CN113467418A - Method for measuring performance index of control loop - Google Patents
Method for measuring performance index of control loop Download PDFInfo
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- CN113467418A CN113467418A CN202110723044.7A CN202110723044A CN113467418A CN 113467418 A CN113467418 A CN 113467418A CN 202110723044 A CN202110723044 A CN 202110723044A CN 113467418 A CN113467418 A CN 113467418A
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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
- G05B23/0256—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 injecting test signals and analyzing monitored process response, e.g. injecting the test signal while interrupting the normal operation of the monitored system; superimposing the test signal onto a control signal during normal operation of the monitored system
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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
- G05B2219/00—Program-control systems
- G05B2219/20—Pc systems
- G05B2219/24—Pc safety
- G05B2219/24065—Real time diagnostics
Abstract
The invention discloses a method for measuring performance indexes of a control loop, which adopts the idea of dynamic frequency searching, does not need to sweep frequency like the traditional frequency response method and has high detection speed. 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 the closed loop optimization design of the control system.
Description
Technical Field
The invention belongs to the technical field of control, and particularly relates to a method for measuring performance indexes of a control loop.
Background
Based on the automatic control theory, the controlled object in the field of electrical engineering is often simplified into a linear steady system. Such systems facilitate mathematical modeling and analysis, and their control systems are typically cascaded from a single or multiple control loops. The control loops are independent of each other and controlled by respective loop regulators (linear or non-linear). Therefore, the design of the loop regulator is the core of the whole control system design, and the given performance indexes (namely, the loop bandwidth and the phase angle margin) need to be followed to meet the expected dynamic and static performance requirements of the system. However, due to the influence of system model errors, parameter disturbance and other factors, an error always exists between the design performance index and the actual performance index of the regulator, and the dynamic and static performance requirements of the control system are difficult to accurately meet. The fundamental reason is that the design idea of the loop regulator for deducing the open-loop transfer function according to the model belongs to an open-loop design method, and the feedback of actual loop performance index information is lacked. In view of this, accurately measure the actual performance index information of control loop, to the closed loop optimal design of regulator, the dynamic and static performance guarantee of control system has extremely important meaning.
The measurement of the performance index of the control loop comprises two parts of measurement of a control bandwidth and a phase angle margin, wherein the control bandwidth reflects the dynamic performance of the control loop, and the phase angle margin represents a stability margin. The phase angle margin can be solved directly by controlling the bandwidth and the open-loop transfer function, so the core task of measurement is to control the measurement of the bandwidth. The control bandwidth measurement methods commonly used at present can be roughly divided into two types: 1) a step response method; 2) frequency response method. The step response method can only estimate the bandwidth value through an empirical formula, and is not suitable for the condition that the controlled object has resonance. The frequency response method is simple in principle, but is difficult to realize. If the test is carried out by the aid of a dynamic signal analyzer, the frequency sweep data output rate is limited by the baud rate of the serial port, and a large error exists in a bandwidth measured value at high frequency.
Disclosure of Invention
The invention aims to provide a method for measuring performance indexes of a control loop aiming at the defects in the prior art, so as to realize the measurement of the cut-off frequency and the phase angle margin of the control loop and provide important information support for the closed loop optimization design of a control system regulator, thereby ensuring the dynamic and static performance of the control system under the condition of parameter disturbance.
