CN109271703B - Current fractional order integral control type memristor - Google Patents
Current fractional order integral control type memristor Download PDFInfo
- Publication number
- CN109271703B CN109271703B CN201811060007.7A CN201811060007A CN109271703B CN 109271703 B CN109271703 B CN 109271703B CN 201811060007 A CN201811060007 A CN 201811060007A CN 109271703 B CN109271703 B CN 109271703B
- Authority
- CN
- China
- Prior art keywords
- voltage
- current
- controlled
- fractional order
- control
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D10/00—Energy efficient computing, e.g. low power processors, power management or thermal management
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Computer Hardware Design (AREA)
- Theoretical Computer Science (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Networks Using Active Elements (AREA)
- Ac-Ac Conversion (AREA)
Abstract
The invention discloses a current fractional order integral control type memristor, which comprises a pin a, a pin b and a voltage-controlled resistor U R Resistor R, current control voltage source I U And voltage fractional order integrator A, voltage-controlled resistor U R Comprising a voltage control terminal u c And a controlled resistance R u Voltage-controlled resistor U R Internal controlled resistance R u The resistance value of (a) is controlled by a voltage control terminal u c Voltage value control of (2), current control voltage source I U Comprising a current control terminal i and a voltage source output terminal u i Current control voltage source I U An internal voltage source output terminal u i The voltage value of (a) is controlled by the current value of the current control terminal i, and the voltage fractional order integrator A comprises a voltage input terminal u i And a voltage output terminal u c . The electrical characteristics of the pins a and b of the current fractional order integral control type memristor are equivalent to the A, B pin characteristics of the memristor M, and the two pins are used for further reducing the complexity and the element number of the existing current fractional order integral control type memristor, and the memristor has the advantages of no requirement of one-end grounding, flexible memristor value change range and wide working voltage range.
Description
Technical Field
The invention relates to the field of novel circuit design, in particular to a current fractional order integral control type memristor.
Background
The fractional impedance (fractional) is an abbreviation of fractional-order impedance, and is an electronic component or system with fractional-order calculus (fractional-order calculus) operation function. The basic elements required for the circuit to implement fractional calculus operations are called components. The ideal component reactance element is not existed, and the corresponding approximation implementation circuit is called a component reactance approximation circuit. The fractional reactance, the fractional reactance element and the fractional reactance approximation circuit are key components of fractional order circuits and systems, and the fractional order circuits and the systems are an emerging interdisciplinary research field.
In 2001, W.Ahmad et al replaced the capacitor in a classical Wien bridge oscillator (Wien-bridge oscillator) with a fractional-order Wien bridge oscillator. In 2008, a.g. radwan and a.s. elwakil et al give the operation principle of fractional order oscillators and circuit implementation cases of various fractional order oscillators. Since the real inductor and capacitor have fractional order operation characteristics, in 2013, wangFa-Qiang et al combined with fractional order calculus, studied the continuous conduction mode characteristics of the open loop Buck converter transfer function and performed PSIM simulation analysis of the circuit. In 2011, a.g. radwan et al carefully analyzed a series circuit consisting of capacitive and inductive components and gave numeric calculation and circuit simulation results. In 2014, cunning et al, li Jie, chen Diyi, systematically analyzed and summarized the basic characteristics and rules of fractional order circuits consisting of resistors, capacitive and inductive components in parallel, and analyzed the pure virtual impedance problem specific to the circuits under the fractional order conditions. 2016, a.e. calik et al analyzed the law of change over time of the charge of the series circuit of capacitive and inductive components. The fractional reactance element is also a key element for realizing a fractional order Hopfield neural network circuit, and the fractional order Hopfield neural network has excellent performance when applied to the field of chip cloning resistance. In summary, applying the fractional element capable of implementing fractional calculus operation to the classical circuit to obtain the fractional circuit has become one of the research hot spots of circuits and systems, and the fractional circuit and the system gradually show their unique advantages.
Memristors (memristors) are basic circuit elements describing the relationship between magnetic flux and charge, are recognized as the 4 th basic circuit element following resistance, capacitance and inductance, and are resistors with memory functions. In 2008, the hewlett-packard (HP) laboratory successfully implemented memristors physically for the first time, raising the hot flashes of worldwide memristor research. Memristors are proved to have wide application prospects in the fields of computer science, neural networks, bioengineering, communication engineering, nonlinear circuits and the like.
