude of the signal to be measured (x _out ) on the right side into the formula, and then the injection frequency can be judged according to the relationship between e _|x| and 0

The magnitude of the relationship with the cutoff frequency;

时，当前角频率

即为控制环路的截止频率(ω_c)；截止频率(ω_c)即为控制环路的带宽；When e _|x| = 0, that is

, the current corner frequency

is the cut-off frequency (ω _{c ) of the control loop; the cut-off frequency (ω c )} is the bandwidth of the control loop;

下，将

减去

得到的值输入到一个PI调节器，将PI调节器的输出加上当前角频率

即可得到注入信号(x_p)的新的角频率

然后将注入信号(x_p)中的

调整为

继续执行步骤(2)的提取检测信号过程，并将在新的角频率

下的左侧正弦信号(x_in)与右侧正弦信号(x_out)的幅值代入e_|x|＝|x_out|-|x_in|，若此时仍然e_|x|≠1，不断重复上述过程，不断调整角频率，直至e_|x|＝0，实现动态寻频；When e _|x| ≠ 1, then at the current angular frequency

down, will

minus

The obtained value is input to a PI regulator, and the output of the PI regulator is added to the current corner frequency

The new angular frequency of the injected signal (x _p ) can be obtained

Then inject the signal into the signal (x _p )

tweak to

Continue to perform the extraction detection signal process of step (2), and

The amplitudes of the left sinusoidal signal (x _in ) and the right sinusoidal signal (x _out ) below are substituted into e _|x| = |x _out |-|x _in |, if e _|x| Repeat the above process, continuously adjust the angular frequency, until e _|x| =0, to achieve dynamic frequency search;

(4) Calculation of phase angle margin

According to the cut-off frequency (ω _c ) obtained in step (3), substitute the phase angle between the left sinusoidal signal (x _in ) and the right sinusoidal signal (x _out ) at the angular frequency into the formula PM=∠x _out − ∠x _in , the phase angle margin of the control loop under test is obtained.

Compared with the prior art, the beneficial effects of the present invention are as follows: the method for measuring the performance index of the control loop proposed by the present invention adopts the idea of dynamic frequency seeking, and combines the second-order high-pass filter H(s) and the second-order band-pass filter. The combination of B(s) and PI regulator, the measurement time (within 10ms) is much shorter than the traditional sine frequency sweep method, the detection speed is fast, the accuracy is high, and it can be applied to the AC power grid with rich background harmonics. This performance index measurement method can measure the cut-off frequency and phase angle margin of the control loop, which provides valuable reference information for the stability analysis, closed-loop parameter design, and online adaptive adjustment of the control system.

Description of drawings

FIG. 1 is a control loop structure diagram of an embodiment of a method for measuring a control loop performance index based on a second-order filter of the present invention.

FIG. 2 is a schematic diagram of a bandwidth measurement principle of a method for measuring a performance index of a control loop based on a second-order filter of the present invention.

FIG. 3 is a measurement principle block diagram of an embodiment of a method for measuring a performance index of a control loop based on a second-order filter according to the present invention.

Fig. 4 is a method for measuring the performance index of the control loop based on a second-order filter of the present invention to change the single-phase grid-connected inverter (containing 5% background harmonics) for the control loop i _G loop in Fig. 1 multiple times. ) of the grid-connected impedance Z _G when the measurement results.

FIG. 5 is a partial enlarged view of FIG. 4 .

specific embodiment

The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings.

In this embodiment, the control loop under test adopts a relatively common single-phase full-bridge inverter circuit, and the filter is an LCL type filter. As shown in Figure 1, the method for measuring the performance index of the control loop provided by the present invention (ie, the stability margin monitor in Figure 1), in order to reflect its anti-noise performance and dynamic performance, a 5% background harmonic is introduced into the power grid. In this scenario, the cutoff frequency and phase margin of the outermost loop, i.e., the _{iG loop} (which can be regarded as a current closed-loop system), are tested.

The present invention provides a method for measuring a control loop performance index based on a second-order filter, the method comprising the following steps:

(1) inject small signal

其中，A为正弦波小信号x_p的幅值，

为正弦波小信号x_p的角频率；t为时间，下同；本实施例中，往控制环路中注入一个幅值A为0.5、角频率初始值

为1000Hz的正弦波小信号。A small sine wave signal x _p with variable angular frequency is injected into the control loop under test, and its expression is

Among them, A is the amplitude of the sine wave small signal x _p ,

is the angular frequency of the sine wave small signal x _p ; t is the time, the same below; in this embodiment, an amplitude A is 0.5 and the initial value of the angular frequency is injected into the control loop

It is a 1000Hz sine wave small signal.

