CN107219764A - The computational methods and device of a kind of vibration parameters based on high-order describing function method - Google Patents
The computational methods and device of a kind of vibration parameters based on high-order describing function method Download PDFInfo
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Abstract
The embodiment of the invention discloses a kind of computational methods of vibration parameters based on high-order describing function method and device, utilize the frequency-domain model pre-established, initial odd harmonic signal is handled, the target output signal and target odd harmonic signal of control system can be obtained；According to the initial odd harmonic signal and target odd harmonic signal, it may be determined that go out the goal condition and higher hamonic wave of periodic vibration and the Amplitude Ration and phase difference of fundamental wave, so as to further determine that out target phase difference and the corresponding relation of vibration angular frequency；According to the corresponding relation and goal condition, it may be determined that go out the vibration angular frequency of control system；Again according to angular frequency and target output signal, it may be determined that go out the Oscillation Amplitude of control system.By analyzing the influence of the Amplitude Ratio and phase difference of higher hamonic wave and fundamental wave to control system phase-frequency characteristic, so that the vibration parameters of control system are more precisely calculated.
Description
Technical field
The present invention relates to control system technical field, more particularly to a kind of vibration parameters based on high-order describing function method
Computational methods and device.
Background technology
Control system refers to there is own target and the pipe of function by what control main body, control object and control media were constituted
Reason system.Control system has been widely used in the every field of human society.With the continuous increase of control system complexity,
Nonlinear element and its caused Non-Linear Vibration hamper the raising of control system performance.Mainly showing is, larger vibration
Amplitude will reduce control accuracy, and easily resonance is induced when vibration frequency is close with system resonance frequencies.
In traditional approach, the vibration parameters of control system are estimated using classical describing function method, but be due to
It ignores higher hamonic wave completely, thus vibration parameters estimation error is larger or even mistake.
It can be seen that, how the vibration parameters of accurate calculating control system, be those skilled in the art's urgent problem to be solved.
The content of the invention
The purpose of the embodiment of the present invention be to provide a kind of computational methods of the vibration parameters based on high-order describing function method with
Device, can accurate calculating control system vibration parameters.
In order to solve the above technical problems, the embodiments of the invention provide a kind of vibration parameters based on high-order describing function method
Computational methods, including：
Using the frequency-domain model pre-established, initial odd harmonic signal is handled, the target of control system is obtained
Output signal and target odd harmonic signal；
According to the initial odd harmonic signal and the target odd harmonic signal, the target bar of periodic vibration is determined
The Amplitude Ration and phase difference of part and higher hamonic wave and fundamental wave；
According to the Amplitude Ration, the phase difference and the initial odd harmonic signal, determine target phase difference with
Vibrate the corresponding relation of angular frequency；
According to the corresponding relation and the goal condition, the vibration angular frequency of control system is determined；
According to the angular frequency and the target output signal, the Oscillation Amplitude of control system is determined.
Optionally, it is described using the frequency-domain model pre-established, initial odd harmonic signal is handled, controlled
The target output signal and target odd harmonic signal of system include：
Initial odd harmonic signal is handled using switching function is switched, the first output signal is obtained；
First output signal is sampled and controlled device processing, obtain the target output signal of control system；
The target output signal is subjected to the processing of anti-phase and controller, corresponding target odd harmonic signal is obtained.
Optionally, it is described according to the corresponding relation and the goal condition, determine the vibration angular frequency of control system
Including：
According to the corresponding relation and the goal condition, angle of throw frequency function is determined；
The angle of throw frequency function is handled using diagram method, the vibration angular frequency of control system is obtained.
Optionally, in addition to：
According to the stable condition of vibration angular frequency, judge whether the vibration angular frequency of the control system is stablized.
