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

Second-order filter-based control loop performance index measurement method Download PDF

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CN114740827A
CN114740827A CN202210438424.0A CN202210438424A CN114740827A CN 114740827 A CN114740827 A CN 114740827A CN 202210438424 A CN202210438424 A CN 202210438424A CN 114740827 A CN114740827 A CN 114740827A
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signal
frequency
control loop
angular frequency
detection signal
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王嘉晨
刘青
侯琪
曾祥辰
黄山
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Hebei University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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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

Control loop performance index measuring method based on second-order filter
Technical Field
The invention belongs to the technical field of automatic control systems, mainly realizes continuous and rapid measurement of cut-off frequency and phase angle margin of a control loop, and particularly relates to a second-order filter-based control loop performance index measurement method.
Background
In automatic control theory, control loop performance indicators (including cut-off frequency and phase margin) can characterize control system dynamic performance and steady state performance. In the design stage of the control system, a designer needs to design parameters of the controller scientifically and reasonably to adjust the parameters so as to ensure that the control system obtains satisfactory static and dynamic performances. Therefore, the performance indexes of the control loop are widely applied, such as online dynamic performance monitoring of a server/spacecraft power supply, stability analysis of a cascade power converter, new energy grid-connected stability analysis, adaptive online adjustment of controller parameters and the like.
Generally, the control loop performance index is obtained by theoretically deriving a transfer function between a controlled variable and a controlled variable based on a small signal linearization model of a control system. However, there is an error between the theoretically derived result and the actual value for two reasons: 1) a large number of nonlinear devices (such as arc welding machines, saturation transformers, motors and the like) and switching devices (such as operational amplifiers, switching tubes and the like) exist in an electrical system, and a linearization model of the strong nonlinear and strong coupling system cannot completely and equivalently represent an actual system; 2) due to the composite influence of various factors such as load change, state change, temperature drift, aging and the like, system parameters can change on a short time scale/a long time scale. Therefore, the method can quickly and accurately measure the actual performance index information of the control loop, and has extremely important significance for closed loop optimization design of the regulator, dynamic and static performance guarantee of the control system and self-adaptive control of the time-varying system.
The existing measurement method is generally realized based on a small signal injection method, and the method has two main types with wide application: 1) a sine sweep frequency method; 2) broadband measurement method. The sine frequency sweeping method not only needs to inject signals with different frequencies successively, but also needs Fourier decomposition processing to obtain an accurate result, so that the measuring 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, loop gain measurement is carried out by only one injection, and the measurement time is successfully shortened to 100 milliseconds (measurement spectrum: 10Hz-100 kHz). However, in the weak grid, the loop gain should be measured as soon as possible, and the existing method still cannot meet the requirement of adaptive control of the power converter in the weak grid.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a control loop performance index measuring method based on a second-order filter in order to further shorten the measuring time and better meet the situation that the gain of a loop is changed quickly due to the fact that the impedance of a microgrid is influenced, so that the measurement of the cut-off frequency and the phase angle margin of the control loop can be completed within a few milliseconds, important information support is provided for the closed-loop optimization design of a control system regulator, and the dynamic and static performances of the control system under the condition of parameter disturbance are guaranteed. At the same time, it also provides the additional advantage of satisfying harmonic attenuation, which is valuable in background harmonic rich ac microgrid applications.