With the deep research of the related technology, the implementation of a memristor circuit with fractional calculus operation performance is attracting attention of researchers, and the memristor circuit is one of the research fronts of fractional circuits and systems. 2010, ivo
The method comprises the steps of obtaining a fractional order memristive Chua's circuit for the first time, solving a circuit equation numerically, and analyzing the dynamic behavior and stability of the circuit, wherein the circuit is a circuit which contains both the memristor and is reported in a published literature for the first time. In 2015, yajuan et al put forward a fractional order HPTiO2 linear memristor based on the fact that the thickness of the doped layer of the HP TiO2 linear memristor cannot be equal to zero or the thickness of the whole device, and studied the influence rule of an operation order on the memristor dynamic range and the output voltage dynamic amplitude when being stimulated outside a period, but did not give a design scheme of the fractional order HPTiO2 linear memristor circuit or device. In 2016, puYi-Fei et al proposed and analyzed the concept and theory of memristors, given the position in Chua's periodic Table, andin 2017, attempts were made to replace the resistance in the trellis-scale memristive equivalent circuit with the memristive equivalent circuit, with analog circuits implementing the memristive. In 2017, gangquan Si et al gave a fractional order charge-controlled memristor containing fractional order integration of current, and Gangquan Si et al performed theoretical analysis and numerical simulation experiments. In 2017, somia H.Rahead et al used components such as a fractional reactance approximation circuit, a current transmitter and a multiplier, and the circuit realized a current fractional order integrated control type memristor, which was a very good attempt. However, the current fractional order integral control memristor of somiah.raspad et al requires one end to be grounded, and the voltage range of the input signal is limited by the supply voltage of the internal current transmitter.
The current fractional order integral control type memristor introduces the operation order index of the fractional order integrator, is more flexible than the current integral control type memristor, and can be regarded as a special case that the operation order of the current fractional order integral control type memristor extends to 1. The application circuit is built by using the current fractional order integral control type memristor element in circuit simulation software such as Multisim and the like, and the method has important significance in testing analysis characteristics and promoting application of the application circuit. But the circuit simulation software element library has no directly usable current fractional order integral control type memristor. It is desirable to design a current fractional order integrated controlled memristor that can be used in circuit simulation software, with both pins not limited by ground requirements.
Disclosure of Invention
The invention aims to solve the technical problem of providing a current fractional order integral control type memristor, which solves the problems that one end of the existing current fractional order integral control type memristor is required to be grounded and the voltage range of an input signal is limited by the supply voltage of an internal current transmitter.
The technical scheme for solving the technical problems is as follows: a current fractional order integral control type memristor comprises a pin a, a pin b and a voltage-controlled resistor U R Resistor R, current control voltage source I U And a voltage fractional order integrator A, the voltage-controlled resistor U R Comprising a voltage control terminal u c And a controlled resistance R u The voltage-controlled resistor U R Internal controlled resistance R u The resistance value of (a) is controlled by a voltage control terminal u c Voltage value control of the current control voltage source I U Comprising a current control terminal i and a voltage source output terminal u i The current controls the voltage source I U An internal voltage source output terminal u i The voltage value of the voltage (A) is controlled by the current value of the current control terminal (i), and the voltage fractional order integrator (A) comprises a voltage input terminal (u) i And a voltage output terminal u c The pin a and the voltage-controlled resistor U R Internal controlled resistance R u Resistor R, current control voltage source I U The internal current control end and the pin b are in series connection, and the current control voltage source I U The voltage output end of the voltage fractional order integrator is connected with the voltage control end of the voltage-controlled resistor; from time 0 to t, the voltage value of the voltage output terminal in the voltage fractional order integrator A
K i For the proportionality coefficient of the voltage fractional order integrator A, the operation order-1 < mu < 0, < 0->
The integral operation symbol is that the time 0 is the lower limit of the fractional integration, and the time t is the upper limit of the fractional integration.
On the basis of the technical scheme, the invention can be improved as follows.
Further, the voltage-controlled resistor U R Internal controlled resistance R u Resistance value R of (2) u ＝K r ×u c ，K r Is a voltage-controlled resistor U R Is set, and is set to be a control coefficient of the control system.