(2) Extract the detection signal

(j为虚数单位，下同)与右侧检测信号

左侧检测信号

与右侧检测信号

均分别通过二阶带通滤波器B(s)和二阶高通滤波器H(s)进行处理，分别得到此时检测信号在当前角频率

下的左侧正弦信号x_in与右侧正弦信号x_out的实部和虚部，

表示左侧正弦信号x_in的实部与虚部，

表示右侧正弦信号x_out的实部和虚部。其中，

k_pB和k_pH分别为两个滤波器的常数参数，两个滤波器中的常数参数取值相同或不同；s代表S域(复频域)中的复频率，通过拉普拉斯变换得到。There are detection signal interfaces on the left and right sides of the signal injection point of the control loop, which are respectively used for real-time detection of the detection signal on the left side of the signal injection point.

(j is an imaginary unit, the same below) and the right side detection signal

Left detection signal

with right side heartbeat

Both are processed by the second-order band-pass filter B(s) and the second-order high-pass filter H(s), respectively, to obtain the detection signal at the current corner frequency.

The real and imaginary parts of the left sinusoidal signal x _in and the right sinusoidal signal x _out below,

represents the real and imaginary parts of the left sinusoidal signal x _in ,

Represents the real and imaginary parts of the right sinusoidal signal x _out . in,

k _pB and k _pH are the constant parameters of the two filters respectively, and the constant parameters in the two filters are the same or different; s represents the complex frequency in the S domain (complex frequency domain), which is obtained by Laplace transform .

得到左侧待测信号x_in与右侧待测信号x_out的幅值与相角。use

Obtain the amplitude and phase angle of the signal to be measured on the left x _in and the signal to be measured on the right x _out .

In this example, the constant parameters k _pB and k _pH in the second-order band-pass filter B(s) and the second-order high-pass filter H(s) are both 0.2.

(3) Dynamic frequency seeking

即在角频率

下，满足|T_m|＝|x_out|/|x_in|。令e_|x|＝|x_out|-|x_in|，将步骤(2)中得到左侧待测信号x_in与右侧待测信号x_out的幅值代入到该公式中，即可依据e_|x|与0的大小关系来判断此时注入频率

与截止频率的大小关系；The intersection point ω _c of the open-loop transfer function T _m of the control loop to be measured and the abscissa is the expected cut-off frequency;

i.e. at angular frequency

, satisfy |T _m |=|x _out |/|x _in |. Let e _|x| = |x _out |-|x _in |, and substitute the amplitudes of the signal to be measured on the left x _in and the signal to be measured on the right x _out obtained in step (2) into the formula, then the The relationship between e _|x| and 0 determines the injection frequency at this time

The magnitude of the relationship with the cutoff frequency;

时，当前角频率

即为控制环路的截止频率ω_c；截止频率ω_c即为控制环路的带宽。When e _|x| = 0, that is

, the current corner frequency

is the cut-off frequency ω _{c of the control loop; the cut-off frequency ω c is} the bandwidth of the control loop.

下，将

减去

得到的值输入到一个PI调节器(即比例积分调节器，附图中符号为G_PI(s)，本实施例采用G_PI(s)＝11660+2668000/s，s代表S域中的复频率)，将PI调节器的输出加上当前角频率

即可得到注入信号x_p的新的角频率

然后将注入信号x_p中的

调整为

继续执行步骤(2)的提取检测信号过程，并将在新的角频率

下的左侧正弦信号x_in与右侧正弦信号x_out的幅值代入e_|x|＝|x_out|-|x_in|，若此时仍然e_|x|≠1，不断重复上述过程，不断调整角频率，直至e_|x|＝0，实现动态寻频；When e _|x| ≠ 1, then at the current angular frequency

down, will

minus

The obtained value is input to a PI regulator (that is, a proportional-integral regulator, the symbol in the figure is G _PI (s), this embodiment adopts G _PI (s)=11660+2668000/s, s represents the complex in the S domain. frequency), add the output of the PI regulator to the current corner frequency

The new angular frequency of the injected signal x _p can be obtained

will then _inject the

tweak to

Continue to perform the extraction detection signal process of step (2), and

The amplitudes of the left sinusoidal signal x _in and the right sinusoidal signal x _out are substituted into e _|x| = |x _out |-|x _in |, if e _|x| ≠ 1 at this time, repeat the above process continuously, Constantly adjust the angular frequency until e _|x| = 0 to achieve dynamic frequency searching;

(4) Calculation of phase angle margin

According to the cut-off frequency ω _c obtained in step (3), substitute the phase angle between the left sinusoidal signal x _in and the right sinusoidal signal x _out at the angular frequency into the formula PM=∠x _out -∠x _in , to obtain the Measure the phase angle margin of the control loop.