The technical scheme for solving the technical problems is as follows: a method for measuring the performance index of a control loop based on a second-order filter is designed, and comprises the following steps:
(1) injecting small signals
Injecting a sine wave small signal (x) with variable angular frequency into the measured control loopp) The expression is
Figure BDA0003607219020000031
Wherein A is sine wave small signal (x)p) The amplitude of (a) of (b) is,
Figure BDA0003607219020000032
is a sine wave small signal (x)p) The angular frequency of (d);
(2) extracting a detection signal
Detection signal interfaces are arranged on the left side and the right side of a signal injection point of the control loop and are respectively used for detecting detection signals on the left side of the signal injection point in real time
Figure BDA0003607219020000033
And right side detection signal
Figure BDA0003607219020000034
Left side detection signal
Figure BDA0003607219020000035
And right side detection signal
Figure BDA0003607219020000036
The two signals are respectively processed by a second-order band-pass filter B(s) and a second-order high-pass filter H(s) to respectively obtain the current angular frequency of the detection signal at the moment
Figure BDA0003607219020000037
Lower left sinusoidal signal (x)in) With the right sinusoidal signal (x)out) The real and imaginary parts of (a) and (b),
Figure BDA0003607219020000038
representing the left-hand sinusoidal signal (x)in) The real and imaginary parts of (a) and (b),
Figure BDA0003607219020000039
representing the right sinusoidal signal (x)out) The real and imaginary parts of (c); by using
Figure BDA00036072190200000310
Figure BDA00036072190200000311
Obtain the left signal (x) to be measuredin) And the signal to be measured on the right side (x)out) Amplitude and phase angle of;
(3) dynamic frequency finding
Open loop transfer function (T) of control loop under testm) Intersection with abscissa (ω)c) Is the desired cut-off frequency; due to the fact that
Figure BDA00036072190200000312
I.e. at angular frequency
Figure BDA00036072190200000313
Below, satisfy | Tm|＝|xout|/|xinL, |; let e|x|＝|xout|-|xinIf yes, obtaining the left side signal (x) to be detected in the step (2)in) And the signal to be measured on the right side (x)out) Is substituted into the formula, i.e. according to e|x|The injection frequency at this time is judged according to the magnitude relation with 0
Figure BDA00036072190200000314
Magnitude relation with cut-off frequency;
when e is|x|When equal to 0, i.e.
Figure BDA00036072190200000315
Time of current angular frequency
Figure BDA00036072190200000316
I.e. the cut-off frequency (omega) of the control loopc) (ii) a Cut-off frequency (omega)c) I.e. the bandwidth of the control loop;
when e is|x|When not equal to 1, then at the current angular frequency
Figure BDA0003607219020000041
Then, will
Figure BDA0003607219020000042
Minus one (C) of
Figure BDA0003607219020000043
The obtained value is input to a PI regulator, and the output of the PI regulator is added to the current angular frequency
Figure BDA0003607219020000044
The injection signal (x) can be obtainedp) New angular frequency of
Figure BDA0003607219020000045
Then inject the signal (x)p) In (1)
Figure BDA0003607219020000046
Is adjusted to
Figure BDA0003607219020000047
Continuing to execute the process of extracting the detection signal in the step (2), and enabling the new angular frequency to be obtained
Figure BDA0003607219020000048
Lower left sinusoidal signal (x)in) With the right-hand sinusoidal signal (x)out) Amplitude of (d) is substituted into e|x|＝|xout|-|xinIf then e is still present|x|Not equal to 1, continuously repeating the above process, and continuously adjusting the angular frequency until e|x|When the frequency is equal to 0, realizing dynamic frequency searching;
(4) phase angle margin calculation
The cut-off frequency (omega) obtained according to the step (3)c) The left-hand sinusoidal signal (x) at this angular frequencyin) With the right-hand sinusoidal signal (x)out) Substituting the phase angle into a formula PM ═ xout-∠xinAnd obtaining the phase angle margin of the monitored control loop.
Compared with the prior art, the invention has the beneficial effects that: the method for measuring the performance index of the control loop adopts the idea of dynamic frequency searching, combines a second-order high-pass filter H(s), a second-order band-pass filter B(s) and a PI regulator, has the measurement time (within 10 ms) far shorter than that of a traditional sine frequency sweeping 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.
Drawings
Fig. 1 is a control loop structure diagram of an embodiment of a second order filter-based control loop performance index measurement method according to the present invention.