Further, the current control voltage source I U Output voltage u of internal voltage output terminal i ＝K j ×i，K j Controlling a voltage source I for current U Is set, and is set to be a control coefficient of the control system.
The beneficial effects of the invention are as follows: in the invention, the electrical characteristics of the current fractional order integral control type memristor pins a and b are equivalent to the theoretical port characteristics of the memristor, are two pins, and have the advantages of no requirement of one-end grounding and wide working voltage range.
Drawings
FIG. 1 is a schematic diagram of the present invention
FIG. 2 is a theoretical graph of volt-ampere relationship between current value of sinusoidal current source i (t) and corresponding port voltage u (t) at operation order μ= -0.4 in the embodiment of the present invention
FIG. 3 is a theoretical graph of volt-ampere relationship between current value of sinusoidal current source i (t) and corresponding port voltage u (t) at operation order μ= -0.6 in the embodiment of the invention
FIG. 4 is a theoretical graph of volt-ampere relationship between current value of string current source i (t) and corresponding port voltage u (t) when operation order μ= -0.8 in the embodiment of the invention
FIG. 5 is a graph showing amplitude-frequency characteristics in an embodiment of the present invention
FIG. 6 is a graph showing the phase-frequency characteristics in an embodiment of the present invention
FIG. 7 is a graph showing the step frequency characteristics in an embodiment of the present invention
FIG. 8 is a F-curve diagram of an embodiment of the present invention
FIG. 9 is a graph showing amplitude-frequency characteristic simulation in an embodiment of the present invention
FIG. 10 is a graph of phase-frequency characteristic simulation in an embodiment of the present invention
Fig. 11 is a simulation graph of volt-ampere relationship between current value of sinusoidal current source i (t) and corresponding port voltage u (t) at operation order μ= -0.4 (frequency f=3 Hz) in the embodiment of the present invention
Fig. 12 is a simulation graph of volt-ampere relationship between current value of sinusoidal current source i (t) and corresponding port voltage u (t) at operation order μ= -0.4 (frequency f=30hz) in the embodiment of the present invention
Fig. 13 is a simulation graph of volt-ampere relationship between current value of string current source i (t) and corresponding port voltage u (t) when operation order μ= -0.4 in the embodiment of the present invention (frequency f=300 Hz)
Detailed Description
The principles and features of the present invention are described below with reference to the drawings, the examples are illustrated for the purpose of illustrating the invention and are not to be construed as limiting the scope of the invention.
As shown in FIG. 1, a current fractional order integrated control type memristor comprises a pin a, a pin b and a voltage-controlled resistor U R Resistor R, current control voltage source I U And voltage fractional order integrator A, voltage-controlled resistor U R Comprising a voltage control terminal u c And a controlled resistance R u Voltage-controlled resistor U R Internal controlled resistance R u The resistance value of (a) is controlled by a voltage control terminal u c Voltage value control of (2), current control voltage source I U Comprising a current control terminal i and a voltage source output terminal u i Current control voltage source I U An internal voltage source output terminal u i The voltage value of (a) is controlled by the current value of the current control terminal i, and the voltage fractional order integrator A comprises a voltage input terminal u i And a voltage output terminal u c Pin a and voltage-controlled resistor U R Internal controlled resistance R u Resistor R, current control voltage source I U The internal current control end and the pin b are in series connection, and the current controls the voltage source I U The voltage output end of the voltage fractional order integrator is connected with the voltage control end of the voltage-controlled resistor; from time 0 to t, the voltage value of the voltage output terminal in the voltage fractional order integrator A
K i For the proportionality coefficient of the voltage fractional order integrator A, the operation order-1 is smaller than mu and smaller than 0,
for the fractional integration operation symbol, time 0 is the lower limit of the fractional integration, and time t is the upper limit of the fractional integration.
In the embodiment of the invention, the voltage-controlled resistor U R Internal controlled resistance R u Resistance value R of (2) u ＝K r ×u c ，K r Is a voltage-controlled resistor U R Is set, and is set to be a control coefficient of the control system.
