CN110209051A - A kind of uncertain periodic perturbation removing method based on self-adaptive model generation device - Google Patents
A kind of uncertain periodic perturbation removing method based on self-adaptive model generation device Download PDFInfo
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Abstract
The invention belongs to automatic control technology fields, in particular relate to a kind of uncertain periodic perturbation removing method based on self-adaptive model generation device, the following steps are included: the state-space expression to self-adaptive model generation device carries out time scale transformation and frequency normalization, expression formula of the self-adaptive model generation device about time scale transformation parameter t is obtained；Using the systematic error e of control system as the input of self-adaptive model generation device, acquire self-adaptive model generation device it is average after frequency more new formulaAccording to the frequency more new formula after being averagedIt obtains the convergence point of control system, and then show that the error e of control system is the output of 0 and self-adaptive model generation device, the elimination of uncertain periodic perturbation signal is realized by output and the uncertain periodic perturbation signal cancellation of self-adaptive model generation device.The method of the invention realizes the eliminations of uncertain periodic perturbation, while can obtain the amplitude and frequency of uncertain periodic perturbation signal.
Description
Technical field
The invention belongs to automatic control technology fields, in particular relate to a kind of not true based on self-adaptive model generation device
Fixed cycle disturbance elimination method.
Background technique
Industrial production and design in, the process there are uncertain periodic perturbation signal be it is generally existing, especially
In the productions and design process with cyclophysis such as electric system, optical disc controller production.In such industrial production and set
Signal frequency, amplitude, the uncertainty of phase size, the uncertainty of stable object parameters disturbed in meter, makes pair
The accurate elimination of uncertain periodic perturbation signal is more difficult.In order to meet the control requirement of such system, propose a kind of not true
The control method of fixed cycle Eliminating disturbance is necessary.
Summary of the invention
According to problems of the prior art, it is uncertain based on self-adaptive model generation device that the present invention provides a kind of
Periodic perturbation removing method realizes the elimination of uncertain periodic perturbation, while can obtain uncertain periodic perturbation signal
Amplitude and frequency.
For achieving the above object, the present invention provides a kind of uncertain periods based on self-adaptive model generation device to disturb
Dynamic removing method, the control system based on self-adaptive model generation device includes the self-adaptive model generation device and PID being connected in parallel
Controller；Removing method includes the following steps:
S1 carries out time scale transformation and frequency normalization to the state-space expression of self-adaptive model generation device, obtains
Expression formula to self-adaptive model generation device about time scale transformation parameter t；
S2 acquires self-adaptive model generation using the systematic error e of control system as the input of self-adaptive model generation device
Device it is average after frequency more new formula
S3, according to the frequency more new formula after being averagedIt obtains the convergence point of control system, and then obtains control system
Systematic error e is the output x of 0 and self-adaptive model generation device1, by the output x of self-adaptive model generation device1With uncertain week
Phase disturbing signal offsets the elimination for realizing uncertain periodic perturbation signal.
Preferably, the step S1 includes the following steps:
The state space equation of S11, self-adaptive model generation device indicate are as follows:
Wherein, τ indicates the time variable of self-adaptive model generation device, x1(τ) and x2(τ) indicates self-adaptive model generation device
Two state variables, and x1(τ) is the output of self-adaptive model generation device, and ω (τ) indicates uncertain periodic perturbation signal estimation
The transient value of frequency, e (τ) indicate the systematic error of self-adaptive model generation device, and μ indicates the adjustable ginseng of self-adaptive model generation device
Number, γ are adaptive updates speed adjustable gain；
The expression formula of uncertain periodic perturbation input v is
Wherein a0Indicate the amplitude of uncertain periodic perturbation signal, ω0Indicate the frequency of uncertain periodic perturbation signal,
Indicate the phase of uncertain periodic perturbation signal；
S12 is based on time scale transformation parameterWith the normalization of self-adaptive model generation device adaptive frequency
Parameter θ=ω (τ)/ω0Time scale transformation and frequency normalization are carried out to (1) formula, obtain the shape of self-adaptive model generation device
Expression formula of the state space equation about time scale transformation parameter t:
Wherein, x1=x1(t), x2=x2(t), two state variables of self-adaptive model generation device are indicated； Indicate derivative of two state variables of self-adaptive model generation device about time scale transformation parameter t；For normalizing
Change derivative of the parameter θ about time scale transformation parameter t, indicates the renewal equation of self-adaptive model generation device adaptive frequency
Expression formula；E=e (t) indicates the error of self-adaptive model generation device.