Fig. 2 is a schematic diagram of a bandwidth measurement principle of the second-order filter-based control loop performance index measurement method of the present invention.
Fig. 3 is a measurement schematic block diagram of an embodiment of a second-order filter-based control loop performance index measurement method according to the present invention.
FIG. 4 is a diagram of a method for measuring performance index of control loop in FIG. 1 based on second order filter according to the present inventionGIs surrounded byGrid-connected impedance Z of secondary-change single-phase grid-connected inverter (containing 5% background harmonic wave)GTime measurement result graph.
Fig. 5 is a partially enlarged view of fig. 4.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.
In this embodiment, the monitored control loop employs a relatively common single-phase full-bridge inverter circuit, and the filter is an LCL type filter. As shown in fig. 1, in order to reflect the anti-noise performance and dynamic performance of the control loop performance index measuring method (i.e., the stability margin monitor in fig. 1), 5% of background harmonics are introduced into the power grid, and the grid-connected impedance Z is changed for many timesGChanging the performance index of the system, and testing the outermost ring i in the current sceneGThe cut-off frequency and phase margin of the loop (which can be considered a system of current closed loops).
The invention provides a method for measuring performance indexes of a control loop based on a second-order filter, which comprises the following steps:
(1) injecting small signals
Injecting a sine wave small signal x with variable angular frequency into a measured control looppThe expression is
Figure BDA0003607219020000051
Wherein A is sine wave small signal xpThe amplitude of (a) of (b) is,
Figure BDA0003607219020000052
is a sine wave small signal xpThe angular frequency of (d); t is time, the same applies below; in this embodiment, an initial value of angular frequency with an amplitude A of 0.5 is injected into the control loop
Figure BDA0003607219020000053
A sine wave small signal at 1000 Hz.
(2) Extracting a detection signal
Detection signal interfaces are arranged on the left side and the right side of a signal injection point of the control loop and are respectively used for detecting signal injection in real timeLeft side detection signal of point
Figure BDA0003607219020000061
(j is an imaginary unit, the same applies below) and the right side detection signal
Figure BDA0003607219020000062
Left side detection signal
Figure BDA0003607219020000063
And right side detection signal
Figure BDA0003607219020000064
The two signals are respectively processed by a second-order band-pass filter B(s) and a second-order high-pass filter H(s) to respectively obtain the current angular frequency of the detection signal at the moment
Figure BDA0003607219020000065
Lower left-hand sinusoidal signal xinWith the right-hand sinusoidal signal xoutThe real and imaginary parts of (a) and (b),
Figure BDA0003607219020000066
representing the left-hand sinusoidal signal xinThe real and imaginary parts of (a) and (b),
Figure BDA0003607219020000067
representing the right sinusoidal signal xoutReal and imaginary parts of (c). Wherein,
Figure BDA0003607219020000068
kpBand kpHConstant parameters of the two filters are respectively, and the values of the constant parameters in the two filters are the same or different; s represents a complex frequency in the S domain (complex frequency domain) and is obtained by laplace transform.
By using
Figure BDA0003607219020000069
Figure BDA00036072190200000610
To obtain the left side waitingMeasuring signal xinAnd the right side signal x to be measuredoutAmplitude and phase angle of.
In the present example, the constant parameter k in the second order band-pass filter B(s) and the second order high-pass filter H(s)pBAnd kpHAll values of (A) are 0.2.
(3) Dynamic frequency searching
Open loop transfer function T of control loop to be testedmIntersection with abscissa ωcIs the desired cut-off frequency; due to the fact that
Figure BDA00036072190200000611
I.e. at angular frequency
Figure BDA00036072190200000612
Below, satisfy | Tm|＝|xout|/|xinL. the method is used for the preparation of the medicament. Let e|x|＝|xout|-|xinIf yes, obtaining the left side signal x to be detected in the step (2)inAnd the right side signal x to be measuredoutThe amplitude of (e) is substituted into the formula, i.e. according to e|x|The injection frequency at this time is judged according to the magnitude relation with 0
Figure BDA00036072190200000613
Magnitude relation to cut-off frequency;
when e is|x|When equal to 0, i.e.