In an embodiment of the invention, the current controls the voltage source I U Output voltage u of internal voltage output terminal i ＝K j ×i，K j Controlling a voltage source I for current U Control system of (2)A number.
The working principle of the invention is as follows:
common fractional calculus definitions are the Riemann-Liouville (Riemann-Liouville) definition, the Kaplan (Caputo) definition, the lattice Lin Waer-Latenickov (Grunwald-Letikov) definition, and the like. From the time instant 0 to the time instant t,
the-mu-order Riemann-LiuVill fractional order integral, called function f (t), where +.>
For integrating arithmetic symbols, ++>
As a gamma function, time 0 is the lower limit of the fractional integration and time t is the upper limit of the fractional integration. When the initial value of the function f (t) and its derivatives is 0, if f (t) =sin (ω) 0 t), there is->
If f (t) =cos (ω) 0 t), there is->
ω 0 Is the angular frequency of the signal.
If the initial values of the function f (t) and its derivatives are all 0, the Laplacian transform of the fractional calculus is
s is a Laplace variable, also known as an operand variable.
The fractional order integrator A used in the invention has the voltage transfer function in the Laplace transform domain
(-1 < mu < 0). For a given fractional value μ, the voltage transfer function H(s) of the fractional integrator a is an irrational function. Electronic components which are not commercially available at present are directly put into practiceThe existing transfer function H(s) has no directly usable elements or functions in Multisim circuit simulation software, matlab scientific calculation software and the like to realize the operation function of H(s). The real coefficient rational function H is typically accomplished by a circuit implementation (i.e., a fractional approximation circuit) or a software construction operation module k An arithmetic function of(s) for approximating an irrational fractional order transfer function H(s) at a certain frequency and a certain accuracy:
wherein, the non-negative integer variable k epsilon N represents the number of approximation stage times, and the positive integer parameter N k And d k Respectively represent molecular polynomials N k (s) and denominator polynomial D k (s) times.
Rational function H k Common implementations of(s) are Carlson rational approximation using regular newton iteration, eustaloup rational approximation using pole-zero progressive distribution fitting, charef rational approximation of fractional power pole and pole-zero model, matsuda rational approximation of log-spaced frequency point-continuous division expansion, and the like. In the embodiment of the invention, the eustaloup rational approximation is used.
The standard form of the Oustaloup rational approximation is
N is the number of approaching stages, zero +.>
Pole->
Gain->
Scaling factor K i Is set by a user according to the needs. The specific algorithm is as follows: (1) Inputting fractional operation order mu, selecting approximation frequency segment omega b (Low frequency points) and ω h (high frequency point), set ratioCoefficient K i And approximation stage number N; (2) Calculating omega u Then, omega is calculated by vector point operation k 、ω' k And K; (3) Constructing an Oustaloup rational approximation function according to the values obtained in the step (1) and the step (2) and the standard form of the Oustaloup rational approximation O H k (s)。
For visual analysis of Oustaloup rational approximation function in frequency domain O H k (s) approximates the performance of the voltage transfer function H(s). Taking the Laplace variable s=jω and letting the frequency index variable
Rational approximation function of Oustaloup O H k Amplitude-frequency characteristic of(s)>
Phase frequency characteristics->
Frequency-order characteristic->
And F feature->
Amplitude-frequency characteristic of the voltage transfer function H(s), respectively +.>
Phase frequency characteristics
Frequency-order characteristic->
And F feature
Is a graph of the comparison of the curves of (a). The amplitude-frequency characteristic function and the phase-frequency characteristic function respectively describe the input voltage signal of the fractional order integrator A in the frequency domainThe frequency-order characteristic function characterizes the fractional operation order mu of the fractional integrator A in the frequency domain, and the F characteristic function characterizes the proportionality coefficient K of the fractional integrator A in the frequency domain i 。
If the voltages u (t) at the a and b ends of the current fractional integral control type memristor model and the flowing current i (t) adopt the associated reference directions, the volt-ampere relation describing the characteristics is u (t) =M (q) x i (t), M (q) is the memristance of the current fractional integral control type memristor, and the memristance M (q) =R u (q) +R, q is time [0, t]Fractional integral value of current i (t) during the period, and q (t) = 0 D t Mu i (t), mu represents the fractional order, R u (q)＝K r ×K j ×K i ×q(t)。
The mathematical relationship of the current fractional order integral control memristor can be expressed as:
u(t)＝M(q)×i(t)，M(q)＝R+K r ×K j ×K i ×q(t)，
memristance M (q) depends on a fractional integral value q (t) of current i (t), q (t) being an internal state variable.