The embodiment of the present invention additionally provides a kind of computing device of the vibration parameters based on high-order describing function method, including place
Unit and determining unit are managed,
The processing unit, for using the frequency-domain model pre-established, handling initial odd harmonic signal, obtaining
To the target output signal and target odd harmonic signal of control system；
The determining unit, for according to the initial odd harmonic signal and the target odd harmonic signal, it is determined that
Go out the goal condition and higher hamonic wave of periodic vibration and the Amplitude Ration and phase difference of fundamental wave；
The determining unit is additionally operable to according to the Amplitude Ration, the phase difference and the initial odd harmonic signal,
Determine target phase difference and the corresponding relation of vibration angular frequency；
The determining unit also according to the corresponding relation and the goal condition, determines the vibration angular frequency of control system
Rate；
The determining unit is additionally operable to, according to the angular frequency and the target output signal, determine shaking for control system
Dynamic amplitude.
Optionally, the processing unit includes switch switching subelement, obtains subelement and feedback subelement,
The switch switching subelement, for being handled initial odd harmonic signal using switching switching function, is obtained
To the first output signal；
It is described to obtain subelement, for first output signal is sampled and controlled device processing, controlled
The target output signal of system；
The feedback subelement, handles for the target output signal to be carried out into anti-phase and controller, obtains corresponding
Target odd harmonic signal.
Optionally, the determining unit is specifically for according to the corresponding relation and the goal condition, determining vibration
Angular frequency function；And the angle of throw frequency function is handled using diagram method, obtain the vibration angular frequency of control system.
Optionally, in addition to judging unit,
The judging unit, for the stable condition according to vibration angular frequency, judges the vibration angular frequency of the control system
Whether rate is stablized.
Using the frequency-domain model pre-established it can be seen from above-mentioned technical proposal, initial odd harmonic signal is carried out
Processing, can obtain the target output signal and target odd harmonic signal of control system；According to the initial odd harmonic signal
With target odd harmonic signal, it may be determined that go out the goal condition and higher hamonic wave of periodic vibration and the Amplitude Ration and phase of fundamental wave
Potential difference；According to the Amplitude Ration, the phase difference and the initial odd harmonic signal, target phase may further determine that out
Potential difference and the corresponding relation of vibration angular frequency；According to the corresponding relation and the goal condition, it may be determined that go out control system
Vibration angular frequency；Again according to the angular frequency and the target output signal, it may be determined that go out the Oscillation Amplitude of control system.
Multiple frequency signals are considered in this process and are superimposed influence to nonlinear element, by analyzing higher hamonic wave and fundamental wave
The influence of Amplitude Ratio and phase difference to control system phase-frequency characteristic, so as to more precisely compute out the vibration ginseng of control system
Number.
Brief description of the drawings
In order to illustrate the embodiments of the present invention more clearly, the required accompanying drawing used in embodiment will be done simply below
Introduce, it should be apparent that, drawings in the following description are only some embodiments of the present invention, for ordinary skill people
For member, on the premise of not paying creative work, other accompanying drawings can also be obtained according to these accompanying drawings.
Fig. 1 is a kind of stream of the computational methods of the vibration parameters based on high-order describing function method provided in an embodiment of the present invention
Cheng Tu；
Fig. 2 is a kind of structural representation of frequency-domain model provided in an embodiment of the present invention；
Fig. 3 is the schematic diagram of open loop phase-frequency characteristic curve provided in an embodiment of the present invention；
Fig. 4 is a kind of knot of the computing device of the vibration parameters based on high-order describing function method provided in an embodiment of the present invention
Structure schematic diagram.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.Based on this
Embodiment in invention, those of ordinary skill in the art are not under the premise of creative work is made, and what is obtained is every other
Embodiment, belongs to the scope of the present invention.
In order that those skilled in the art more fully understand the present invention program, with reference to the accompanying drawings and detailed description
The present invention is described in further detail.
Next, a kind of vibration parameters based on high-order describing function method that the embodiment of the present invention is provided are discussed in detail
Computational methods.Fig. 1 is a kind of computational methods of the vibration parameters based on high-order describing function method provided in an embodiment of the present invention
Flow chart, this method includes：
S101：Using the frequency-domain model pre-established, initial odd harmonic signal is handled, control system is obtained
Target output signal and target odd harmonic signal.
