CN112987081B - Analog circuit of unidirectional coupling fractional order self-sustaining electromechanical seismometer system - Google Patents
Analog circuit of unidirectional coupling fractional order self-sustaining electromechanical seismometer system Download PDFInfo
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Abstract
The invention relates to an analog circuit of a unidirectional coupling fractional order self-sustaining electromechanical seismometer system, and belongs to the technical field of seismometer system control. The analog circuit includes: the driving system circuit and the response system circuit are connected through a coupling term circuit; the driving system circuit and the response system circuit respectively include: an external harmonic excitation signal, two voltage summing circuits, four fractional order proportional integral equivalent operational amplifier circuits, four inverse proportional operational amplifier circuits and three multiplier sections. The circuit can accurately describe the dynamic characteristics of the seismometer system, improves the degree of freedom of design, and realizes fractional order characteristics; and the observation result of the analog circuit is highly consistent with the dynamic analysis result.
Description
Technical Field
The invention belongs to the technical field of seismometer system control, and relates to an analog circuit of a unidirectional coupling fractional order self-sustaining electromechanical seismometer system.
Background
A self-contained electromechanical seismometer system with complex dynamic characteristics belongs to a sensitive instrument which can record ground motion and waves propagated at a certain frequency. The research of the multi-stability, chaotic oscillation, abrupt jump, attraction and other nonlinear dynamics under different working conditions has important practical significance. The fractional order modeling can describe the real motion process of the engineering object more accurately than the integer order modeling. In view of the advantages of simple implementation, easy modeling and the like of the analog circuit, it is necessary to construct an analog experimental circuit to verify the results of the kinetic analysis.
So far, only sporadic references report such seismic recording systems, while they focus mainly on chaotic control. Siewe et al first discuss nonlinear dynamics in a multi-scale approach and control the chaos of the seismometer system through damping. They then apply the melnikov theory to suppress instability of this system. Hegaz investigated the nonlinear oscillations of seismometer systems using a multiscale method. However, their work is limited to integer order models of seismometer systems and does not reflect the operation of the system well. Meanwhile, the chaotic control method is highly dependent on accurate mathematical modeling, which is impractical in practical applications. Furthermore, equivalent analog circuits and experimental analysis around the seismometer dynamics are not involved. In view of this, many researchers have adopted electronic analog circuits with high response speed and good reproducibility to verify the numerical study of chaotic systems. Autonomous circuits and map electronics have been proposed to reveal various non-linear behaviors. However, both of these methods are difficult to apply to complex dynamic systems because the integrating op-amp and the inverting proportional op-amp are not considered. To address the above limitations, elsaminom et al constructed a new 4D system circuit, and saminom and samilan designed an analog circuit for the dufin mems resonator. They do not address the difficulties of electromagnetic interference and fractional order circuit implementation.
Disclosure of Invention
In view of the above, the present invention aims to provide an analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system, which can accurately describe the dynamic characteristics of the system, improve the degree of freedom of design, and realize fractional order characteristics.