The technical scheme for solving the technical problems is as follows: a method for measuring performance indexes of a control loop is designed, and is characterized by comprising the following steps:
a method for measuring performance indexes of a control loop is characterized by comprising the following steps:
(1) injecting small signals
Injecting a variable-frequency sine wave small signal (x) into the controlled control loopp(jωest) ); from sine-wave small signals (x)p(jωest) Amplitude (| x)p(jωest) I) and angular frequency (omega)est) The injection signal (x) can be obtainedp) Is expressed as xp＝|xp(jωest)|sin(ωestt)；
(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 (x) on the left side of the signal injection point in real timein(jωest) And the right side detection signal (x)out(jωest) ); left side detection signal (x)in(jωest) And the right side detection signal (x)out(jωest) Respectively extract the current angular frequency (ω) in the detection signal at that time by the SOGIest) Lower left sinusoidal signal (x)inAnd right side sinusoidal signal (x)out) The real and imaginary parts of (c); by using
The left side sinusoidal signal (x) is obtainedinAnd right side sinusoidal signal (x)out) Amplitude and phase angle of;
(3) dynamic frequency finding
Intersection (omega) of the open loop transfer function (T) of the control loop with the abscissac) Is the corresponding cut-off frequency; due to T (j omega)est)＝-xout(jωest)/xin(jωest) I.e. at angular frequency (ω)est) In the following, | T | ═ xout|/|xinL, obtaining the left side sinusoidal signal (x) in the step (2)inAnd right side sinusoidal signal (x)out) Is substituted into the equation, when | T | ═ 1, i.e., | xout(jωest)|＝|xin(jωest) When, the current angular frequency (ω)est) 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 | T | ≠ 1, then at the current angular frequency (ω)est) Next, | xout(jωest) Subtract | xin(jωest) The value obtained by I passes through a PI regulator to obtain an injection signal (x)p) New frequency of
Multiplying it by 2 pi to obtain new angular frequency
New angular frequency
Omega is obtained through an integration link1 estt; according to omega1 estt, will inject signal (x)p) Sin (ω) of (1)estt) is adjusted to sin (ω)1 estt), continuing to execute the process of extracting the detection signal in the step (2), and enabling the frequency to be at the new angular frequency
Lower left sinusoidal signal (x)inAnd right side sinusoidal signal (x)out) Substituting the amplitude of | T | ═ xout|/|xinIf | T | ≠ 1 at this time, continuously repeating the above process, and continuously adjusting the angular frequency until | T | ═ 1, thereby realizing dynamic frequency searching;
(4) phase angle margin calculation
The cut-off frequency (omega) obtained according to the step (3)c) And corresponding to the left-hand sinusoidal signal (x) at angular frequencyinAnd right side sinusoidal signal (x)out) Substituting the phase angle into the formula PM ═ xout(jωest)-∠xin(jωest) And 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, does not need to sweep frequency like the traditional frequency response method, and has high detection speed. 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 the closed loop optimization design of the control system.
Drawings
Fig. 1 is a control loop structure diagram of an embodiment of a method for measuring a performance index of a control loop according to the present invention.
Fig. 2 is a schematic diagram of a bandwidth testing principle of the method for measuring a performance index of a control loop according to the present invention.
Fig. 3 is a schematic block diagram of extracting detection signals according to an embodiment of the method for measuring a performance index of a control loop of the present invention.
FIG. 4 is a block diagram of an embodiment of a method for measuring a performance index of a control loop according to the present inventionpAngular frequency of (omega)estIs a 400Hz left-side sinusoidal signal xinRight side sinusoidal signal xoutA waveform diagram of (a).
FIG. 5 is a block diagram of an embodiment of a method for measuring a performance indicator of a control loop according to the present inventionpAngular frequency of (omega)estIs a left-side sinusoidal signal x at 880HzinRight side sinusoidal signal xoutA waveform diagram of (a).
Detailed Description
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 adopts a relatively common single-phase full-bridge inverter circuit, the filter is an LCL type filter, and the control loop is iL-Vo-igThe control mode of the three-loop control mode (the left side is an inner loop, and the right side is an outer loop) is specifically a DB-DB-PI control mode. As shown in FIG. 1, the outermost ring, i, is now testedgBandwidth of the loop (which may be considered a system of current closed loops);
the invention provides a method for measuring performance index of a control loop, which is used for measuring i in a circuit shown in figure 1gThe loop control loop bandwidth includes the following steps:
(1) injecting small signals
To the measured control loop (i)gRing) is injected with a frequency-variable sine-wave small signal xp(jωest) The input of the frequency-converted signal may be realized by a disturbing signal generator. From sine-wave small signals xp(jωest) Amplitude | x ofp(jωest) I and angular frequency omegaestObtaining the injection signal xpIs expressed as xp＝|xp(jωest)|sin(ωestt); where j is an imaginary unit. In this embodiment, an amplitude | x is injected into the control loopp(jωest) I is 1, angular frequency omegaestSine wave small signal with initial value of 400 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 a detection signal x on the left side of the signal injection point in real timein(jωest) And the right side detection signal xout(jωest) (ii) a Left side detection signal xin(jωest) And the right side detection signal xout(jωest) The angular frequency omega in the detection signal at this moment is extracted by a SOGI (second-order generalized integrator)estLower left sinusoidal signal xinRight side sinusoidal signal xoutThe real part (the subscript R denotes the real part) and the imaginary part (the subscript I denotes the imaginary part) of (c). By using
Obtain the left side sinusoidal signal xinRight side sinusoidal signal xoutAmplitude and phase angle of.