In this example, the control bandwidth and phase angle margin of the control system are changed by changing the grid-connected impedance Z _G of the single-phase grid-connected inverter (containing 5% of the background harmonics) multiple times, where the grid-connected 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 ^* is set to 10A).

It can be seen from Figure 4 that the phase angle margin (PM) can be measured in sequence as 60°→52°→47° in about 0.2s, and the control bandwidth (BW, which is the cut-off frequency) is 1kHz→813Hz→ 692Hz, and the measurement result is stable during multiple changes, i _G =10A. Moreover, as can be seen from the partial enlarged view in Figure 5, the measurement results in one scenario can be obtained within 10ms.

For the control loop in this embodiment, after theoretical calculation, the grid-connected impedance Z _G is 0.5Ω+0.5mH, the cut-off frequency is 1kHz, and the phase angle margin is 60°; the grid-connected impedance Z _G is 0.5Ω+1mH, its The cutoff frequency is 813Hz, the phase angle margin is 53°, the grid-connected impedance Z _G is 0.5Ω+1.5mH, the cutoff frequency is 692Hz, and the phase angle margin is 47°. From the measurement result, the theoretical value of the performance index of the control loop is consistent with the result obtained by the method for measuring the performance index of the control loop of the present invention, so the measurement result is accurate within the allowable error range.

What is not described in the present invention applies to the prior art.

Claims (1)

1. a method for measuring a control loop performance index based on a second-order filter, is characterized in that, the method comprises the steps: (1) inject small signal A small sine wave signal (x _p ) with variable angular frequency is injected into the control loop under test, and its expression is

where A is the amplitude of the sine wave small signal (x _p ),

is the angular frequency of the sine wave small signal (x _p ); (2) Extract the detection signal There are detection signal interfaces on the left and right sides of the signal injection point of the control loop, which are respectively used for real-time detection of the detection signal on the left side of the signal injection point.

with right side heartbeat

Left detection signal

with right side heartbeat

Both are processed by the second-order band-pass filter B(s) and the second-order high-pass filter H(s), respectively, to obtain the detection signal at the current corner frequency.

The real and imaginary parts of the left sinusoidal signal (x _in ) and the right sinusoidal signal (x _out ) below,

represents the real and imaginary parts of the left sinusoidal signal (x _in ),

represents the real and imaginary parts of the right-hand sinusoidal signal (x _out ); using

Obtain the amplitude and phase angle of the left sinusoidal signal (x _in ) and the right sinusoidal signal (x _out ); (3) Dynamic frequency seeking The intersection (ω _c ) of the open-loop transfer function (T _m ) of the control loop under test and the abscissa is the desired cut-off frequency; since

i.e. at angular frequency

, satisfy |T _m |=|x _out |/|x _in |; let e _|x| =|x _out |-|x _{in |} Substitute the amplitude of the signal to be measured (x _out ) on the right side into the formula, and then the injection frequency can be judged according to the relationship between e _|x| and 0

The magnitude of the relationship with the cutoff frequency; When e _|x| = 0, that is

, the current corner frequency

is the cut-off frequency (ω _{c ) of the control loop; the cut-off frequency (ω c )} is the bandwidth of the control loop; When e _|x| ≠ 1, then at the current angular frequency

down, will

minus

The obtained value is input to a PI regulator, and the output of the PI regulator is added to the current corner frequency

The new angular frequency of the injected signal (x _p ) can be obtained

Then inject the signal into the signal (x _p )

tweak to

Continue to perform the extraction detection signal process of step (2), and

The amplitudes of the left sinusoidal signal (x _in ) and the right sinusoidal signal (x _out ) below are substituted into e _|x| = |x _out |-|x _in |, if e _|x| Repeat the above process, continuously adjust the angular frequency, until e _|x| =0, to achieve dynamic frequency search; (4) Calculation of phase angle margin According to the cutoff frequency (ω _c ) obtained in step (3), substitute the phase angle of the left sinusoidal signal (x _in ) and the right sinusoidal signal (x _out ) at the angular frequency into the formula PM=∠x _out -∠x _in , the phase angle margin of the control loop under test is obtained.

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