The vibration parameters of control system can include Oscillation Amplitude and vibration angular frequency, in order to more accurately calculate control
The vibration parameters of system processed, have taken into full account shadow of multiple frequency signal superpositions to nonlinear element in embodiments of the present invention
Ring, so as to analyze higher hamonic wave and the phase ratio with the Amplitude Ratio of fundamental wave.
In the specific implementation, the block diagram for the frequency-domain model being referred to shown in Fig. 2, is realized to initial odd harmonic signal
Processing, wherein, yr(t) it is the output desired value of control system, y (t) is the output signal of control system, e (t) misses for control
Difference, control system includes controller GC(s), switch switching function Msign [u0(t)], sampling functionAnd controlled device
Handle function G (s).In embodiments of the present invention, in order to lift the efficiency of calculating control system vibration parameters, y can be mader(t)
≡0。
Initial odd harmonic signal is handled using switching function is switched, the first output signal can be obtained.
The input for switching switching function is initial odd harmonic signal, and its formula is as follows：
Wherein, A2i+1The Oscillation Amplitude of control system is represented, ω represents the vibration angular frequency of control system,Represent control
The phase angle of system processed.
The purpose of the embodiment of the present invention is the Oscillation Amplitude A for calculating control system2i+1With taking for vibration angular frequency
Value.
Fundamental signal phase is set as 0, i.e.,Because u0(t) it is still that offset is 0, the cycle believes for 2 π/ω cycle
Number, therefore the first output signal u (t) of nonlinear element is cycle T=2 π/ω, dutycycle is equal to 0.5 square-wave signal.By
In u0(t) synergistic effect of each higher hamonic wave, u in0(t) there is phase difference with fundamental waveAndBy u0(t) width of each harmonic wave in
Degree and phase decision, thus, u (t) can be decomposed into each odd harmonic by Fourier transformation, and its formula is as follows：
First output signal is sampled and controlled device processing, the target output letter of control system can be obtained
Number, its formula is as follows：
Wherein,
The target output signal is subjected to the processing of anti-phase and controller, corresponding target odd harmonic letter can be obtained
Number, its formula is as follows：
S102：According to the initial odd harmonic signal and the target odd harmonic signal, periodic vibration is determined
The Amplitude Ration and phase difference of goal condition and higher hamonic wave and fundamental wave.
When the fundamental wave of initial odd harmonic signal and target odd harmonic signal is equal, closed-loop system can have a cycle and shake
It is dynamic, namely the goal condition of periodic vibration can be determined by formula (1) and formula (4), its formula is as follows：
To ensure that formula (5) is set up, then sinusoidal phase must be equal, i.e.,
By formula (6) it can be seen that vibration angular frequency is by phase differenceInfluence, want to calculate vibration angular frequency
Value, it is thus necessary to determine that go out phase differenceWith the corresponding relation between vibration angular frequency.Wherein, phase differenceBy fundamental wave and odd
Harmonic superposition is produced, thus can jointly be determined by the Amplitude Ratio and phase difference of higher hamonic wave and fundamental wave.For the ease of and high order
The phase difference of harmonic wave and fundamental wave makes a distinction, in embodiments of the present invention can be by phase differenceReferred to as target phase difference.
Below the detailed process of Amplitude Ration and phase difference to calculating higher hamonic wave and fundamental wave is deployed to introduce.
It can show that the amplitude expression formula of higher hamonic wave is as follows according to formula (4)：
It can show that the phase expression formula of higher hamonic wave is as follows with reference to formula (6)：
Wherein, k=1,3,5,7,9 ... ...
The amplitude and phase of fundamental wave can be determined according to formula (5), higher hamonic wave can be calculated with reference to formula (7a)
With the Amplitude Ratio of fundamental wave, its formula is as follows：
The phase difference of higher hamonic wave and fundamental wave can be calculated with reference to formula (7b), its formula is as follows：
S103：According to the Amplitude Ration, the phase difference and the initial odd harmonic signal, target phase is determined
Difference and the corresponding relation of vibration angular frequency.