In order to achieve the above purpose, the present invention provides the following technical solutions:
an analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system, comprising: the driving system circuit and the response system circuit are connected through a coupling term circuit;
the driving system circuit and the response system circuit respectively comprise: an external harmonic excitation signal, two voltage summing circuits (such as R1, R2, R13-R16, or R28-R33), four fractional order proportional-integral equivalent operational amplifier circuits, four inverse proportional operational amplifier circuits, and three multiplier parts;
the first input end of the voltage summing circuit I is connected with an external harmonic excitation signal, and the output end of the voltage summing circuit I is connected with the fractional proportional integral equivalent operational amplifier circuit I, the inverting proportional operational amplifier circuit I, the fractional proportional integral equivalent operational amplifier circuit II, the inverting proportional operational amplifier circuit II and the multiplier part I in a ring shape; the output end of the inverting proportion operational amplifier circuit I is also connected with the second input end of the voltage summation circuit I; the output end of the voltage summing circuit II is sequentially connected with the fractional proportional integral equivalent operational amplifier circuit III, the reverse proportional operational amplifier circuit III, the fractional proportional integral equivalent operational amplifier circuit IV and the reverse proportional operational amplifier circuit IV; the input end of the multiplier part II is connected with the output end of the inverse proportion operational amplifier circuit III, and the output end of the multiplier part II is connected with the input end of the voltage summation circuit II; the input end of the multiplier part III is connected with the output end of the inverse proportion operational amplifier circuit IV, the first output end of the multiplier part III is connected with the input end of the voltage summation circuit II, and the second output end of the multiplier part III is connected with the coupling term circuit. Further, the coupling term circuit includes: an in-phase proportional operational amplifier circuit (e.g., U17 and R77) and a voltage summing circuit III (e.g., R79 and R80); the input end of the voltage summation circuit III is respectively connected with the output end of the multiplier part III of the driving system circuit and the response system circuit; and the output end of the voltage summation circuit III is connected with an in-phase proportional operational amplifier circuit.
Further, the fractional order proportional-integral equivalent operational amplifier circuit I and the fractional order proportional-integral equivalent operational amplifier circuit III have the same structure and are composed of two capacitors (such as C5-C6 or C9-C10), two fixed-value resistors (such as R3, R17 or R35-R36) and an inverting amplifier (such as U1A or U5A); the two capacitors are respectively connected with a resistor in parallel and then connected in series, and the two ends of the capacitor after being connected in series are connected with the reverse input end and the output end of the inverting amplifier;
the fractional order proportional-integral equivalent operational amplifier circuit II and the fractional order proportional-integral equivalent operational amplifier circuit IV have the same structure and are composed of two capacitors (such as C7-C8 or C11-C12), two constant value resistors (such as R18, R34 or R37-R38), three constant value resistors (such as R7-R9 or R22-R24) and an inverting amplifier (such as U3A or U7A); the two capacitors are respectively connected with a resistor in parallel and then connected in series, and the two ends of the capacitor after being connected in series are connected with the reverse input end and the output end of the inverting amplifier; two ends of one fixed resistor are respectively connected with the positive input end and the grounding end of the inverting amplifier.
Further, the four inverting proportion operational amplifier circuits have the same structure and are composed of three constant value resistors (such as R4-R6, R10-R12, R19-R21, or R25-R27) and an inverting operational amplifier (such as U2A, U4A, U A or U8A); two ends of one fixed value resistor are respectively connected with the reverse input end and the output end of the inverting operational amplifier, and the other two fixed value resistors are respectively connected with the input end of the inverting operational amplifier.
Further, the voltage summing circuit I consists of six constant value resistors; the voltage summing circuit II consists of six fixed-value resistors.
Further, the multiplier section I is composed of three multipliers (e.g., A1 to A3); the multiplier part II consists of two multipliers (such as A7-A8);
the multiplier section III in the driving system circuit is composed of four multipliers (such as A4-A6 and A9), and the multiplier section III in the response system circuit is composed of three multipliers.
Further, the fractional order proportional integral equivalent operational amplifier circuit is routedCell circuit configuration, design implementation->The corresponding transfer function H(s) of the unit circuit is:
wherein C is o Representing capacitance parameter, C a And C b Represents selected capacitance, R a And R is b Representing the selected resistance, s representing the laplace operator.
Further, the voltage v across the operational amplifier i I=1, …,4 corresponds to the variable x in the dynamic equation of the driving self-sustaining electromechanical seismometer system i I=1, …,4, or a variable y in the corresponding response self-sustaining electro-mechanical seismometer system dynamics equation i ,i＝1,…,4；
The dynamic equation of the driving self-sustaining electro-mechanical seismometer system is as follows:
wherein, x 1 ＝x c ，x 3 ＝x z ，/>carpento derivative, ω, representing α > 0 m Representing dimensionless parameters omega e 、x c And x z Represents a dimensionless variable, a 0 、a 1 And a 2 Representing the linear, cubic and penta spring rates, m, B and l represent the mass, magnetic field and length of the wire, f, respectively 0 And ω represents the amplitude and frequency of the excitation, x represents the elongation of the nonlinear spring, L represents the linear inductance, α, R and I 0 Respectively represent fractional order coefficient, resistance and initial current, O c And O d Representing the average coefficient, Q, of a nonlinear capacitor 0 Representing reference charge, C 0 Represents the linear part, mu, of the capacitor 0 Representing the damping coefficient;
the dynamic equation of the response self-sustaining electro-mechanical seismometer system is as follows:
wherein k=r/R c Representing the resistive coupling parameter.
Further, the multiplier is used to generate a nonlinear term that drives or responds to a nonlinear term in the self-contained electromechanical seismometer system.
The invention has the beneficial effects that: the analog circuit of the unidirectional coupling fractional order self-sustaining electromechanical seismometer system built by the invention can accurately describe the dynamic characteristics of the system, improves the degree of freedom of design and realizes fractional order characteristics; and the simulation circuit constructed by the invention has high coincidence degree between the observation result and the dynamic analysis result.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
Drawings
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
FIG. 1 is a schematic diagram of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system;
FIG. 2 is an overall block diagram of an analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system;
FIG. 3 is a circuit diagram of an analog circuit of the unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system;
FIG. 4 is a phase diagram of a single drive self-sustaining electromechanical fractional order seismometer system in an analog circuit;
FIG. 5 is a phase diagram of a single-response self-sustaining electromechanical fractional order seismometer system in an analog circuit;
FIG. 6 is a phase diagram of a response system in a single-direction coupling fractional order self-sustaining electro-mechanical seismometer system in an analog circuit;
FIG. 7 is a phase diagram of a single drive self-sustaining electro-mechanical seismometer system;
FIG. 8 is a phase diagram of a single-response self-sustaining electro-mechanical seismometer system;
FIG. 9 is a phase diagram of a response system in a single-direction coupled fractional order self-sustaining electro-mechanical seismometer system.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to limit the invention; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numbers in the drawings of embodiments of the invention correspond to the same or similar components; in the description of the present invention, it should be understood that, if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc., that indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but not for indicating or suggesting that the referred device or element must have a specific azimuth, be constructed and operated in a specific azimuth, so that the terms describing the positional relationship in the drawings are merely for exemplary illustration and should not be construed as limiting the present invention, and that the specific meaning of the above terms may be understood by those of ordinary skill in the art according to the specific circumstances.
Referring to fig. 1-9, the invention constructs a unidirectional coupling fractional order self-sustaining electromechanical seismometer system dynamics model closely related to an analog circuit. The analog circuit consists of a driving system circuit, a response system circuit and a coupling term circuit. The driving system circuit and the response system circuit are respectively composed of four integral operational amplifiers, four inverting proportional operational amplifiers, an external harmonic excitation signal, a fractional order proportional integral equivalent operational amplifier circuit formed by parallel and serial connection of four groups of capacitance resistors, nine AD633 multipliers capable of generating nonlinear terms, six integral drift resistors with saturation or cut-off behaviors caused by integral drift, six static balance resistors for compensating bias current offset and 18 assemblies formed by common chromatic circle resistors and precision adjustable potentiometers. The coupling term circuit consists of an in-phase proportional operational amplifier circuit and a voltage summation circuit III.
Example 1:
1. construction of System dynamics model
Single fractional order self-sustaining electro-mechanical seismometer systems are typically composed of two parts, an electrical part and a mechanical part. The electric part comprises a linear inductance L and a nonlinear capacitance C NL Nonlinear resistor R NR And electromotive force e mounted in series with the first three electronic components v . The mechanical part of the device is hung on the shell and consists of a shock absorber, a seismic mass and an adjustable spring. The two parts are coupled by a coupling magnet coil and a magnet, thereby generating a magnetic fieldWesterlund and Ekstam have shown the fractional order characteristics of different dielectrics of capacitors, e.g. +.>Wherein C is 0 ,τ,/>And->Representing the linear part of the capacitor, time, current and voltage, respectively.
