CN101789860A - Chaotic signal generator - Google Patents

Abstract

The invention relates to a chaotic signal generator which comprises a micro control unit, a magnetic coupling isolating circuit and a D/A converting circuit, wherein the micro control unit comprises a plurality of groups of signal output interfaces, and one group of the signal output interfaces is used for outputting a one-dimensional digital voltage signal; the signal output interfaces are sequentially connected with the magnetic coupling isolating circuit and the D/A converting circuit; a plurality of voltage signal output of the D/A converting circuit form a multi-dimensional analog voltage signal output; and the multi-dimensional analog voltage signal is a chaotic signal. The chaotic signal generator can output phase rail maps of chaotic or hyperchaotic attractors based on different chaotic systems with different types of single scroll, double scroll, multiple scroll, multiple wing, grid scroll, and the like and time domain waveforms of the signals corresponding to different state variables.

Description

Chaotic signal generator

Technical field

The present invention relates to a kind of chaotic signal generator.

Background technology

Because randomlikeness, the continuous wide band power spectrum characteristic of chaotic signal, be easy to produce, be difficult to by time domain commonly used and frequency domain handle predict with separate, chaos system intrinsic characteristics such as sensitive dependence to initial condition, make chaotic signal be specially adapted to fields such as secure communication (particularly military communication) and information encryption, the chaotic oscillating circuit of therefore realizing having different chaotic characteristics is focus that the researcher paid close attention to for a long time.

Realize the research angle analysis from the circuit of chaotic signal generator, mainly be divided into two classes, a class is to utilize discrete components and parts such as operational amplifier, resistance and electric capacity to form separately independently functional module to connect to form breadboardin hardware and realize; Another kind of then is that the digital processing chips such as the ultra-large FPGA of employing, DSP that rose are in recent years changed output forming circuit Digital Implementation through D/A.

Because the discreteness of discrete component is bigger, bring certain difficulty to circuit design and debugging, and only corresponding to certain Special Chaotic System, the circuit versatility is poor, is unfavorable for promotion and application.Along with evolution of embedded technology, existing document adopts digital processing technology, to continuous time the dimensionless state equation carry out discretization and handle, realized grid scrollwork Cai Shi chaos attractor with the FPGA technology; Also have document based on Digital Signal Processing DSP Builder, produce chaotic signal with the FPGA technology.Because FPGA need consume a large amount of hardware resources when realizing, in order to guarantee the precision of algorithm, can only satisfy some better simply chaotic signals.

Summary of the invention

Technical problem to be solved by this invention provide a kind of simple in structure, can timing controlled operating time of power consumption equipment and the chaotic signal generator of period.

For solving the problems of the technologies described above, the invention provides a kind of chaotic signal generator, comprising: micro-control unit, magnetic coupling buffer circuit and D/A change-over circuit; Micro-control unit comprises many group signal output interfaces, and one group of signal output interface is used to export the one dimension digital voltage signal; Each group group signal output interface is connected with magnetic coupling buffer circuit and D/A change-over circuit in turn; The voltage signal output of a plurality of D/A change-over circuits constitutes the output of multidimensional simulation voltage signal, and this multidimensional simulation voltage signal is chaotic signal; The multidimensional digital voltage signal of micro-control unit output, be that a four-dimensional grid scrollwork hyperchaotic system that obtains based on three rank single scroll chaotic Colpitts oscillator model is carried out drawing after discretization is handled, or modified model Colpitts oscillator model carried out drawing after discretization is handled, or modified model Generalized Lorenz system carried out drawing after discretization is handled.The present invention adopts MCU to realize the general chaos and the digital circuit of hyperchaos signal, by programming sequential is controlled.This circuit highly versatile is not subjected to the restriction of hardware resource, and software portability is good, can produce dissimilar chaos and hyperchaos signals such as single scrollwork, two scrollwork, many scrollworks, multiple wing and grid scrollwork.

Further, described each group group signal output interface comprises: control signal output ends, clock signal output terminal and digital signal serial output terminal.

Further, described D/A change-over circuit has been selected 16 figure place weighted-voltage D/A converter spares based on ∑-Δ structure for use.

Further, the voltage signal output end of described D/A change-over circuit is provided with in-phase amplification circuit.

Further, be connected with on the described micro-control unit and be used to control the parameter selector switch of respectively organizing signal output interface output chaos or hyperchaos signal.