From above-mentioned introduction, target phase differenceGeneration is superimposed with odd harmonic by fundamental wave, thus by Δ Ak,1WithIt is common to determine, so formula (8a) and formula (8b) can be substituted into formula (1), u0(t) it can be expressed as again：
Wherein, target phase difference
In embodiments of the present invention, it can useApproximate calculation method, by u0(t) it is being approximately angular frequency for ω just
String function, so as to obtain functionOn ω display expression formula, i.e. phase angle with vibration angular frequency corresponding relation, its
Formula is as follows：
S104：According to the corresponding relation and the goal condition, the vibration angular frequency of control system is determined.
According to the corresponding relation and the goal condition, it may be determined that go out angle of throw frequency function, its formula is as follows：
Wherein, ωnRepresent the value of vibration angular frequency.
OrderFormula (11) can be changed into following form：
The angle of throw frequency function can be handled using diagram method in embodiments of the present invention, obtain control system
The vibration angular frequency of system.
(1) selection frequency analysis scope ωn∈(0,2π/Td]；
(2) in the frequency range, the open loop phase-frequency characteristic curve of control system, i.e. angle of throw frequency function correspondence are drawn
Characteristic, with ωnFor abscissa,For ordinate, the characteristic curve schematic diagram is as shown in Figure 3.
(3) vibration angular frequency is found from curvenSo that
Three vibration angular frequency respectively ω can be found from Fig. 3n1、ωn2And ωn3。
S105：According to the angular frequency and the target output signal, the Oscillation Amplitude of control system is determined.
The relation of Oscillation Amplitude and vibration angular frequency can be drawn according to target output signal, according to the angle of throw calculated
Frequency, it can be deduced that the Oscillation Amplitude of each harmonic in target output signal：
First harmonic magnitude：
Triple-frequency harmonics amplitude：
Quintuple harmonics amplitude：
K subharmonic amplitudes：
Using the frequency-domain model pre-established it can be seen from above-mentioned technical proposal, initial odd harmonic signal is carried out
Processing, can obtain the target output signal and target odd harmonic signal of control system；According to the initial odd harmonic signal
With target odd harmonic signal, it may be determined that go out the goal condition and higher hamonic wave of periodic vibration and the Amplitude Ration and phase of fundamental wave
Potential difference；According to the Amplitude Ration, the phase difference and the initial odd harmonic signal, target phase may further determine that out
Potential difference and the corresponding relation of vibration angular frequency；According to the corresponding relation and the goal condition, it may be determined that go out control system
Vibration angular frequency；Again according to the angular frequency and the target output signal, it may be determined that go out the Oscillation Amplitude of control system.
Multiple frequency signals are considered in this process and are superimposed influence to nonlinear element, by analyzing higher hamonic wave and fundamental wave
The influence of Amplitude Ratio and phase difference to control system phase-frequency characteristic, so as to more precisely compute out the vibration ginseng of control system
Number.
By above-mentioned technical proposal, the vibration parameters of the control system calculated can be regarded as and control system is vibrated
Whether the predicted value of parameter, the predicted value has reference value, it is necessary to judge it.Specifically, can be according to angle of throw
The stable condition of frequency, judges whether the vibration angular frequency of the control system is stablized.
According to frequency method general principle, if open loop phase hysteresis is more than-π, vibration angular frequency will increase；If open loop phase
Position hysteresis is less than-π, then vibrating angular frequency will reduce；Therefore for any primary angular frequency Δ ω>0, if
AndThen angle of throw frequency stabilization；IfAndThen vibrate angular frequency
Rate is unstable；
Therefore, by small-signal method of perturbation, obtain vibrating the stable condition of angular frequency：
To avoid complicated calculations, diagram method can be used in embodiments of the present invention.
Specifically, phase-frequency characteristic curve that can be according to Fig. 3, ifIn ω=ωnIt is negative to locate slope, then shakes
Dynamic angular frequency is stable, and and then show that the vibration of the control system is stable；IfIn ω=ωnIt is just, then to locate slope
Vibrate angular frequency unstable.