It is further preferred that the step S2 includes the following steps:
S21, the system for taking control system input r=0, and using the systematic error e of control system as adaptive internal model control
The input of device processed, then obtain x1、x2, e can fast convergence be following formula:
Wherein A is constant, and φ is control system in ω0Delay under frequency, AeIt is set as
S22 can be obtained by formula (2), and the adaptive frequency renewal equation of self-adaptive model generation device indicates are as follows:
The adaptive frequency renewal equation of the self-adaptive model generation device is obtained in adaptive with average value theorem
Mould controller it is average after adaptive frequency more new formulaAre as follows:
Wherein,Indicate self-adaptive model generation device it is average after adaptive frequency；T is self-adaptive model generation device
The system period is set as 2 π.
Still more preferably, the step S3 includes the following steps:
S31, wushu (3) substitute into formula (4) and obtain:
When showing that the convergence point of control system is at θ=1, by frequency normalization formula θ=ω (τ)/ω0It can be concluded that control
The convergence point of system processed is i.e. in ω (τ)=ω0Place；
θ=1 is substituted into formula (3), obtained by S32:
It is the output x of 0 and self-adaptive model generation device by the systematic error e that above formula obtains control system1, by adaptive
Answer the output x of internal mode controller1The elimination of uncertain periodic perturbation signal is realized with uncertain periodic perturbation signal cancellation.
The beneficial effects of the present invention are:
1) elimination control method of the invention uses systematic error to pass through frequency as the input of self-adaptive model generation device
More new formula obtains the amplitude and frequency of periodic perturbation, and a signal opposite with uncertain periodic perturbation signal is as adaptive
The output of internal mode controller, so that the accurate elimination of uncertain periodic perturbation signal is realized, so that the systematic error of control system
It is zero.Therefore, the elimination control method in the present invention realizes the elimination of uncertain periodic perturbation, meets the control of control system
System requires.
2) present invention is by obtaining the output x of the self-adaptive model generation device when systematic error e of control system is 01,
While realizing the Eliminating disturbance of uncertain periodic perturbation signal, the amplitude and frequency of uncertain periodic perturbation signal have been obtained,
Uncertain periodic perturbation signal is used for engineer application convenient for the later period.
Detailed description of the invention
Fig. 1 is the schematic diagram of the control system based on self-adaptive model generation device；
Fig. 2 is the input picture of uncertain periodic perturbation signal；
Fig. 3 is the estimation image of uncertain periodic perturbation signal frequency；
Fig. 4 is the estimation image of uncertain periodic perturbation signal amplitude；
Fig. 5 is the error signal of self-adaptive model generation device system.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
As shown in FIG. 1, FIG. 1 is the schematic diagram of the control system of the invention based on self-adaptive model generation device, control systems
System includes the self-adaptive model generation device being connected in parallel and PID controller.
It is below the uncertain periodic perturbation removing method of the invention based on self-adaptive model generation device, including walks as follows
It is rapid:
1, time scale transformation and frequency normalization are carried out to the state-space expression of self-adaptive model generation device, obtained
Expression formula of the self-adaptive model generation device about time scale transformation parameter t；
Specifically include the following steps:
1) state space equation of self-adaptive model generation device indicates are as follows:
Wherein, τ indicates the time variable of self-adaptive model generation device, x1(τ) and x2(τ) indicates self-adaptive model generation device
Two state variables, and x1(τ) is the output of self-adaptive model generation device, and ω (τ) indicates uncertain periodic perturbation signal estimation
The transient value of frequency, e (τ) indicate the systematic error of self-adaptive model generation device, and μ indicates the adjustable ginseng of self-adaptive model generation device
Number, γ are adaptive updates speed adjustable gain；
The expression formula of uncertain periodic perturbation input v is
Wherein a0Indicate the amplitude of uncertain periodic perturbation signal, ω0Indicate the frequency of uncertain periodic perturbation signal,
Indicate the phase of uncertain periodic perturbation signal；
2) it is based on time scale transformation parameterNormalization with self-adaptive model generation device adaptive frequency is joined
Number θ=ω (τ)/ω0Time scale transformation and frequency normalization are carried out to (1) formula, obtain the state of self-adaptive model generation device
Expression formula of the space equation about time scale transformation parameter t:
Wherein, x1=x1(t), x2=x2(t), two state variables of self-adaptive model generation device are indicated； Indicate derivative of two state variables of self-adaptive model generation device about time scale transformation parameter t；For normalizing
Change derivative of the parameter θ about time scale transformation parameter t, indicates the renewal equation of self-adaptive model generation device adaptive frequency
Expression formula；E=e (t) indicates the error of self-adaptive model generation device.
2, using the systematic error e of control system as the input of self-adaptive model generation device, self-adaptive model generation is acquired
Device it is average after frequency more new formula
Specifically include the following steps:
1) system for taking control system inputs r=0, and using the systematic error e of control system as self-adaptive model generation
The input of device, then obtain x1、x2, e can fast convergence be following formula:
Wherein A is constant, and φ is control system in ω0Delay under frequency, AeIt is set as
2) it can be obtained by formula (2), the adaptive frequency renewal equation of self-adaptive model generation device indicates are as follows:
The adaptive frequency renewal equation of the self-adaptive model generation device is obtained in adaptive with average value theorem
Mould controller it is average after adaptive frequency more new formulaAre as follows:
Wherein,Indicate self-adaptive model generation device it is average after adaptive frequency；T is self-adaptive model generation device
The system period is set as 2 π.
3, the frequency more new formula after basis is averageObtain the convergence point of control system, and then obtain control system is
Error e of uniting is the output x of 0 and self-adaptive model generation device1, by the output x of self-adaptive model generation device1With the uncertain period
Disturbing signal offsets the elimination for realizing uncertain periodic perturbation signal.
Specifically include the following steps:
1) wushu (3) substitutes into formula (4) and obtains:
When showing that the convergence point of control system is at θ=1, by frequency normalization formula θ=ω (τ)/ω0It can be concluded that control
The convergence point of system processed is i.e. in ω (τ)=ω0Place；
2) θ=1 is substituted into formula (3), obtained:
It is the output x of 0 and self-adaptive model generation device by the systematic error e that above formula obtains control system1, by adaptive
Answer the output x of internal mode controller1The elimination of uncertain periodic perturbation signal is realized with uncertain periodic perturbation signal cancellation.
Obtaining the output of control system by system input r=0, the systematic error e=0 of control system is 0, i.e., adaptive interior
The output x of mould controller1It is equal with amplitude, the frequency of uncertain periodic perturbation signal, it is contrary；It is not known by above formula
Transient value ω (τ)=ω of the estimation frequency of periodic perturbation signal0And amplitude
Fig. 2 is the input picture of uncertain periodic perturbation signal, and as can be seen from the figure the amplitude of input signal is 1, frequency
Rate takes 20rad/s, the segment cycle signal of 50rad/s, 40rad/s respectively；
Fig. 3 is the estimation image of uncertain periodic perturbation signal frequency, and as can be seen from the figure frequency estimation can be preferably
Converge to true value；
Fig. 4 is the estimation image of uncertain periodic perturbation signal amplitude, and as can be seen from the figure estimated amplitude can be preferable
Converge to true value；
Fig. 5 is the error signal of self-adaptive model generation device system, and as can be seen from the figure systematic error accurate convergence arrives
Zero.
In conclusion the present invention provides a kind of uncertain periodic perturbation elimination side based on self-adaptive model generation device
Method realizes the elimination of uncertain periodic perturbation, while can obtain the amplitude and frequency of uncertain periodic perturbation signal.
Claims (4)
1. a kind of uncertain periodic perturbation removing method based on self-adaptive model generation device, which is characterized in that based on adaptive
The control system of internal mode controller includes the self-adaptive model generation device being connected in parallel and PID controller；Removing method includes such as
Lower step:
S1 carries out time scale transformation and frequency normalization to the state-space expression of self-adaptive model generation device, obtains certainly
Adapt to expression formula of the internal mode controller about time scale transformation parameter t；
S2 acquires self-adaptive model generation device using the systematic error e of control system as the input of self-adaptive model generation device
Frequency more new formula after average
S3, according to the frequency more new formula after being averagedIt obtains the convergence point of control system, and then obtains the error e of control system
For 0 and the output of self-adaptive model generation device, supported by the output and uncertain periodic perturbation signal of self-adaptive model generation device
Disappear and realizes the elimination of uncertain periodic perturbation signal.
2. a kind of uncertain periodic perturbation removing method based on self-adaptive model generation device according to claim 1,
It is characterized in that, the step S1 includes the following steps:
The state space equation of S11, self-adaptive model generation device indicate are as follows:
Wherein, τ indicates the time variable of self-adaptive model generation device, x1(τ) and x2(τ) indicates self-adaptive model generation device two
State variable, and x1(τ) is the output of self-adaptive model generation device, and ω (τ) indicates that uncertain periodic perturbation signal estimates frequency
Transient value, e (τ) indicate self-adaptive model generation device systematic error, μ indicate self-adaptive model generation device adjustable parameter,
γ is adaptive updates speed adjustable gain；
The expression formula of uncertain periodic perturbation input v is
Wherein a0Indicate the amplitude of uncertain periodic perturbation signal, ω0Indicate the frequency of uncertain periodic perturbation signal,It indicates
The phase of uncertain periodic perturbation signal；
S12 is based on time scale transformation parameterWith the normalized parameter of self-adaptive model generation device adaptive frequency
θ=ω (τ)/ω0Time scale transformation and frequency normalization are carried out to (1) formula, the state for obtaining self-adaptive model generation device is empty
Between expression formula of the equation about time scale transformation parameter t:
Wherein, x1=x1(t), x2=x2(t), two state variables of self-adaptive model generation device are indicated；
Indicate derivative of two state variables of self-adaptive model generation device about time scale transformation parameter t；For the pass normalized parameter θ
In the derivative of time scale transformation parameter t, the renewal equation expression formula of self-adaptive model generation device adaptive frequency is indicated；e
=e (t) indicates the error of self-adaptive model generation device.
3. a kind of uncertain periodic perturbation removing method based on self-adaptive model generation device according to claim 2,
It is characterized in that, the step S2 includes the following steps:
S21, the system for taking control system input r=0, and using the systematic error e of control system as self-adaptive model generation device
Input, then obtain x1、x2, e can fast convergence be following formula:
Wherein A is constant, and φ is control system in ω0Delay under frequency, AeIt is set as
S22 can be obtained by formula (2), and the adaptive frequency renewal equation of self-adaptive model generation device indicates are as follows:
Adaptive internal model control is obtained with average value theorem to the adaptive frequency renewal equation of the self-adaptive model generation device
Device processed it is average after adaptive frequency more new formulaAre as follows:
Wherein,Indicate self-adaptive model generation device it is average after adaptive frequency；T is the system of self-adaptive model generation device
Period is set as 2 π.
4. a kind of uncertain periodic perturbation removing method based on self-adaptive model generation device according to claim 3,
It is characterized in that, the step S3 includes the following steps:
S31, wushu (3) substitute into formula (4) and obtain:
When showing that the convergence point of control system is at θ=1, by frequency normalization formula θ=ω (τ)/ω0It can be concluded that control system
The convergence point of system is i.e. in ω (τ)=ω0Place；
θ=1 is substituted into formula (3), obtained by S32:
It is the output x of 0 and self-adaptive model generation device by the systematic error e that above formula obtains control system1, by adaptive internal model
The output x of controller1The elimination of uncertain periodic perturbation signal is realized with uncertain periodic perturbation signal cancellation.
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| CN111310303A (en) * | 2020-01-17 | 2020-06-19 | 合肥工业大学 | Amplitude exponential decay sine wave parameter identification method |
| CN112338914A (en) * | 2020-10-27 | 2021-02-09 | 东北大学 | Single-link manipulator fuzzy control algorithm based on random system under output limitation and input hysteresis |
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Application publication date: 20190906 |