The present invention has positive effect: (1) the present invention is based on microcontroller (MCU) and has designed a general chaotic signal generator, it carries out the Digital Discrete processing by adopting the Euler algorithm to the chaos or the hyperchaotic system of different dimensions, and select the linear-scale conversion ratio of suitable system state variables, work out out program based on MCU, exportable single scrollwork with the C language based on different chaos systems, two scrollworks, many scrollworks, multiple wing and dissimilar chaos or the figure of rail mutually of hyperchaos attractor and the time domain waveforms of corresponding different conditions variable signal such as grid scrollwork.(2) the present invention is based on the digital circuit that microcontroller has designed general chaotic signal generator, adopt the Euler algorithm to carry out the discretization processing to each chaos and hyperchaotic system, and can on this circuit, realize the chaos and the hyperchaos attractor of dissimilar scrollworks (wing) by programming simultaneously.Based on the implementation method of MCU Digital Implementation chaos circuit, and the discretization of general continuous chaotic system handled thinking, also extend in the digitizer design of other chaos system and go.Realize sequencing control by software programming, its hardware circuit not only has versatility, and software design thinking portable, has stronger operability and realizability, for the generation and the control of chaotic signal has proposed a kind of new approaches, potential future in engineering applications is arranged.

Description of drawings

For the easier quilt of content of the present invention is clearly understood, below the specific embodiment and in conjunction with the accompanying drawings of basis, the present invention is further detailed explanation, wherein

Fig. 1 is the circuit theory diagrams based on the grid scrollwork hyperchaos circuit of MCU among the embodiment;

Fig. 2 be among the embodiment when K=3 the sawtooth waveforms function f _KCurve chart (ξ);

Fig. 3 is for adopting the Euler algorithm to carry out the flow chart that discretization is handled to four-dimensional grid scrollwork hyperchaotic system among the embodiment;

Fig. 4 (a) and (b) are 9 * 7 grid scroll chaotic attractors among the embodiment

Fig. 5 (a) and (b) are 9 * 7 grid scrollwork hyperchaos attractors among the embodiment;

Fig. 6 (a) and (b) are 7 scroll chaotic attractors among the embodiment;

Fig. 7 (a) and (b) are the folding chaos attractor of the class Lorenz system among the embodiment;

Fig. 8 (a) and (b) are the folding chaos attractor of the class Chen system among the embodiment;

Fig. 9 (a) and (b) are the folding chaos attractor of the class L ü system among the embodiment;

Figure 10 is the multiple-pulse function when M=3 among the embodiment;

Figure 11 (a) and (b), (c), (d) are the butterfly-like chaos attractor of multiple wing among the embodiment.

Embodiment

See Fig. 1-11, the chaotic signal generator of present embodiment, be designed to example with four-dimensional grid scrollwork hyperchaos signal generator, mainly comprise as shown in Figure 1 based on the hard-wired schematic diagram of microcontroller (MCU): micro controller unit, magnetic coupling buffer circuit, D/A change-over circuit etc.; Four paths modularized designs are programmed to Flash in the MCU sheet by jtag interface, realize x, y, z, the four-dimensional voltage signal output of w.Acp chip MCU adopts AVR microcontroller device ATmega128L, under the effect of timer internal module, by software control PB0～PB2, PD0～PD2, PE0～PE2, PF0～PF2 interface, output SPI clock signal is set up data link with four road D/A change-over circuits.PB0, PD0, PE0, PF0 export control signal, PB1, PD1, PE1, PF1 clock signal, PB2, PD2, PE2, PF2 serial output digital signal.

The D/A change-over circuit has been selected the 16 figure place weighted-voltage D/A converter spares (model is AD420) based on ∑-Δ structure for use, and it has the SPI serial communication interface, joins by LATCH port, CLOCK port, DATA IN port and microcontroller, and maximum rate can reach 3.3Mb/s.The LATCH end is the internal buffer memory control input end, the CLOCK end is input end of clock, the DATAIN end is the serial digital signal input. when LATCH end control signal is effective, trigger by CLOCK end clock, the AD420 internal buffer memory is receiving digital signals continuously, realize continual and steady analog quantity output, be very suitable for the high accuracy tele-control system.

In order to improve the reliability of system, suppress mutual interference mutually between digital signal and the analog signal, between microcontroller and D/A change-over circuit, be provided with the digital signal channel isolation, it adopts the magnetic coupling digital isolator (model is ADUM1410) based on the chip-scale transformer, compare with traditional photoelectrical coupler (as TLP521 series), because the magnetic coupling isolator has been cancelled and has been influenced the opto-electronic conversion of conversion efficiency link, therefore its power consumption only is 1/10～1/60 of a photoelectrical coupler, improved the stability of current delivery, reduced the nonlinear distortion of signal transmission, pulse-width distortion＜3ns and have the direct current calibration function, has higher message transmission rate than photoelectrical coupler, time sequence precision and transient state common mode inhibition capacity have guaranteed the stability of D/A change-over circuit output analog signal.

See Fig. 1, the D/A change-over circuit has adopted the voltage mode design, the voltage output range of VOUT end be 0V～+ 5V.In order in experiment, to obtain wideer voltage dynamic range, increased the one-level in-phase amplification circuit, the model that the OP1-4 operational amplifier among Fig. 1 is selected for use is TL082, and resistance R is got 5k Ω, can obtain 2 times voltage gain, the output voltage dynamic range be extended to 0V ~+10V.

SW is the parameter selector switch, pull-up resistor R ₁Get 1k Ω, when SW is in ON or OFF position, PG3 port input low level or high level.Judge the PG3 logic state by software, select different Control Parameter, realize the output of chaos or hyperchaos signal.

Being achieved as follows of four-dimensional grid scroll chaotic and the output of hyperchaos signal:

1). system model

Obtained a four-dimensional grid scrollwork hyperchaotic system based on three rank single scroll chaotic Colpitts oscillator model, its state equation is expressed as:

$\left\{\begin{array}{c}\stackrel{\·}{x}=\mathrm{\μ}[z-f_M\left(y\right)],\\ \stackrel{\·}{y}=\mathrm{\μ}[z+f_N\left(w\right)],\\ \stackrel{\·}{z}=-0.5(x+y)/\mathrm{\μ}-z,\\ \stackrel{\·}{w}=x+y,\end{array}\right.---\left(1\right)$

Control Parameter μ＞0 wherein, M and N are positive integer, f _M(y) and f _N(w) be two sawtooth waveforms functions with unit amplitude and unit frequency of oscillation. can utilize f _K(ξ) unified expression f _M(y) and f _N(w), its mathematical notation formula is

$f_K\left(\mathrm{\ξ}\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\left\{\mathrm{sgn}\right[\mathrm{\ξ}+(k-0.5)]+\mathrm{sgn}[\mathrm{\ξ}-(k-0.5)\left]\right\}-2\mathrm{\ξ},---\left(2\right)$

K is a positive integer in the formula.Fig. 2 has provided K=3 time unit sawtooth waveforms function f _KCurve legend (ξ) can be easy to determine the characteristic of each linearity range, as slope and zero point from Fig. 2.

2). Digital Realization

Before the said system model is carried out Digital Implementation, need carry out discretization to it and handle.Three kinds of discretization methods are arranged usually, i.e. Euler algorithm, improved Euler algorithm and Runge-Kutta method, the method for these three kinds of discretizations respectively has pluses and minuses, and wherein Runge-Kutta method precision is higher.Here the simplest discretization method of our employings is the discretization processing that the Euler algorithm carries out system (1), obtains

$\left\{\begin{array}{c}{x}_{n+1}=\mathrm{h\μ}[z_n-f_M\left(y_n\right)]+x_n,\\ y_{n+1}=\mathrm{h\μ}[z_n+f_N\left(w_n\right)]+y_n,\\ z_{n+1}=h[-0.5(x_n+y_n)/\mathrm{\μ}-z_n]+z_n,\\ w_{n+1}=h(x_n+y_n)+w_n,\end{array}\right.---\left(3\right)$

Wherein h is the sampling interval, and has

$f_K\left({\mathrm{\ξ}}_n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\left\{\mathrm{sgn}\right[{\mathrm{\ξ}}_n+(k-0.5)]+\mathrm{sgn}[{\mathrm{\ξ}}_n-(k-0.5)\left]\right\}-2{\mathrm{\ξ}}_n,---\left(4\right)$

According to above-mentioned discretization system (3), can design program with the C language based on MCU, its program flow diagram is as shown in Figure 3. and h gets 0.05 in the program, and n is an iterations, and the value of μ is by the state decision of parameter selector switch SW.μ=0.5 o'clock is output as chaos attractor, and μ=1 o'clock is output as the hyperchaos attractor.Evaluation in the program adopts floating number, because result of calculation only need be preserved the n time and n+1 correlations value, so microcontroller SRAM space is not subjected to the restriction of iterations n, promptly system hardware resources is not influenced by n.

3). experimental observation

Select sawtooth waveforms parameter M=4 and N=3, but adopt the experimental observation of Agilent DSO7032A digital oscilloscope to the figure of rail mutually of discretization system (3), respectively as shown in Figure 4 and Figure 5 on x-w plane and y-w plane.Fig. 4 shows is the experiment output of 9 * 7 grid scroll chaotic attractors on x-w plane and y-w plane of μ=0.5 o'clock, is the experiment output of 9 * 7 grid scrollwork hyperchaos attractors on x-w plane and y-w plane of μ=1 o'clock and Fig. 5 shows.