By taking Fig. 3 as an example, it can be seen that ωn1And ωn3The stable vibration of correspondence, and ωn2The unstable vibration of correspondence.
Fig. 4 is a kind of knot of the computing device of the vibration parameters based on high-order describing function method provided in an embodiment of the present invention
Structure schematic diagram, including processing unit and determining unit,
The processing unit, for using the frequency-domain model pre-established, handling initial odd harmonic signal, obtaining
To the target output signal and target odd harmonic signal of control system；
The determining unit, for according to the initial odd harmonic signal and the target odd harmonic signal, it is determined that
Go out the goal condition and higher hamonic wave of periodic vibration and the Amplitude Ration and phase difference of fundamental wave；
The determining unit is additionally operable to according to the Amplitude Ration, the phase difference and the initial odd harmonic signal,
Determine target phase difference and the corresponding relation of vibration angular frequency；
The determining unit also according to the corresponding relation and the goal condition, determines the vibration angular frequency of control system
Rate；
The determining unit is additionally operable to, according to the angular frequency and the target output signal, determine shaking for control system
Dynamic amplitude.
Optionally, the processing unit includes switch switching subelement, obtains subelement and feedback subelement,
The switch switching subelement, for being handled initial odd harmonic signal using switching switching function, is obtained
To the first output signal；
It is described to obtain subelement, for first output signal is sampled and controlled device processing, controlled
The target output signal of system；
The feedback subelement, handles for the target output signal to be carried out into anti-phase and controller, obtains corresponding
Target odd harmonic signal.
Optionally, the determining unit is specifically for according to the corresponding relation and the goal condition, determining vibration
Angular frequency function；And the angle of throw frequency function is handled using diagram method, obtain the vibration angular frequency of control system.
Optionally, in addition to judging unit,
The judging unit, for the stable condition according to vibration angular frequency, judges the vibration angular frequency of the control system
Whether rate is stablized.
Using the frequency-domain model pre-established it can be seen from above-mentioned technical proposal, initial odd harmonic signal is carried out
Processing, can obtain the target output signal and target odd harmonic signal of control system；According to the initial odd harmonic signal
With target odd harmonic signal, it may be determined that go out the goal condition and higher hamonic wave of periodic vibration and the Amplitude Ration and phase of fundamental wave
Potential difference；According to the Amplitude Ration, the phase difference and the initial odd harmonic signal, target phase may further determine that out
Potential difference and the corresponding relation of vibration angular frequency；According to the corresponding relation and the goal condition, it may be determined that go out control system
Vibration angular frequency；Again according to the angular frequency and the target output signal, it may be determined that go out the Oscillation Amplitude of control system.
Multiple frequency signals are considered in this process and are superimposed influence to nonlinear element, by analyzing higher hamonic wave and fundamental wave
The influence of Amplitude Ratio and phase difference to control system phase-frequency characteristic, so as to more precisely compute out the vibration ginseng of control system
Number.
The explanation of feature may refer to the related description of embodiment corresponding to Fig. 1 in embodiment corresponding to Fig. 4, here no longer
Repeat one by one.
A kind of computational methods of the vibration parameters based on high-order describing function method provided above the embodiment of the present invention
It is described in detail with device.The embodiment of each in specification is described by the way of progressive, and each embodiment is stressed
Be all between difference with other embodiment, each embodiment identical similar portion mutually referring to.For implementing
For the disclosed device of example, because it is corresponded to the method disclosed in Example, so description is fairly simple, related part is joined
See method part illustration.It should be pointed out that for those skilled in the art, not departing from original of the invention
On the premise of reason, some improvement and modification can also be carried out to the present invention, these are improved and modification also falls into right of the present invention and wanted
In the protection domain asked.
Professional further appreciates that, with reference to the unit of each example of the embodiments described herein description
And algorithm steps, can be realized with electronic hardware, computer software or the combination of the two, in order to clearly demonstrate hardware and
The interchangeability of software, generally describes the composition and step of each example according to function in the above description.These
Function is performed with hardware or software mode actually, depending on the application-specific and design constraint of technical scheme.Specialty
Technical staff can realize described function to each specific application using distinct methods, but this realization should not
Think beyond the scope of this invention.