(3) Dynamic frequency finding
Intersection omega of control loop open loop transfer function T and abscissacThe corresponding cut-off frequency. Due to T (j omega)est)＝-xout(jωest)/xin(jωest) I.e. at angular frequency omegaestIn the following, | T | ═ xout |/| xinL, obtaining the left side sinusoidal signal x in the step (2)inRight side sinusoidal signal xoutWhen | T | ═ 1, that is, | xout(jωest)|＝|xin(jωest) When, the current angular frequency ωestI.e. the cut-off frequency omega of the control loopc。
When | T | ≠ 1, then at the current angular frequency ωestNext, | xout(jωest) Subtract | xin(jωest) The value obtained is passed through a PI regulator (symbol G in the figure)f(s), a proportional-integral regulator, the present embodiment employs: s' ═ gf (S) ═ 11660+2668000/S), resulting in the injection signal xpNew frequency of
Then multiplying the value by 2 pi to obtain a new angular frequency
New angular frequency
ω is obtained through an integral element (denoted by ^ in the drawing, and transfer function g(s) ═ 1/s)1 estt. According to omega1 estt, will inject signal xpSi in (1)n(ωestt) is adjusted to sin (ω)1 estt), continuing to execute the process of extracting the detection signal in the step (2), and enabling the frequency to be at the new angular frequency
Lower left sinusoidal signal xinAnd the right side sinusoidal signal xoutSubstituting the amplitude of | T | ═ xout|/|xinIf | T | ≠ 1 at this time, continuously repeating the above process, and continuously adjusting the angular frequency until | T | ═ 1, thereby realizing dynamic frequency searching;
when | xout(jωest)|＞|xin(jωest) In case of | the injection signal x at this time is describedpAngular frequency of (omega)estGreater than the cut-off frequency omegacThe injection signal x needs to be reducedpAngular frequency of (omega)est(ii) a When | xout(jωest)|＜|xin(jωest) When l, inject signal xpAngular frequency of (omega)estLess than the cut-off frequency omegacThe injection signal x needs to be increasedpAngular frequency of (omega)est；
Continuously regulating until | xout(jωest)|＝|xin(jωest) I.e. the left-hand sinusoidal signal xinAmplitude of and right side sinusoidal signal xoutAre equal in amplitude, when the injection signal x ispAngular frequency of (omega)estI.e. the cut-off frequency omega of the control loopc. Cut-off frequency omegacI.e. the bandwidth of the control loop. A
Judging and changing the injection signal x according to the above conditionspAngular frequency of (omega)estIt can be quickly brought to the cut-off frequency omegacClose up until omegaest＝ωcTherefore, the purpose of fast frequency searching is realized. The cut-off frequency of the open-loop transfer function is very close to the bandwidth of the control loop, and the cut-off frequency is generally not distinguished in engineering application, so that the method realizes the measurement of the bandwidth of the control loop.
When x ispAngular frequency of (omega)estLeft side sinusoidal signal x at 400Hzin、Right side sinusoidal signal xoutThe waveform of (2) is shown in fig. 4. As can be seen from FIG. 4, the left-hand sinusoidal signal xinIs smaller than the right-side sinusoidal signal xoutIndicating that the cutoff frequency of the loop under test is now above 400 Hz. Increasing the injection signal x continuouslypAngular frequency of (omega)estUp to the left-hand sinusoidal signal xinAmplitude of and right side sinusoidal signal xoutAre equal in magnitude. When injecting signal xpAngular frequency of (omega)estAt 880Hz, the left-side sinusoidal signal xinRight side sinusoidal signal xoutIs shown in fig. 5, at this time, the left side sinusoidal signal xinAmplitude of and right side sinusoidal signal xoutIs equal, then 880Hz is the cut-off frequency ω of the systemcI.e. the bandwidth of the control loop is 880 Hz.
(4) Phase angle margin calculation
The cut-off frequency omega obtained according to the step (3)cLeft-sided sinusoidal signal x at 880Hz and corresponding angular frequencyinRight side sinusoidal signal xoutSubstituting the phase angle into the formula PM ═ xout(jωest)-∠xin(jωest) Obtaining the phase angle margin PM of the monitored control loopestIs 42 deg..
In the control loop in the embodiment, the cutoff frequency is 900Hz and the phase angle margin is 45 degrees through theoretical calculation, the actual cutoff frequency and the phase angle margin of the control loop are lower than the actual cutoff frequency and the phase angle margin, and the theoretical value of the control loop is identical to the result obtained by the method for measuring the performance index of the control loop in the invention from the measurement result, so that the measurement result is accurate within the range of error allowance.
The method for measuring the performance index of the control loop only needs to inject small signals into the input reference value of the original control loop, extracts the amplitude and the size of the sine wave at the corresponding frequency according to the output sampling signal in the original control loop, and can obtain the bandwidth and the phase angle margin of the control loop by adjusting the frequency of the input signals.
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 is characterized by comprising the following steps:
(1) injecting small signals
Injecting a variable-frequency sine wave small signal (x) into the controlled control loopp(jωest) ); from sine-wave small signals (x)p(jωest) Amplitude (| x)p(jωest) I) and angular frequency (omega)est) The injection signal (x) can be obtainedp) Is expressed as xp＝|xp(jωest)|sin(ωestt)；
(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 (x) on the left side of the signal injection point in real timein(jωest) And the right side detection signal (x)out(jωest) ); left side detection signal (x)in(jωest) And the right side detection signal (x)out(jωest) Respectively extract the current angular frequency (ω) in the detection signal at that time by the SOGIest) Lower left sinusoidal signal (x)inAnd right side sinusoidal signal (x)out) The real and imaginary parts of (c); by using
The left side sinusoidal signal (x) is obtainedinAnd right side sinusoidal signal (x)out) Amplitude and phase angle of;
(3) dynamic frequency finding
Intersection (omega) of the open loop transfer function (T) of the control loop with the abscissac) Is the corresponding cut-off frequency; due to T (j omega)est)＝-xout(jωest)/xin(jωest) I.e. at angular frequency (ω)est) In the following, | T | ═ xout|/|xinL, obtaining the left side sinusoidal signal (x) in the step (2)inAnd right side sinusoidal signal (x)out) Amplitude ofInto this equation, when | T | ═ 1, that is, xout(jωest)|＝xin(jωest) When, the current angular frequency (ω)est) 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 | T | ≠ 1, then at the current angular frequency (ω)est) Next, | xout(jωest) Subtract | xin(jωest) The value obtained by I passes through a PI regulator to obtain an injection signal (x)p) New frequency of
Then multiplying the value by 2 pi to obtain a new angular frequency
New angular frequency
Omega is obtained through an integration link1 estt; according to omega1 estt, will inject signal (x)p) Sin (ω) of (1)estt) is adjusted to sin (ω)1 estt), continuing to execute the process of extracting the detection signal in the step (2), and enabling the frequency to be at the new angular frequency
Lower left sinusoidal signal (x)inAnd right side sinusoidal signal (x)out) Substituting the amplitude of | T | ═ xout|/|xinIf | T | ≠ 1 at this time, continuously repeating the above process, and continuously adjusting the angular frequency until | T | ═ 1, thereby realizing dynamic frequency searching;
(4) phase angle margin calculation
The cut-off frequency (omega) obtained according to the step (3)c) And corresponding to the left-hand sinusoidal signal (x) at angular frequencyinAnd right side sinusoidal signal (x)out) Substituting the phase angle into the formula PM ═ xout(jωest)--∠xin(jωest)，And obtaining the phase angle margin of the monitored control loop.
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