The chaotic signal output of other type

1). many scrollworks Colpitts chaos system

Based on Colpitts oscillator model, modified model Colpitts oscillator model can be expressed as

$\left\{\begin{array}{c}\stackrel{\·}{x}=a[y+z],\\ \stackrel{\·}{y}=-a{s}_K\left(z\right),\\ \stackrel{\·}{z}=-0.5(x+y)/a-\mathrm{bz},\end{array}\right.---\left(5\right)$

Control Parameter a and b are arithmetic number in the formula, s _K(z) be that a sawtooth waveforms function with unit amplitude and unit frequency of oscillation comes, the mathematical notation formula is

$s_K\left(z\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\left\{\mathrm{sgn}\right[z+(k-0.5)]+\mathrm{sgn}[z-(k-0.5)\left]\right\}-2z.---\left(6\right)$

Wherein K is a positive integer.

Corresponding discretization system is

$\left\{\begin{array}{c}{x}_{n+1}=\mathrm{ha}[y_n+z_n]+x_n,\\ y_{n+1}=-h{\mathrm{as}}_K\left(z_n\right)+y_n,\\ z_{n+1}=h[-0.5(x_n+y_n)/a-{\mathrm{bz}}_n]+z_n,\end{array}\right.---\left(7\right)$

Wherein h is the sampling interval, and n is an iterations, and has

$s_K\left(z_n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\left\{\mathrm{sgn}\right[z_n+(k-0.5)]+\mathrm{sgn}[z_n-(k-0.5)\left]\right\}-2z_n.---\left(8\right)$

According to above-mentioned discretization system (7), can work out out the program of moving based on the MCU chip with the C language.Three state variables are composed initial values (0.5,0.5,0.5) in the program, and h gets 0.05, preset parameter a=0.6 and b=0.2, based on the experiment output of the multi-scroll chaotic system of MCU Digital Implementation as shown in Figure 6.

2). modified model Generalized Lorenz system

Modified model Generalized Lorenz system, its mathematic(al) representation is as follows:

Wherein, x=[x y z] ^T, λ ₃∈ R, and A is one 2 * 2 real matrix

$A=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right),---\left(10\right)$

Its characteristic root λ ₁, λ ₂∈ R, and have-λ ₂＞λ ₁＞-λ ₃＞0.Here, a ₂₃Be called folding factor, it can cause the chaos attractor generation of system (9) folding, and its folding direction depends on a ₂₃The distinct symbols value.

According to a in (10) formula _ra ₂₁,

With

System has provided classification to the autonomous Generalized Lorenz of three-dimensional.According to its sorting technique, can carry out respective classified to system (9), be called class Lorenz, class Chen and class L ü chaos system, wherein class Lorenz system satisfies: a ₁₂a ₂₁＞0; Class Chen system satisfies: a ₁₂a ₂₁＜0; Class L ü system satisfies: a ₁₂a ₂₁=0.Similarly, exist

With Under the meaning, class Chen system is the dual system of class Lorenz system, and class L ü system has then represented the conversion between class Lorenz system and the class Chen system.

At first three state variables in (9) formula are done the linear-scale conversion of same ratio, correspondingly narrowed down to 1/10 of original dynamic amplitude, then (9) formula is carried out discretization and handle, obtain

X wherein _x=[x _xy _xz _x] ^T, h is the sampling interval, n is an iterations.

According to above-mentioned discretization system (11), can work out out the program of moving based on the MCU chip with the C language.Three state variables are composed initial value (1,1,1) in the program, and h gets 0.002, gives (10) formula different parameter values, can obtain exporting respectively as Fig. 7, Fig. 8 and shown in Figure 9 based on the experiment of modified model Generalized Lorenz system on the x-z plane of MCU Digital Implementation.Here, Fig. 7 is pairing to be class Lorenz system, and canonical parameter is a ₁₁=-a ₁₂=-10, a ₂₁=44, a ₂₂=-1 and λ ₃=8/3; Fig. 8 is pairing to be class Chen system, and canonical parameter is a ₁₁=-a ₁₂=-35, a ₂₁=-6, a ₂₂=29 and λ ₃=3; Fig. 9 is pairing to be class L ü system, and canonical parameter is a ₁₁=-a ₁₂=-36, a ₂₁=0, a ₂₂=27.5 and λ ₃=3.

The experimental result explanation of Fig. 7, Fig. 8 and Fig. 9: modified model Generalized Lorenz system can generate folding attractor of complicated two scrollworks and the folding attractor of single scrollwork, and its folding direction can be switched by the symbol of folding factor.

3). multiple wing L ü system

Chaos L ü system belongs to a connected system in family of Lorenz system, the chaos attractor that is produced has typical butterfly-like topological structure.By introducing a multiple-pulse function, the differential equation of L ü system becomes

$\left\{\begin{array}{c}\stackrel{\·}{x}=a(y-x),\\ \stackrel{\·}{y}=\mathrm{cy}-20xz,\\ \stackrel{\·}{z}=20\mathrm{xy}-\mathrm{bz}+\mathrm{Ap}\left(x\right),\end{array}\right.---\left(12\right)$

Here the amplitude of all variablees can be dwindled by following linear transformation in the system (1):

(x，y，z)→(20x，20y，20z)， (13)

And p (x) is a multiple-pulse function, and it is made up of several pulses, definition:

$p\left(x\right)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{p}_i\left(x\right)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}[\mathrm{sgn}(x+B_i)-\mathrm{sgn}(x-B_i)-2].---\left(14\right)$

M is a positive integer in the formula, p _i(x) be i pulse function, have width 2B _iWith amplitude 2.The example of multiple-pulse function when Figure 10 shows M=3.

Corresponding discretization system is

$\left\{\begin{array}{c}{x}_{n+1}=\mathrm{ha}(y_n-x_n)+x_n,\\ y_{n+1}=h({\mathrm{cy}}_n-20x_n{z}_n)+y_n,\\ z_{n+1}=h[20x_n{y}_n-{\mathrm{bz}}_n+\mathrm{Ap}\left(x_n\right)]+z_n,\end{array}\right.---\left(15\right)$

Wherein h is the sampling interval, and n is an iterations, and has

$p\left(x_n\right)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{p}_i\left(x_n\right)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}[\mathrm{sgn}(x_n+B_i)-\mathrm{sgn}(x_n-B_i)-2].---\left(16\right)$

According to above-mentioned discretization system (15), can work out out the program of moving based on the MCU chip with the C language.Three state variables are composed initial value (0.3,0.3,0) in the program, and h gets 0.0001, and selective system parameter a=36, b=3 and c=20 select multiple-pulse function parameter A=8, B simultaneously ₁=0.8, B ₂=1.17, B ₃=1.46, B ₄=1.7.Based on the experiment output of the multiple wing chaos system of four wings, six wings, eight wings and the butterfly-like attractor of ten wings of MCU Digital Implementation as shown in figure 11, four results correspond respectively to p (x) and are made up of 1 ~ 4 pulse function here.

The foregoing description only is for example of the present invention clearly is described, and is not to be qualification to embodiments of the present invention.For those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.Here need not also can't give exhaustive to all execution modes.

Claims (5)

1. a chaotic signal generator is characterized in that comprising: micro-control unit, magnetic coupling buffer circuit and D/A change-over circuit;

Micro-control unit comprises many group signal output interfaces, and one group of signal output interface is used to export the one dimension digital voltage signal; Each group group signal output interface is connected with magnetic coupling buffer circuit and D/A change-over circuit in turn;

The voltage signal output of a plurality of D/A change-over circuits constitutes the output of multidimensional simulation voltage signal, and this multidimensional simulation voltage signal is chaotic signal;

The multidimensional digital voltage signal of micro-control unit output, be that a four-dimensional grid scrollwork hyperchaotic system that obtains based on three rank single scroll chaotic Colpitts oscillator model is carried out drawing after discretization is handled, or modified model Colpitts oscillator model carried out drawing after discretization is handled, or modified model Generalized Lorenz system carried out drawing after discretization is handled.

2. chaotic signal generator according to claim 1 is characterized in that: described each group group signal output interface comprises: control signal output ends, clock signal output terminal and digital signal serial output terminal;

The signal of described control signal output ends, clock signal output terminal and the output of digital signal serial output terminal links to each other with LATCH port, CLOCK port, DATA IN port in the D/A change-over circuit respectively after magnetic coupling is isolated.

3. chaotic signal generator according to claim 1 is characterized in that: described D/A change-over circuit has been selected 16 figure place weighted-voltage D/A converter spares based on ∑-Δ structure for use.

4. chaotic signal generator according to claim 1 is characterized in that: the voltage signal output end of described D/A change-over circuit is provided with in-phase amplification circuit.

5. chaotic signal generator according to claim 1 is characterized in that: be connected with on the described micro-control unit to be used to control and respectively organize the parameter selector switch that signal output interface is exported chaos or hyperchaos signal.

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