Directly it can be held with reference to the step of the method or algorithm that the embodiments described herein is described with hardware, processor
Capable software module, or the two combination are implemented.Software module can be placed in random access memory (RAM), internal memory, read-only deposit
Reservoir (ROM), electrically programmable ROM, electrically erasable ROM, register, hard disk, moveable magnetic disc, CD-ROM or technology
In any other form of storage medium well known in field.
Claims (8)
1. a kind of computational methods of the vibration parameters based on high-order describing function method, it is characterised in that including：
Using the frequency-domain model pre-established, initial odd harmonic signal is handled, the target output of control system is obtained
Signal and target odd harmonic signal；
According to the initial odd harmonic signal and the target odd harmonic signal, determine the goal condition of periodic vibration with
And the Amplitude Ration and phase difference of higher hamonic wave and fundamental wave；
According to the Amplitude Ration, the phase difference and the initial odd harmonic signal, target phase difference and vibration are determined
The corresponding relation of angular frequency；
According to the corresponding relation and the goal condition, the vibration angular frequency of control system is determined；
According to the angular frequency and the target output signal, the Oscillation Amplitude of control system is determined.
2. according to the method described in claim 1, it is characterised in that described using the frequency-domain model pre-established, to initial strange
Rd harmonic signal is handled, and is obtained the target output signal and target odd harmonic signal of control system and is included：
Initial odd harmonic signal is handled using switching function is switched, the first output signal is obtained；
First output signal is sampled and controlled device processing, obtain the target output signal of control system；
The target output signal is subjected to the processing of anti-phase and controller, corresponding target odd harmonic signal is obtained.
3. method according to claim 2, it is characterised in that described according to the corresponding relation and the goal condition,
Determining the vibration angular frequency of control system includes：
According to the corresponding relation and the goal condition, angle of throw frequency function is determined；
The angle of throw frequency function is handled using diagram method, the vibration angular frequency of control system is obtained.
4. the method according to claim 1-3 any one, it is characterised in that also include：
According to the stable condition of vibration angular frequency, judge whether the vibration angular frequency of the control system is stablized.
5. a kind of computing device of the vibration parameters based on high-order describing function method, it is characterised in that including processing unit and really
Order member,
The processing unit, for using the frequency-domain model pre-established, handling initial odd harmonic signal, being controlled
The target output signal and target odd harmonic signal of system processed；
The determining unit, for according to the initial odd harmonic signal and the target odd harmonic signal, determining week
The goal condition of phase vibration and the Amplitude Ration and phase difference of higher hamonic wave and fundamental wave；
The determining unit is additionally operable to according to the Amplitude Ration, the phase difference and the initial odd harmonic signal, it is determined that
Go out target phase difference and the corresponding relation of vibration angular frequency；
The determining unit also according to the corresponding relation and the goal condition, determines the vibration angular frequency of control system；
The determining unit is additionally operable to determine the vibration width of control system according to the angular frequency and the target output signal
Degree.
6. device according to claim 5, it is characterised in that the processing unit includes switch switching subelement, obtained
Subelement and feedback subelement,
The switch switching subelement, for handling initial odd harmonic signal using switching switching function, obtains
One output signal；
It is described to obtain subelement, for first output signal is sampled and controlled device processing, obtain control system
Target output signal；
The feedback subelement, handles for the target output signal to be carried out into anti-phase and controller, obtains corresponding target
Odd harmonic signal.
7. device according to claim 6, it is characterised in that the determining unit is specifically for according to the corresponding relation
With the goal condition, angle of throw frequency function is determined；And the angle of throw frequency function is handled using diagram method,
Obtain the vibration angular frequency of control system.
8. the device according to claim 5-7 any one, it is characterised in that also including judging unit,
The judging unit, for the stable condition according to vibration angular frequency, judging the vibration angular frequency of the control system is
No stabilization.
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