The voltages associated with nonlinear resistors and capacitors can be expressed in fractional steps
Wherein α, q, R and I 0 Respectively representing fractional order coefficient, charge, resistance and initial current, O c And O d Represents the average coefficient, d, of the nonlinear capacitor α q/dτ α =i, I is current.
In practical applications, it is inevitable that both friction and air resistance are present in the governor system. Thus, for a single seismometer system, a spring force with a nonlinear stiffness can be written as
F d ＝a 0 +a 1 x 2 +a 2 x 4 (2)
Wherein x represents the extension of the nonlinear spring, a 0 ,a 1 And a 2 Representing the linear, three and five spring rates.
Due to the influence of the strong interaction between the permanent magnet and the coupling coil, the laplace force of the mechanical part and the lenz electromotive force of the electrical part should be considered. Utilizing Newton's second law and kirchhoff's law to establish a kinetic equation of a single fractional order electromechanical seismometer system
Wherein m, B and l respectively represent the mass, magnetic field and length of the wire, f 1 、f 0 And Ω represent the critical force, amplitude and frequency of the excitation.
FIG. 1 illustrates a unidirectionally coupled fractional order self-sustaining electromechanical seismometer system in which a linear resistor and a current follower are used to connect two fractional order seismometer systems (one of which is referred to as a responsive self-sustaining electromechanical seismometer system and the other of which is referred to as a driven self-sustaining electromechanical seismometer system).
Several dimensionless variables were introduced:
x c ＝x/l，x z ＝q/Q 0 ，t＝τ/w e ，
wherein Q is 0 Representing the reference charge.
Deriving a gyro coupling driving system control equation under the definition of the kappa number order from the steps (3) and (4), wherein the equation can well treat the problem of zero initial condition
Wherein the dimensionless parameters are set as follows:
x 1 ＝x c ，x 3 ＝x z ，/>carpento derivative, ω, representing α > 0 m Representing dimensionless parameters omega e 、x c And x z Represents a dimensionless variable, a 0 、a 1 And a 2 Representing the linear, cubic and penta spring rates, m, B and l represent the mass, magnetic field and length of the wire, f, respectively 0 And ω represents the amplitude and frequency of the excitation, x represents the elongation of the nonlinear spring, L represents the linear inductance, α, R and I 0 Respectively represent fractional order coefficient, resistance and initial current, O c And O d Representing the average coefficient, Q, of a nonlinear capacitor 0 Representing reference charge, C 0 Represents the linear part, mu, of the capacitor 0 Representing the damping coefficient.
Dynamic equation writing of response self-sustaining electromechanical seismometer system
Wherein k=r/R c Representing the resistive coupling parameter.
2. Analog circuit design and dynamic analysis verification
The physical parameters driving the self-sustaining electro-mechanical seismometer system are defined as: mu (mu) 1 ＝0.1，μ 2 ＝0.2，ω 1 ＝1，λ 1 ＝0.01，λ 2 ＝-0.7，β 1 ＝0.01，β 2 ＝0.1，γ 1 ＝0.25，γ 2 ＝0.9，ω＝0.5，F 0 ＝1.2；
The physical parameters of the response self-sustaining electro-mechanical seismometer system are defined as: mu (mu) 1 ＝0.03，μ 2 ＝0.02，ω 1 ＝1，λ 1 ＝0.5，λ 2 ＝0.6，β 1 ＝0.05，β 2 ＝0.13，γ 1 ＝0.65，γ 2 ＝0.4，ω＝0.25，F 0 ＝13.6。
Based on the energy flow theory, the differential equation of the unidirectional coupling fractional order self-sustaining electromechanical seismometer system is consistent with the differential equation of the circuit thereof. This fact is very useful for theoretical analysis of kinetic and electrical measurement techniques. And solving a fractional differential equation by adopting a frequency approximation method to give a dynamic analysis result of the unidirectional coupling fractional order self-sustaining electromechanical seismometer system. Omega is within 0.01 + -100 rad/sec, there is an approximate expression with a maximum distortion of 0.2db
Can realizeIs provided. In analog circuits, implementing unit circuits are providedCorresponding transfer function H(s):
wherein C is o Representing capacitance parameter, C a And C b Represents selected capacitance, R a And R is b Representing the selected resistance. C in unidirectional coupling fractional order self-sustaining electromechanical seismometer system a ＝10.0022nF，C b ＝208.054nF，R a = 976.784mΩ and R b ＝448.251KΩ。
The analog electronics of a one-way coupled fractional order self-sustaining electro-seismometer system consisting of a drive system, coupling terms and response system is shown in fig. 3. Voltage v across operational amplifier (TL 074 CN) i I=1, …,4 plays a role in driving the self-sustaining electromechanical seismometer system as a variable x i Effect of i=1, …, 4. Similarly, the voltage v across the operational amplifier i_1 I=1, …,4 plays the variable y in the response self-sustaining electromechanical seismometer system i Roles of i=1, …, 4. In the circuit, 17 AD633 multipliers are used to generate nonlinear terms, such as in a driven self-sustaining electro-mechanical seismometer systemAnd +.>The in-phase proportional operational amplifier circuit is designed, and the coupling of driving and responding self-sustaining electromechanical seismometer systems is realized. Four integrating operational amplifiers and four inverting proportional operational amplifiers are employed to produce the integrating and inverting effects. External harmonic signal F 0 Driving amplitude F of cos ωt 0 Equal to the excitation amplitude.
Applying kirchhoff's law, the circuit equation in FIG. 3 is written
The circuit equations (9) - (10) are equivalent to the dynamics equation (5), and the circuit equations (11) - (12) are equivalent to the dynamics equation (6).
R 9 ,R 24 ,R 44 And R is 58 Representing the integration drift resistance, saturation or cut-off behavior caused by the integration drift can be suppressed. Introducing static balancing resistance, e.g. R 5 ,R 8 ,R 11 ,R 20 ,R 23 ,R 26 ,R 40 ,R 43 ,R 46 ,R 54 ,R 57 And R is 60 To compensate for the offset of the bias current. The parameters and specifications of all experimental circuit elements are given in fig. 3. All the resistors are combined by common color ring resistor and precision adjustable potentiometer.
The amplitude is F in the experiment 0 Is used to excite the seismometer system. In an electronic analog circuit, fig. 4-5 depict phase diagrams of a single drive and response self-sustaining electromechanical fractional order seismometer system. Fig. 6 shows a phase diagram of a response self-sustaining electro-mechanical seismometer system in a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system. Obviously, the system can generate transient chaos, double periodic motion and transient response of relative chaos oscillation under different conditions. Comparing the observation result of the simulation circuit with the dynamics analysis result (namely, fig. 4 and 7, fig. 5 and 8, and fig. 6 and 9), the high anastomosis between the two diagrams is found, and the effectiveness and scientificity of the simulation circuit of the unidirectional coupling fractional order self-sustaining electromechanical seismometer system constructed by the invention are demonstrated.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.