Figure BDA0003607219020000071
Time, current angular frequency
Figure BDA0003607219020000072
I.e. the cut-off frequency omega of the control loopc(ii) a Cut-off frequency omegacI.e. the bandwidth of the control loop.
When e is|x|When not equal to 1, then at the current angular frequency
Figure BDA0003607219020000073
Then, will
Figure BDA0003607219020000074
Minus one (C) of
Figure BDA0003607219020000075
The resulting value is input to a PI regulator (proportional integral regulator, denoted G in the figure)PI(s), this example uses GPI(S) 11660+2668000/S, S representing the complex frequency in the S domain), the output of the PI regulator is added to the current angular frequency
Figure BDA0003607219020000076
The injection signal x can be obtainedpNew angular frequency of
Figure BDA0003607219020000077
Then inject signal xpIn
Figure BDA0003607219020000078
Is adjusted to
Figure BDA0003607219020000079
Continuing to execute the process of extracting the detection signal in the step (2), and enabling the new angular frequency to be obtained
Figure BDA00036072190200000710
Lower left-hand sinusoidal signal xinWith the right-hand sinusoidal signal xoutAmplitude substitution of e|x|＝|xout|-|xinIf then e is still present|x|Not equal to 1, continuously repeating the above process, and continuously adjusting the angular frequency until e|x|When the frequency is equal to 0, realizing dynamic frequency searching;
(4) phase angle margin calculation
The cut-off frequency omega obtained according to the step (3)cThe left-hand sinusoidal signal x at this angular frequency is divided intoinWith the right-hand sinusoidal signal xoutSubstituting the phase angle into a formula PM ═ xout-∠xinAnd obtaining the phase angle margin of the monitored control loop.
In this example, the grid-tied impedance Z of a single-phase grid-tied inverter (containing 5% background harmonics) is varied a number of timesGTo change the control bandwidth and phase angle margin of the control system, whereinNet impedance ZGThe change of (c) is: 0.5 Ω +0.5mH (Case1) → 0.5 Ω +1mH (Case2) → 0.5 Ω +1.5mH (Case3) → 0.5 Ω +1mH (Case2) → 0.5 Ω +0.5mH (Case1, iG *Set to 10A).
It can be seen from fig. 4 that the phase angle margin (PM) is 60 ° → 52 ° → 47 °, the control bandwidth (BW, i.e. the cut-off frequency) is 1kHz → 813Hz → 692Hz, which can be sequentially measured only about 0.2s, and the measurement result is stable during multiple changes, i G10A. Also, as can be seen from the partially enlarged view of fig. 5, the measurement result in one scene can be obtained within 10 ms.
The control loop in this embodiment is theoretically calculated and the grid-connected impedance ZGThe cut-off frequency is 1kHz, and the phase angle margin is 60 degrees; grid-connected impedance ZG0.5 omega +1mH, the cut-off frequency of the grid-connected impedance Z is 813Hz, the phase angle margin is 53 degreesG0.5 Ω +1.5mH, with a cutoff frequency of 692Hz and a phase angle margin of 47 °. From the measurement result, the theoretical value of the performance index of the control loop is matched with the result obtained by the method for measuring the performance index of the control loop, so that the measurement result is accurate within the range of the error allowance.
Nothing in this specification is said to apply to the prior art.