The current fractional order integral control type memristor a and b pins are connected with a sinusoidal current source I (t) as an excitation signal, and I (t) =i m ×sin(2πft)，I m For the current peak of the current source, f is the frequency of the sinusoidal current source, angular frequency ω=2pi f. Then the current fractional order integral control memristor internal state variable
Memristance +.>
Thus, the voltage of the two pins of the current fractional order integral control type memristor is obtained>
Setting a current fractionResistance r=10Ω in the step integral control memristor, voltage controlled resistance control coefficient K r =100deg.C/V, current control voltage source control coefficient K j =30Ω and voltage fractional integrator scaling factor K i =1. Taking peak value I of excitation sinusoidal current source I (t) m =10ma. When the operation order mu= -0.4 of the voltage fractional order integrator A, the current value of the sinusoidal current source i (t) of the current fractional order integrated control type memristor and the volt-ampere relation theoretical curve of the corresponding two-pin voltage u (t) are respectively shown in fig. 2 when the frequency f of the sinusoidal current source i (t) is 3Hz, 30Hz, 300Hz and 3000 Hz. When the operation order mu= -0.6 of the voltage fractional order integrator A, the current value of the excitation sinusoidal current source i (t) of the current fractional order integrated control type memristor when the frequency f of the sinusoidal current source i (t) is 1Hz, 50Hz and 500Hz respectively and the volt-ampere theoretical curve corresponding to the two-pin voltage u (t) are shown in fig. 3. When the operation order mu= -0.8 of the voltage fractional order integrator A, the current value of the excitation sinusoidal current source i (t) of the current fractional order integrated control type memristor when the frequency f of the sinusoidal current source i (t) is 1Hz, 5Hz and 100Hz respectively and the volt-ampere theoretical curve corresponding to the two-pin voltage u (t) are shown in fig. 4.
The operation function of the voltage transfer function H(s) of the fractional order integrator A is realized for circuit simulation, and the low frequency point omega of the rational approximation of the eustaloup is taken b =0.1 rad/s, high frequency point ω h =1500rad/s, fractional order μ= -0.4, scaling factor K i =1, approximation stage number n=6. Thereby obtaining the Oustaloup rational approximation function in the form of zero pole according to the Oustaloup rational approximation specific algorithm
Oustaloup rational approximation function O H 6 The amplitude-frequency characteristic curves of(s) and the voltage transfer function H(s) are shown in fig. 5, the phase-frequency characteristic curve is shown in fig. 6, the step-frequency characteristic curve is shown in fig. 7, and the F characteristic curve is shown in fig. 8. The ideal curves shown in FIGS. 5, 6, 7 and 8 represent curves corresponding to the voltage transfer function H(s), and the approximation curves represent the Oustaloup rational approximation function O H 6 (s) corresponding curves. From graphs 5, 6, 7 andfig. 8 can be seen: at a low frequency point omega b High frequency point omega h The approximation error is larger, but the frequency band can be avoided, the Oustaloup rational approximation function O H 6 (s) an approximation effect is achieved. The amplitude-frequency characteristic simulation curve obtained by performing Pspice analysis using the alternating current analysis function (ACAnalysis) of Multisim circuit simulation software is shown in fig. 9, and the phase-frequency characteristic simulation curve is shown in fig. 10. The order characteristic simulation curve obtained from the simulation data is shown as a simulation curve in fig. 7, and the F characteristic curve obtained from the simulation data is shown as a simulation curve in fig. 8. Simulation analysis results are consistent with theoretical analysis, and the result proves that the Oustaloup rational approximation function can be used O H 6 (s) to perform the operation function of the fractional voltage transfer function H(s).