Claims (8)
1. An analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system, the analog circuit comprising: the driving system circuit and the response system circuit are connected through a coupling term circuit;
the driving system circuit and the response system circuit respectively comprise: an external harmonic excitation signal, two voltage summing circuits, four fractional order proportional integral equivalent operational amplifier circuits, four inverse proportional operational amplifier circuits and three multiplier parts;
the first input end of the voltage summing circuit I is connected with an external harmonic excitation signal, and the output end of the voltage summing circuit I is connected with the fractional proportional integral equivalent operational amplifier circuit I, the inverting proportional operational amplifier circuit I, the fractional proportional integral equivalent operational amplifier circuit II, the inverting proportional operational amplifier circuit II and the multiplier part I in a ring shape; the output end of the inverting proportion operational amplifier circuit I is also connected with the second input end of the voltage summation circuit I; the output end of the voltage summing circuit II is sequentially connected with the fractional proportional integral equivalent operational amplifier circuit III, the reverse proportional operational amplifier circuit III, the fractional proportional integral equivalent operational amplifier circuit IV and the reverse proportional operational amplifier circuit IV; the input end of the multiplier part II is connected with the output end of the inverse proportional operational amplifier circuit III, and the output end of the multiplier part II is connected with the input end of the voltage summation circuit II; the input end of the multiplier part III is connected with the output end of the inverse proportional operational amplifier circuit IV, the first output end of the multiplier part III is connected with the input end of the voltage summation circuit II, and the second output end of the multiplier part III is connected with the coupling term circuit;
the fractional order proportional integral equivalent operational amplifierCircuit routingCell circuit configuration, design implementation->The corresponding transfer function H(s) of the unit circuit is:
wherein C is o Representing capacitance parameter, C a And C b Represents selected capacitance, R a And R is b Representing the selected resistance, s representing the laplace operator.
2. The analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system of claim 1, wherein said coupling term circuit comprises: an in-phase proportional operational amplifier circuit and a voltage summing circuit III; the input end of the voltage summation circuit III is respectively connected with the output end of the multiplier part III of the driving system circuit and the response system circuit; and the output end of the voltage summation circuit III is connected with an in-phase proportional operational amplifier circuit.
3. The analog circuit of the unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system according to claim 1, wherein the fractional order proportional integral equivalent operational amplification circuit i and the fractional order proportional integral equivalent operational amplification circuit iii have the same structure and are composed of two capacitors, two fixed-value resistors and an inverting amplifier; the two capacitors are respectively connected with a resistor in parallel and then connected in series, and the two ends of the capacitor after being connected in series are connected with the reverse input end and the output end of the inverting amplifier;
the fractional order proportional-integral equivalent operational amplification circuit II and the fractional order proportional-integral equivalent operational amplification circuit IV have the same structure and are composed of two capacitors, three constant value resistors and an inverting amplifier; the two capacitors are respectively connected with a resistor in parallel and then connected in series, and the two ends of the capacitor after being connected in series are connected with the reverse input end and the output end of the inverting amplifier; two ends of one fixed resistor are respectively connected with the positive input end and the grounding end of the inverting amplifier.
4. The analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system according to claim 1, wherein four inverting proportional operational amplifier circuits are identical in structure, each composed of three constant value resistors and one inverting operational amplifier; two ends of one fixed value resistor are respectively connected with the reverse input end and the output end of the inverting operational amplifier, and the other two fixed value resistors are respectively connected with the input end of the inverting operational amplifier.
5. The analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system of claim 1, wherein said voltage summing circuit i and voltage summing circuit ii are each comprised of six fixed value resistors.
6. The analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system according to claim 1, wherein said multiplier section i is composed of three multipliers; the multiplier part II consists of two multipliers;
the multiplier section III in the driving system circuit is composed of four multipliers, and the multiplier section III in the response system circuit is composed of three multipliers.
