CN101266502B - Random resonance control method based on double resonance - Google Patents
Random resonance control method based on double resonance Download PDFInfo
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- CN101266502B CN101266502B CN2008100609917A CN200810060991A CN101266502B CN 101266502 B CN101266502 B CN 101266502B CN 2008100609917 A CN2008100609917 A CN 2008100609917A CN 200810060991 A CN200810060991 A CN 200810060991A CN 101266502 B CN101266502 B CN 101266502B
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Abstract
The invention discloses a random resonance control method based on double resonance, which nonlinearly couples two single bistable systems to form a coupled system, wherein, one bistable system becomes a controlled system with fixed parameter, and the other is as a control system with adjustable parameter, thereby a random resonance is produced by regulating the control system parameter and the coupling coefficient; a single frequency signal can be additionally added to the control system, the change of the frequency of the signal can allow the control system to generate resonance; as a resultof coupling, the resonance of the control system can affect the random resonance of the controlled system, thereby a double resonance phenomenon is formed in the coupled system, realizing using one resonance to affect another resonance, and allowing the random resonance of the controlled system to be more intense. The method effectively control the generation of the random resonance and the intensity of the generated resonance effect, which is specially adapted for system with system parameters that are fixed or difficult to change.
Description
Technical field
The present invention relates to control technology, especially, relate to a kind of random resonance control method of controlling the accidental resonance effect in the bistable system based on double resonance.
Background technology
Accidental resonance is to cause weak periodic signal and the synergistic non-linear phenomena of nonlinear system with noise as media.It has been described in a certain amount of noise background, and nonlinear system can produce strong output response to faint periodic signal, exists noise energy to the signal energy Transfer Mechanism.Since Benzi in 1981 etc. proposed this notion of accidental resonance, people had had comparatively deep research to the rule of accidental resonance and in the performance of natural science every field.But these researchs are to study accidental resonance from the angle of observing rather than from the angle of influence more, the more important thing is its final purpose of achievement as physicism, always be unable to do without successful application, the control of accidental resonance then is accidental resonance key in application link.Accidental resonance control or control accidental resonance are exactly on purpose to strengthen or the generation accidental resonance by control device, thereby produce needed output response with special properties.The most direct a kind of method of control accidental resonance is to change systematic parameter, makes system produce accidental resonance under given noise and signal effect or makes the resonance effects of its generation stronger.Yet, in actual applications, the periodic signal of input and noise are that given, its parameter is unmodifiable, and the structural parameters of nonlinear system are often also fixed, it is difficulty or impossible perhaps will changing its relevant barrier height or threshold value, such as neurocyte, integrated circuit etc.
Summary of the invention
At the problems referred to above, the purpose of this invention is to provide a kind of random resonance control method based on double resonance.Resonance, coupling are combined with the accidental resonance principle, proposed control method based on the bistable system accidental resonance of double resonance.This method is coupled system with two single bistable systems through non-linear being coupled to form, one of them bistable system is used as the fixing controlled system of parameter, another is then as the adjustable control system of parameter, can produce accidental resonance by the parameter of regulating coupling coefficient and control system. add single-frequency signals to control system, changing its frequency size can make control system produce resonance. because the effect of coupling, the resonance of control system will influence the accidental resonance of controlled system, thereby form double resonance phenomenon in coupled system, realized going to influence another resonance, and can make the accidental resonance of controlled system stronger with a resonance.This method is controlled the generation of accidental resonance and the resonance effects intensity size that is produced effectively, is specially adapted to the system that systematic parameter is fixed or is difficult to change.
The objective of the invention is to be achieved through the following technical solutions: a kind of random resonance control method based on double resonance, concrete steps are as follows:
(1) signal and noise are introduced controlled system, produce output signal through this controlled system, described controlled system is a preset parameter bistable system.
(2) controlled system and another control system are done non-linear coupling, the output after coupling affacts controlled system once more with original signal and noise; By the may command coupling coefficient of adjusting coupling terms and the systematic parameter of control system, make controlled system under signal, noise acting in conjunction, accidental resonance take place; Described control system is a changeable parameters bistable system.
(3) add the single-frequency signals input to control system, the frequency size that changes simple signal makes control system produce resonance; Because the effect of coupling, the resonance of control system will influence the accidental resonance of controlled system, form double resonance, thereby realize accidental resonance control.
Further, described step (1) is implemented as follows: signal S (t)=Acos (ω t) and noise ξ (t) as input item, are input to the controlled system of preset parameter
Wherein, a
0And b
0It is the intrinsic unmodifiable parameter of bistable system; Signal S (t) in the practical application and noise ξ (t) are generally uncontrollable, and what obtain through the preset parameter bistable system is uncontrollable output signal.
Described step (2) is implemented as follows: with controlled system and control system
Output signal be input to the coupling unit jointly and do non-linear coupling, coupling coefficient is γ; Wherein, a is the controllable parameter of bistable system; The output of coupling unit is input to controlled system once more with signal S (t), noise ξ (t); Regulate the systematic parameter a of coupling coefficient γ and control system, make the interaction of controlled system, the collaborative accidental resonance that produces at signal and noise.
Described step (3) is implemented as follows: give control system
Add single-frequency signals input Bcos (Ω t+ φ), the frequency size of change simple signal equals Ω or near 2 ω, the intrinsic vibration of effect that add this moment and system is in step with, and will produce resonance in control system; The resonance of control system will influence the accidental resonance of controlled system, form double resonance, thereby realize accidental resonance control.
The invention has the beneficial effects as follows that the present invention utilizes the double resonance phenomenon in the coupled system, realize going to influence another resonance, reach the purpose that the accidental resonance of controlled system is controlled with a resonance.Make control system produce resonance by changing the frequency size that the control bistable system adds single-frequency signals, the resonance of control system influence the accidental resonance of controlled system, finally formation double resonance phenomenon in coupled system through coupling.The accidental resonance of controlled system and the resonance of control system influence each other, and have realized going to influence another resonance with a resonance, and can control the accidental resonance of controlled system effectively.This method is controlled the generation of accidental resonance and the resonance effects intensity size that is produced effectively, is specially adapted to the system that systematic parameter is fixed or is difficult to change.This method has enlarged the may command ability of accidental resonance control, and can greatly widen the range of application of accidental resonance, has a good application prospect.
Description of drawings
The time domain waveform figure that accompanying drawing 2 only fluctuates in single potential well for x (t),
The power spectrum chart that accompanying drawing 3 only fluctuates in single potential well for x (t),
Accompanying drawing 4 is γ=0.35 o'clock, the time waveform figure of two variable x of coupled system (t) and y (t),
Accompanying drawing 5 is γ=0.35 o'clock, the power spectrum chart of the x of coupled system (t),
Accompanying drawing 6 is theoretical waveform and the simulation waveform figure of coupled system variable y (t),
Accompanying drawing 7 is the time waveform and outer actuating signal oscillogram of coupled system variable y (t) under the double resonance control,
Accompanying drawing 8 is two variable x (t) of coupled system under the two-frequency signal effect and the time waveform figure of y (t),
Accompanying drawing 9 is the power spectrum chart of the x (t) of coupled system under the two-frequency signal effect.
Embodiment
The whole control structure of the present invention mainly is made up of signal input part, controlled bistable system, the control bistable system that adds simple signal and coupling unit four bulks, and its theory diagram as shown in Figure 1.Signal S (t)=Acos (ω t) and noise ξ (t) as input item, are input to controlled bistable system
(a
0And b
0Be the intrinsic unmodifiable parameter of bistable system).With controlled bistable system and control bistable system
The output signal of (a is the controllable parameter of bistable system) is input to the coupling unit jointly and does non-linear coupling, and coupling coefficient is γ.The output of coupling unit is input to controlled bistable system once more with signal S (t), noise ξ (t).The variation of the systematic parameter a of coupling coefficient γ and control bistable system will make the barrier height of system and Kramers escapement ratio change, thereby influence the inherent characteristic of controlled bistable system, the interaction of system, signal and noise is worked in coordination with and the generation accidental resonance through suitable adjusting.Give the control bistable system again
Add single-frequency signals input Bcos (Ω t+ φ), the frequency size Ω of change simple signal equals Ω or near 2 ω, the intrinsic vibration of effect that add this moment and system is in step with, and will produce resonance in control system.The resonance of control system will influence the accidental resonance of controlled system, form double resonance, reach the purpose of accidental resonance control.The available following coupled wave equation of relation in the control procedure between each variable and the parameter is represented
By the following examples content of the present invention is done further explanation.Adopt Coupling Control and double resonance control method that the Stochastic Resonance Phenomenon of controlled system is studied respectively.At first, if the parameter a of controlled system
0=0.5, b
0=1, as the periodic signal amplitude A=0.05 that affacts controlled system, frequencies omega=2 π 0.01, during noise intensity D=0.18, owing to the too high x of controlled system barrier height (t) can only fluctuate in a potential well, as shown in Figure 2, because Satisfying Matching Conditions and can not produce accidental resonance not between controlled system and input signal, the noise, also can't realize the energy conversion between noise and the signal, x (t) is very little in the power spectral value at frequency input signal place, has only P
s(2 π 0.01)=0.0011, as shown in Figure 3.Adopt coupling process, setup parameter a=1 can make system produce accidental resonance by regulating coupling coefficient γ, is illustrated in figure 4 as γ=0.35 o'clock, the time waveform of two variable x of coupled system (t) and y (t), and as seen y (t) is being slightly less than
Near make fuctuation within a narrow range, and x (t) vibrated between two potential wells round x=0 o'clock, power spectrum significantly amplifies, P
sFig. 5 is seen in (2 π 0.01)=0.1205.This moment y (t) and＜y (t) curve as shown in Figure 6, dotted line is simulation curve (being the amplification of y among Fig. 4 (t)) among the figure, the solid line theoretical curve.When adopting mode shown in Figure 1 to add single-frequency signals, B parameter=0.3, Ω=2 ω=0.02,
The time, the effect of adding is synchronous with y (t), and control system reaches resonance.As shown in Figure 7, solid line is that outer actuating signal, dotted line are y (t).Illustrate that the resonance of control system has greatly influenced the accidental resonance of controlled system.As Fig. 8, shown in Figure 9, signal to noise ratio (S/N ratio) and the power spectrum of coupled system output x (t) obviously increase P
s(2 π 0.01)=0.1930, output signal x (t) has higher quality.Simulation result shows, exists the double resonance phenomenon in coupled system, and can make accidental resonance stronger.As seen, the double resonance of coupled system has strengthened the accidental resonance effect of controlled system greatly, can reach the unapproachable degree of single resonance, can make faint effect produce significant more effect, and help people to obtain more information.
Claims (3)
1. random resonance control method based on double resonance is characterized in that concrete steps are as follows:
(1) signal and noise are introduced controlled system, produce output signal through this controlled system, described controlled system is a preset parameter bistable system;
(2) controlled system and another control system are done non-linear coupling, the output after coupling affacts controlled system once more with original signal and noise; By the may command coupling coefficient of adjusting coupling terms and the systematic parameter of control system, make controlled system under signal, noise acting in conjunction, accidental resonance take place; Described control system is a changeable parameters bistable system;
(3) add the single-frequency signals input to control system, the frequency size that changes simple signal makes control system produce resonance; Because the effect of coupling, the resonance of control system will influence the accidental resonance of controlled system, form double resonance, thereby realize accidental resonance control.
2. the random resonance control method based on double resonance according to claim 1, it is characterized in that, described step (1) is implemented as follows: signal S (t)=Acos (ω t) and noise ξ (t) as input item, are input to the controlled system x=a of preset parameter
0X-b
0x
3, wherein, a
0And b
0It is the intrinsic unmodifiable parameter of bistable system; Signal S (t) in the practical application and noise ξ (t) are generally uncontrollable, and what obtain through the preset parameter bistable system is uncontrollable output signal.
3. the random resonance control method based on double resonance according to claim 2 is characterized in that, described step (2) is implemented as follows: with controlled system and control system y=ay-y
3Output signal be input to the coupling unit jointly and do non-linear coupling, coupling coefficient is γ; Wherein, a is the controllable parameter of bistable system; The output of coupling unit is input to controlled system once more with signal S (t), noise ξ (t); Regulate the systematic parameter a of coupling coefficient γ and control system, make the interaction of controlled system, the collaborative accidental resonance that produces at signal and noise.
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| CN102147265B (en) * | 2011-01-14 | 2012-06-13 | 华中科技大学 | Precise sensor-measuring method for low frequency signal by utilizing noise nonlinear effect |
| CN106706320B (en) * | 2016-12-27 | 2018-12-04 | 中国计量大学 | A kind of Bearing Initial Fault Diagnosis method based on feedforward control accidental resonance |
| CN106500779B (en) * | 2016-12-27 | 2023-04-18 | 中国计量大学 | Vortex street signal detection device with feedforward controller and stochastic resonance |
| CN106840281B (en) * | 2016-12-27 | 2019-05-14 | 中国计量大学 | A kind of vortex street frequency detection method based on class square wave feedforward control accidental resonance |
| CN112034899B (en) * | 2019-06-04 | 2021-07-23 | 湖南中烟工业有限责任公司 | Ultrasonic atomization sheet oscillation control method and control system |
| CN110705128A (en) * | 2019-10-25 | 2020-01-17 | 陕西师范大学 | Parameter-adjustable stochastic resonance simulation system |
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| US5568096A (en) * | 1995-04-19 | 1996-10-22 | Telefonaktiebolaget Lm Ericsson | Apparatus and method for using negative FM feedback in high quality oscillator devices |
| CN1595180A (en) * | 2004-07-09 | 2005-03-16 | 天津大学 | Frequency self-tracing dimension-variation stochastic resonance fault diagnosis system |
| CN1710804A (en) * | 2004-06-18 | 2005-12-21 | 罗姆股份有限公司 | Oscillator |
| US20070171964A1 (en) * | 2005-10-20 | 2007-07-26 | Syracuse University | Optimized Stochastic Resonance Method for Signal Detection and Image Processing |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5568096A (en) * | 1995-04-19 | 1996-10-22 | Telefonaktiebolaget Lm Ericsson | Apparatus and method for using negative FM feedback in high quality oscillator devices |
| CN1710804A (en) * | 2004-06-18 | 2005-12-21 | 罗姆股份有限公司 | Oscillator |
| CN1595180A (en) * | 2004-07-09 | 2005-03-16 | 天津大学 | Frequency self-tracing dimension-variation stochastic resonance fault diagnosis system |
| US20070171964A1 (en) * | 2005-10-20 | 2007-07-26 | Syracuse University | Optimized Stochastic Resonance Method for Signal Detection and Image Processing |
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