Building a current fractional order integral control type memristor simulation system in Multisim circuit simulation software according to the structure shown in fig. 1, wherein a voltage transfer function H(s) of a fractional order integrator A uses a verified eustaloup rational approximation function O H 6 (s). The A channel of the oscilloscope tests the voltage of the two pins of the current fractional order integral control type memristor. The Current signal was converted linearly to a voltage signal (scaling factor 1V/mA) using a Current Probe (Current Probe) and connected to the oscilloscope B channel. According to the parameters selected in the case of the volt-ampere relation theoretical curve shown in fig. 2, the volt-ampere relation simulation curve obtained when the frequency f of the sinusoidal current source i (t) is 3Hz is shown in fig. 11, the volt-ampere relation simulation curve obtained when the frequency f of the sinusoidal current source i (t) is 30Hz is shown in fig. 12, the volt-ampere relation simulation curve obtained when the frequency f of the sinusoidal current source i (t) is 300Hz is shown in fig. 13, and the simulation result is consistent with the theoretical curve shown in fig. 2.
The above shows that the theoretical volt-ampere relation curve and the simulation result of the a pin and the b pin of the current fractional order integral control memristor all conform to three essential characteristics of the memristor M: 1. the volt-ampere characteristic curve of the current fractional order integral control type memristor under the excitation of the sinusoidal current source i (t) is a pinch loop; 2. the area of the pinching loop lobe is reduced along with the increase of the sinusoidal current source frequency f; 3. the pinch loop contracts into a straight line when the sinusoidal current source frequency f approaches infinity. The invention and its embodiments have proven to be viable.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (3)
1. A current fractional order integral control type memristor comprises a pin a, a pin b and a voltage-controlled resistor U R Resistor R, current control voltage source I U Characterized by comprising a voltage fractional integrator A, the voltage-controlled resistor U R Comprising a voltage control terminal u c And a controlled resistance R u The voltage-controlled resistor U R Internal controlled resistance R u The resistance value of (a) is controlled by a voltage control terminal u c Voltage value control of the current control voltage source I U Comprising a current control terminal i and a voltage source output terminal u i The current controls the voltage source I U An internal voltage source output terminal u i The voltage value of the voltage (A) is controlled by the current value of the current control terminal (i), and the voltage fractional order integrator (A) comprises a voltage input terminal (u) i And a voltage output terminal u c The pin a and the voltage-controlled resistor U R Internal controlled resistance R u Resistor R, current control voltage source I U The internal current control end and the pin b are in series connection, and the current control voltage source I U The voltage output end of the voltage fractional order integrator is connected with the voltage control end of the voltage-controlled resistor; from time 0 to time t, the voltage value of the voltage output terminal in the voltage fractional order integrator A
K i For the proportionality coefficient of the voltage fractional order integrator A, the operation order-1 < mu < 0, < 0->
For integrating arithmetic symbols, ++>
Mu-th order Riemann-LiuVill fractional order integral called function f (t), ++>
As a gamma function, time 0 is the lower limit of the fractional integration and time t is the upper limit of the fractional integration.
2. The current fractional order integral control memristor of claim 1, wherein the voltage-controlled resistor U R Internal controlled resistance R u Resistance value R of (2) u ＝K r ×u c ，K r Is a voltage-controlled resistor U R Is set, and is set to be a control coefficient of the control system.