Claims (1)

1. A method for measuring performance indexes of a control loop based on a second-order filter is characterized by comprising the following steps:
(1) injecting small signals
Injecting a sine wave small signal (x) with variable angular frequency into the measured control loopp) Of the formula
Figure FDA0003607219010000011
Wherein A is sine wave small signal (x)p) The amplitude of (a) of (b) is,
Figure FDA0003607219010000012
is a sine wave small signal (x)p) The angular frequency of (d);
(2) extracting a detection signal
Detection signal interfaces are arranged on the left side and the right side of a signal injection point of the control loop and are respectively used for detecting a detection signal on the left side of the signal injection point in real time
Figure FDA0003607219010000013
And right side detection signal
Figure FDA0003607219010000014
Left side detection signal
Figure FDA0003607219010000015
And right side detection signal
Figure FDA0003607219010000016
The two signals are respectively processed by a second-order band-pass filter B(s) and a second-order high-pass filter H(s) to respectively obtain the current angular frequency of the detection signal at the moment
Figure FDA0003607219010000017
Lower left sinusoidal signal (x)in) With the right sinusoidal signal (x)out) The real and imaginary parts of (a) and (b),
Figure FDA0003607219010000018
representing the left-hand sinusoidal signal (x)in) The real and imaginary parts of (a) and (b),
Figure FDA0003607219010000019
representing the right sinusoidal signal (x)out) The real and imaginary parts of (c); by using
Figure FDA00036072190100000110
Figure FDA00036072190100000111
The left side sinusoidal signal (x) is obtainedin) With the right-hand sinusoidal signal (x)out) Amplitude and phase angle of;
(3) dynamic frequency finding
Open loop transfer function (T) of control loop under testm) Intersection with abscissa (ω)c) Is the desired cut-off frequency; due to the fact that
Figure FDA00036072190100000112
I.e. at angular frequency
Figure FDA00036072190100000113
Below, satisfy | Tm|＝|xout|/|xinL, |; let e|x|＝|xout|-|xinIf yes, obtaining the left side signal (x) to be detected in the step (2)in) And the signal to be measured on the right side (x)out) Is substituted into the formula, i.e. according to e|x|The injection frequency at this time is judged according to the magnitude relation with 0
Figure FDA00036072190100000114
Magnitude relation with cut-off frequency;
when e is|x|When equal to 0, i.e.
Figure FDA0003607219010000021
Time, current angular frequency
Figure FDA0003607219010000022
I.e. the cut-off frequency (omega) of the control loopc) (ii) a Cut-off frequency (omega)c) I.e. the bandwidth of the control loop;
when e is|x|When not equal to 1, then at the current angular frequency
Figure FDA0003607219010000023
In the following, the
Figure FDA0003607219010000024
Minus
Figure FDA0003607219010000025
The obtained value is input to a PI regulator, and the PI regulator is operatedOutput plus current angular frequency
Figure FDA0003607219010000026
The injection signal (x) can be obtainedp) New angular frequency of
Figure FDA0003607219010000027
Then inject the signal (x)p) In (1)
Figure FDA0003607219010000028
Is adjusted to
Figure FDA0003607219010000029
Continuing to execute the process of extracting the detection signal in the step (2), and enabling the new angular frequency to be obtained
Figure FDA00036072190100000210
Lower left sinusoidal signal (x)in) With the right-hand sinusoidal signal (x)out) Amplitude substitution of e|x|＝|xout|-|xinIf then e is still present|x|Not equal to 1, continuously repeating the above process, and continuously adjusting the angular frequency until e|x|When the frequency is equal to 0, realizing dynamic frequency searching;
(4) phase angle margin calculation
The cut-off frequency (omega) obtained according to the step (3)c) The left-hand sinusoidal signal (x) at this angular frequency is addedin) With the right sinusoidal signal (x)out) Substituting the phase angle into the formula PM ═ xout-∠xinAnd obtaining the phase angle margin of the monitored control loop.
CN202210438424.0A 2022-04-21 2022-04-21 Second-order filter-based control loop performance index measurement method Pending CN114740827A (en)

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113467418A (en) * 2021-06-25 2021-10-01 河北工业大学 Method for measuring performance index of control loop

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113467418A (en) * 2021-06-25 2021-10-01 河北工业大学 Method for measuring performance index of control loop

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