7. The analog circuit of a unidirectional coupling fractional order self-sustaining electro-mechanical seismometer system of claim 4, wherein a voltage v across said operational amplifier i I=1, …,4 corresponds to the variable x in the dynamic equation of the driving self-sustaining electromechanical seismometer system i I=1, …,4, or a variable y in the corresponding response self-sustaining electro-mechanical seismometer system dynamics equation i ,i＝1,…,4；
The dynamic equation of the driving self-sustaining electro-mechanical seismometer system is as follows:
wherein, x 1 ＝x c ，x 3 ＝x z ，/>carpento derivative, ω, representing α > 0 m Representing dimensionless parameters omega e 、x c And x z Represents a dimensionless variable, a 0 、a 1 And a 2 Representing the linear, cubic and penta spring rates, m, B and l represent the mass, magnetic field and length of the wire, f, respectively 0 And ω represents the amplitude and frequency of the excitation, x represents the elongation of the nonlinear spring, L represents the linear inductance, α, R and I 0 Respectively represent fractional order coefficient, resistance and initial current, O c And O d Representing the average coefficient, Q, of a nonlinear capacitor 0 Representing reference charge, C 0 Represents the linear part, mu, of the capacitor 0 Representing the damping coefficient;
the dynamic equation of the response self-sustaining electro-mechanical seismometer system is as follows:
wherein k=r/R c Representing the resistive coupling parameter.
8. The analog circuit of a one-way coupled fractional order self-sustaining electro-mechanical seismometer system of claim 7, wherein the multiplier is configured to generate a nonlinear term driving or responding to a nonlinear term in the self-sustaining electro-mechanical seismometer system.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102385659A (en) * | 2011-12-13 | 2012-03-21 | 滨州学院 | Method for realizing fractional-order three-system automatic-switchover chaotic system and analog circuit |
| WO2017027993A1 (en) * | 2015-08-19 | 2017-02-23 | 王忠林 | 0.5-order mixed and chained fractional order integral switching method and circuit |
| CN108334700A (en) * | 2018-02-05 | 2018-07-27 | 武汉科技大学 | A kind of fractional order recalls the equivalent circuit of container |
| CN109067515A (en) * | 2018-09-19 | 2018-12-21 | 安顺学院 | Fractional order multi-architecture chaotic signal generator |
| CN111077776A (en) * | 2019-12-16 | 2020-04-28 | 重庆航天职业技术学院 | Optimal synchronous control method of coupled fractional order chaotic electromechanical device |
| CN111290015A (en) * | 2020-03-09 | 2020-06-16 | 贵州大学 | Fractional order self-sustaining type electromechanical seismograph system acceleration stability control method with constraint |
| CN214480496U (en) * | 2021-03-23 | 2021-10-22 | 重庆航天职业技术学院 | Analog circuit of fractional order self-sustaining electromechanical seismograph system |
-
2021
- 2021-03-23 CN CN202110310026.6A patent/CN112987081B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102385659A (en) * | 2011-12-13 | 2012-03-21 | 滨州学院 | Method for realizing fractional-order three-system automatic-switchover chaotic system and analog circuit |
| WO2017027993A1 (en) * | 2015-08-19 | 2017-02-23 | 王忠林 | 0.5-order mixed and chained fractional order integral switching method and circuit |
| CN108334700A (en) * | 2018-02-05 | 2018-07-27 | 武汉科技大学 | A kind of fractional order recalls the equivalent circuit of container |
| CN109067515A (en) * | 2018-09-19 | 2018-12-21 | 安顺学院 | Fractional order multi-architecture chaotic signal generator |
| CN111077776A (en) * | 2019-12-16 | 2020-04-28 | 重庆航天职业技术学院 | Optimal synchronous control method of coupled fractional order chaotic electromechanical device |
| CN111290015A (en) * | 2020-03-09 | 2020-06-16 | 贵州大学 | Fractional order self-sustaining type electromechanical seismograph system acceleration stability control method with constraint |
| CN214480496U (en) * | 2021-03-23 | 2021-10-22 | 重庆航天职业技术学院 | Analog circuit of fractional order self-sustaining electromechanical seismograph system |
Non-Patent Citations (1)
| Title |
|---|
| Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems;Riccardo Caponetto 等;Fractional Calculus and Applied Analysis;第16卷(第1期);93–108 * |
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