3. The current fractional order integrally controlled memristor of claim 1, wherein the current control voltage source I U Output voltage u of internal voltage output terminal i ＝K j ×i，K j Controlling a voltage source I for current U Is set, and is set to be a control coefficient of the control system.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811060007.7A CN109271703B (en) | 2018-09-12 | 2018-09-12 | Current fractional order integral control type memristor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811060007.7A CN109271703B (en) | 2018-09-12 | 2018-09-12 | Current fractional order integral control type memristor |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109271703A CN109271703A (en) | 2019-01-25 |
| CN109271703B true CN109271703B (en) | 2023-07-07 |
Family
ID=65187864
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811060007.7A Active CN109271703B (en) | 2018-09-12 | 2018-09-12 | Current fractional order integral control type memristor |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109271703B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111125980B (en) * | 2019-12-12 | 2023-06-02 | 杭州电子科技大学 | Fractional order exponential memristor circuit model |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105680819A (en) * | 2016-04-08 | 2016-06-15 | 蒲亦非 | Capacitive sub memreactive element and inductive sub memreactive element filter |
| CN106067792A (en) * | 2016-07-04 | 2016-11-02 | 华南理工大学 | High-power fractional order electric capacity and the control method thereof that a kind of exponent number is more than 1 |
| CN106655865A (en) * | 2016-11-25 | 2017-05-10 | 华南理工大学 | Fractional order capacitor with adjustable order and capacitance value |
| CN107947914A (en) * | 2017-12-25 | 2018-04-20 | 西安理工大学 | A kind of chaos circuit based on fractional order memristor |
| CN108257628A (en) * | 2018-01-02 | 2018-07-06 | 深圳璞芯智能科技有限公司 | A kind of lattice scale fractional order memristor of arbitrary order high-pass filtering |
| CN108319797A (en) * | 2018-03-09 | 2018-07-24 | 武汉科技大学 | A kind of equivalent circuit of fractional order memristor |
| 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 |
-
2018
- 2018-09-12 CN CN201811060007.7A patent/CN109271703B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105680819A (en) * | 2016-04-08 | 2016-06-15 | 蒲亦非 | Capacitive sub memreactive element and inductive sub memreactive element filter |
| CN106067792A (en) * | 2016-07-04 | 2016-11-02 | 华南理工大学 | High-power fractional order electric capacity and the control method thereof that a kind of exponent number is more than 1 |
| CN106655865A (en) * | 2016-11-25 | 2017-05-10 | 华南理工大学 | Fractional order capacitor with adjustable order and capacitance value |
| CN107947914A (en) * | 2017-12-25 | 2018-04-20 | 西安理工大学 | A kind of chaos circuit based on fractional order memristor |
| CN108257628A (en) * | 2018-01-02 | 2018-07-06 | 深圳璞芯智能科技有限公司 | A kind of lattice scale fractional order memristor of arbitrary order high-pass filtering |
| 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 |
| CN108319797A (en) * | 2018-03-09 | 2018-07-24 | 武汉科技大学 | A kind of equivalent circuit of fractional order memristor |
Non-Patent Citations (1)
| Title |
|---|
| 一种带有非线性漂移函数的分数阶忆阻器模型;甘朝晖 等;《***仿真学报》;20180831;第30卷(第8期);第2884-2899页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109271703A (en) | 2019-01-25 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Chen et al. | Flux–charge analysis of two-memristor-based Chua's circuit: dimensionality decreasing model for detecting extreme multistability | |
| Liang et al. | A practical implementation of a floating memristor-less meminductor emulator | |
| Kuh et al. | Nonlinear circuit theory: Resistive networks | |
| KR101616036B1 (en) | Inductor simulation method and nonlinear equivalent circuit model for inductor | |
| Burdio et al. | A unified discrete-time state-space model for switching converters | |
| KR101616037B1 (en) | Capacitor simulation method and nonlinear equivalent circuit model for capacitor | |
| CN108804840B (en) | Extremely simple floating magnetic control memristor circuit simulation model | |
| Wilson et al. | Modeling frequency-dependent losses in ferrite cores | |
| CN110222425B (en) | Equivalent analog circuit with twin local active domain cubic polynomial magnetic control memristor | |
| CN108846215B (en) | Extremely simple floating ground load control memristor circuit simulation model | |
| CN109271703B (en) | Current fractional order integral control type memristor | |
| CN103490761A (en) | High-power memristor and control method thereof | |
| Mutlu et al. | A methodology for memristance calculation | |
| CN109117590B (en) | Voltage fractional order integral control type memristor | |
| CN108875204B (en) | Extremely simple floating ground load control memory sensor circuit simulation model | |
| CN109308387B (en) | Voltage fractional order integral control type memory container | |
| Biolkova et al. | Memristor modeling based on its constitutive relation | |
| CN108257628B (en) | Lattice scale fractional order memristor for arbitrary order high-pass filtering | |
| CN108173527B (en) | Lattice scale fractional order memristor for arbitrary order low-pass filtering | |
| Petráš et al. | Fractional calculus | |
| CN109308388B (en) | Current fractional order integral control type memory sensor | |
| Kinev et al. | Implementation of pulse-code control in parametric models of induction devises | |
| CN109271742B (en) | Magnetic control memory order element | |
| Michalik et al. | Simulation and analysis of power system transients | |
| CN110198164B (en) | Absolute value flow control memristor simulation circuit |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |