A pressure stability monitoring circuit based on periodic window of chaotic system

Abstract

The present invention discloses a pressure stability monitoring circuit based on the periodic window of a chaotic system, which relates to the technical field of chaotic circuits. The circuit includes multiplier U1, multiplier U2, and multiplier U3, and also includes a current feedback operational amplifier U4, a varistor R4, and an adjustable resistor R5. By utilizing the special periodic window phenomenon of the selected chaotic system, that is, there are multiple periodic sub-intervals in the large chaotic interval, the varistor is used to change the resistance values of some resistors in the circuit structure, so as to realize the regulation of the parameter a in the dynamic system. Further, through the change of the phase trajectory emitted by the physical chaotic circuit signal, the subtle pressure change is converted into an obvious and easily observable chaotic phenomenon. The detection system manufactured based on this principle has high sensitivity and very significant effect phenomena, and excellent performance will be demonstrated in terms of the universality and reliability in the fields of intelligent manufacturing, disaster prevention and mitigation, etc.

Description

Technical Field

[0001] The invention relates to the technical field of chaotic circuits, and in particular to a pressure stability monitoring circuit based on a chaotic system period window. Background Art

[0002] Chaos is a complex dynamic behavior that is prevalent in many disciplines such as biology, physics, meteorology, oceanography, and chemistry, and has a wide range of applications in engineering. The oscillation phenomenon is a very important phenomenon that is prevalent in second-order nonlinear systems, that is, when the system has a non-trivial periodic solution, continuous oscillations will occur. When the order of the nonlinear system increases to third order or even higher, the system will often produce a more complex chaotic oscillation phenomenon. Chaos has properties such as quasi-randomness, sensitivity, and positive Lipschitz exponents. When parameters change in a chaotic system, chaotic oscillations often appear alternately with periodic oscillations, and some systems even have periodic windows. This makes chaotic dynamic systems have broad application prospects in the field of stability detection.

[0003] At present, most of the patents related to chaos focus on the application of chaotic circuits in various fields, while ignoring the complexity of chaotic circuits and the application requirements of specific application scenarios. For example, the application number is 201821328408.1, which is a simple three-dimensional chaotic circuit with a constant term. It uses resistors and reverse integrators to realize the three-dimensional chaotic circuit, but does not consider the problem of combining with the lower-level circuit, and its practicality is insufficient; another example is the application number is 202210358859.4, which is a method for diagnosing early weak faults of planetary gearboxes based on chaos detection. It uses the AO-VMD algorithm and the forward and reverse detection method of the dual-coupled Duffing oscillator. AO-VMD is based on the cosine similarity weighted kurtosis to adaptively search for the optimal penalty factor and the number of modes. It can accurately diagnose the early weak faults of planetary gearboxes, but its circuit structure is relatively complex, and due to the large number of components and large errors, the robustness of the chaotic system is also reduced.

[0004] In fact, making full use of the periodic window in the chaotic system can realize pressure stability monitoring, but no relevant models or papers have been found in the prior art. This patent proposes a specific solution around this direction. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a pressure stability monitoring circuit based on a chaotic system period window, comprising a first branch, a second branch and a third branch constituting a chaotic oscillation circuit, wherein a current feedback operational amplifier U4 is connected between the first branch and the second branch.

[0006] The first branch includes a multiplier U1, a resistor R1, an adjustable resistor R5 and a capacitor C1. The multiplier U1 is powered by an external power supply V pThrough its own VS+ port, external power supply V n It is driven by its own VS-port; the two ends of the resistor R1 are respectively connected to the W output port and the Z output port of the multiplier U1; the X1 port and the Y1 port of the multiplier U1 are both connected to the input signal y, the X2 port is grounded, and the Y2 port is connected to the input signal z through the adjustable resistor R5; the multiplier U1 is connected to the input signal x through the resistor R1, and the output of the multiplication term is transmitted to the input signal x; one end of the capacitor C1 is connected to the input signal x, and the other end is grounded, so as to realize the x-dimensional differential operation of the chaotic oscillation circuit;

[0007] The second branch includes a multiplier U2, a resistor R2 and a capacitor C2. The multiplier U2 is powered by an external power supply V p Through its own VS+ port, external power supply V n Driven by its own VS-port, the two ends of the resistor R2 are respectively connected to the W output port and the Z output port of the multiplier U2; the X1 port of the multiplier U2 is connected to the input signal y, the X2 port and the Y1 port are both connected to the input signal z, and the Y2 port is grounded; the multiplier U2 is connected to the input signal y through the resistor R2, and the output of the multiplication term is transmitted to the input signal y; one end of the capacitor C2 is connected to the input signal y, and the other end is grounded, so as to realize the y-dimensional differential operation of the chaotic oscillation circuit;

[0008] The third branch includes a multiplier U3, a resistor R3 and a capacitor C3. The multiplier U3 is powered by an external power supply V p Through its own VS+ port, external power supply V n Driven by its own VS-port, the two ends of the resistor R3 are respectively connected to the W output port and the Z output port of the multiplier U3; the X1 port of the multiplier U3 is connected to the input signal x, the X2 port is connected to the control voltage Vcc, the Y1 port is connected to the input signal y, and the Y2 port is grounded; the multiplier U3 is connected to the input signal z through the resistor R3, and the output of the multiplication term is transmitted to the input signal z; one end of the capacitor C3 is connected to the input signal z, and the other end is grounded, so as to realize the z-dimensional differential operation of the chaotic oscillation circuit;

[0009] The current feedback operational amplifier U4 is powered by an external power supply V p and V n Drive, its positive input port is connected to the input signal y, the TZ port is connected to the input signal x through the resistor R6, the reverse input port is grounded through the varistor R4, and the output of the output port is x+ay; the parameter a in the chaotic system is realized by the resistor R6 and the varistor R4, and the parameter a changes with the change of the varistor R4, so as to realize the switching between the period window and the chaotic oscillation.

[0010] The technical solution further defined in the present invention is:

[0011] Furthermore, the expression of the chaotic system is

[0012]

[0013] Among them, x, y, and z are state variables in three dimensions respectively; a and b are system parameters respectively.

[0014] The aforementioned pressure stability monitoring circuit based on the periodic window of chaotic system has the following circuit equation:

[0015]

[0016] Among them, x, y, and z are state variables in three dimensions respectively.

[0017] In the aforementioned pressure stability monitoring circuit based on the periodic window of a chaotic system, the resistors R1, R2 and R3 are all set to be equal, and the capacitors C1, C2 and C3 are all set to be equal.

[0018] In the above-mentioned pressure stability monitoring circuit based on the period window of the chaotic system, the resistors R1, R2 and R3 are all set to 1kΩ, the resistor R6 is set to 0Ω, the capacitors C1, C2 and C3 are all set to 10nF, and the external power supply V p Set to 15V, external power supply V n Set to -15V, control voltage Vcc is set to 0V, and chaotic oscillation is achieved when varistor R4 is equal to 10kΩ and adjustable resistor R5 is equal to 1MΩ.

[0019] In the aforementioned pressure stability monitoring circuit based on the periodic window of a chaotic system, the models of the multipliers U1, U2 and U3 are all AD633.

[0020] In the above-mentioned pressure stability monitoring circuit based on the period window of a chaotic system, the model of the current feedback operational amplifier U4 is AD844.

[0021] The beneficial effects of the present invention are:

[0022] (1) In the present invention, the special periodic window phenomenon of the selected chaotic system (i.e., the existence of multiple periodic small intervals in a large chaotic interval) is utilized, and the resistance value of some resistors in the circuit structure is changed by a varistor, so as to realize the regulation of the parameter a in the dynamic system; and further, through the change of the phase track emitted by the real chaotic circuit signal, the subtle pressure change is converted into an obvious and easy-to-observe chaotic phenomenon; the detection system manufactured based on this principle has high sensitivity and significant effect, and its wide application and reliability in the fields of intelligent manufacturing, disaster prevention and mitigation will be excellent;

[0023] (2) In the present invention, on the basis that the simplified system based on the multiplier can effectively reduce the use of operational amplifiers, the model of the current feedback operational amplifier U4 is AD844, so as to further design a simplified circuit, and control the generation and change of the signal by controlling the value of the resistor and the capacitor and the relationship between them. The current feedback operational amplifier improves the utilization rate of the multiplier, and also makes the circuit simplification scheme design based on the current output characteristics of the multiplier more flexible. The signal feedback in the simplified system can freely realize the same phase, anti-phase and even differential operation;

[0024] (3) In the present invention, the model of the current feedback operational amplifier U4 is AD844, and the model of the multiplier is AD633. The workload of the multiplier is reduced by current output, and the voltage following function of its voltage output port also improves the load capacity of the system. At the same time, the linear operation of the current feedback operational amplifier with model AD844 is obviously more accurate, more robust, and more responsive than the nonlinear operation of the multiplier with model AD633. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a phase trajectory diagram of a pressure stability monitoring circuit in an embodiment of the present invention;

[0026] Figure 2 A typical period window phase trajectory diagram of a pressure stability monitoring circuit in an embodiment of the present invention;

[0027] Figure 3 is a schematic diagram of a pressure stability monitoring circuit in an embodiment of the present invention;

[0028] Figure 4 A chaotic phase trajectory diagram in the experimental simulation of the pressure stability monitoring circuit in an embodiment of the present invention;

[0029] Figure 5 1 is a periodic window phase trajectory diagram in the experimental simulation of the pressure stability monitoring circuit in the embodiment of the present invention. DETAILED DESCRIPTION

[0030] This embodiment provides a pressure stability monitoring circuit based on a chaotic system period window, and the expression of the chaotic system used is as follows:

[0031]

[0032] Among them, x, y, and z are state variables in three dimensions respectively; a and b are system parameters respectively.

[0033] like Figure 1 As shown in Figure 2, when parameter a = 0.9, parameter b = 1, and initial value IC = (0.8, -2, 0), the system realizes chaotic oscillation. The phase trajectory diagram of the pressure stability monitoring circuit based on the periodic window of the chaotic system is shown in Figure 2. Figure 1 As shown, the Li index of the chaotic system is (0.1401, 0, -0.8573), where Figure 1 (a) is the phase trajectory diagram in the xy plane, Figure 1 (b) is the phase trajectory diagram in the yz plane, Figure 1 (c) is the phase trajectory diagram in the xz plane, Figure 1 (d) is the phase trajectory diagram in the xyz plane.

[0034] When the system is in a chaotic state, the system maintains the property of positive Lyapunov index, that is, the one-dimensional Lyapunov index is positive; when b = 1, the initial value (0.8, -2, 0) remains unchanged, and the parameter a changes in the interval [0, 1.8], the Lyapunov index spectrum and bifurcation diagram of the system are as follows Figure 5 As shown in the figure, it can be seen that when a is in the interval [0.85, 0.891], the system is in a periodic state; when a changes in the interval [0.891, 0.95], the system is in a chaotic state, but the chaotic interval contains some values ​​that make the system in a periodic state; when a is in the interval [0.95, 1], the system is in a periodic state; that is, in the chaotic interval of this system, there are multiple periodic window states.

[0035] like Figure 2 As shown in Figure 1, it is a typical period window phase trajectory diagram of the pressure stability monitoring circuit based on the period window of the chaotic system, where Figure 2 (a) is the xy plane phase trajectory diagram when a=0.87, Figure 2 (b) is the xy plane phase trajectory diagram when a=0.96. From the phase trajectory and Li index, it can be obtained that the system is in a typical periodic state when the parameter a=0.87 or 0.96, and maintains a multi-periodic phenomenon close to chaos in a small interval of adjacent values.

[0036] like Figure 3 As shown, it is the circuit schematic diagram of the pressure stability monitoring circuit based on the periodic window of the chaotic system. The adjustable amplitude frequency modulation and bias adjustment circuit is realized by introducing the current feedback operational amplifier U4. The chaotic oscillator is realized by simplifying the circuit. Using three multipliers and one operational amplifier, a three-dimensional chaotic system with adjustable amplitude frequency modulation and bias adjustment and high coupling can be realized.

[0037] The circuit equation of the pressure stability monitoring circuit based on the chaotic system period window is as follows:

[0038]

[0039] Among them, x, y, and z are state variables in three dimensions respectively.

[0040] like Figure 3As shown, the simplified circuit of the chaotic system realizes multiplication term coupling through multiplier AD633, and the parameters are set as follows: resistance R1 = resistance R2 = resistance R3 = 1kΩ, resistance R4 = 10kΩ, resistance R5 = 1MΩ, resistance R6 = 0Ω, capacitance C1 = capacitance C2 = capacitance C3 = 10nF, and chaotic oscillation is realized when the control voltage Vcc = 0V.

[0041] A pressure stability monitoring circuit based on a chaotic system period window includes a first branch, a second branch and a third branch. In the first branch, the model of the multiplier U1 is AD633, and the multiplier U1 is powered by an external power supply V p Through its own VS+ port, external power supply V n It is driven by its own VS-port; the two ends of the resistor R1 are respectively connected to the W output port and the Z output port of the multiplier U1; the X1 port and the Y1 port of the multiplier U1 are both connected to the input signal y, the X2 port is grounded, and the Y2 port is connected to the input signal z through the adjustable resistor R5; the multiplier U1 is connected to the input signal x through the resistor R1, and the output of the multiplication term is transmitted to the input signal x; one end of the capacitor C1 is connected to the input signal x, and the other end is grounded, so as to realize the x-dimensional differential operation of the chaotic oscillation circuit.

[0042] In the second branch, the model of multiplier U2 is AD633, and the multiplier U2 is powered by an external power supply V p Through its own VS+ port, external power supply V n Driven by its own VS-port, the two ends of the resistor R2 are respectively connected to the W output port and the Z output port of the multiplier U2; the X1 port of the multiplier U2 is connected to the input signal y, the X2 port and the Y1 port are both connected to the input signal z, and the Y2 port is grounded; the multiplier U2 is connected to the input signal y through the resistor R2, and the output of the multiplication term is transmitted to the input signal y; one end of the capacitor C2 is connected to the input signal y, and the other end is grounded, so as to realize the y-dimensional differential operation of the chaotic oscillation circuit.

[0043] In the third branch, the model of multiplier U3 is AD633, and the multiplier U3 is powered by an external power supply V p Through its own VS+ port, external power supply V n Driven by its own VS-port, the two ends of the resistor R3 are respectively connected to the W output port and the Z output port of the multiplier U3; the X1 port of the multiplier U3 is connected to the input signal x, the X2 port is connected to the control voltage Vcc, the Y1 port is connected to the input signal y, and the Y2 port is grounded; the multiplier U3 is connected to the input signal z through the resistor R3, and the output of the multiplication term is transmitted to the input signal z; one end of the capacitor C3 is connected to the input signal z, and the other end is grounded, so as to realize the z-dimensional differential operation of the chaotic oscillation circuit.

[0044] The first branch and the second branch are connected together through a current feedback operational amplifier U4. The model of the current feedback operational amplifier U4 is AD844. The current feedback operational amplifier U4 is powered by an external power supply V p and V n Drive, its forward input port is connected to the input signal y, the TZ port is connected to the input signal x through the resistor R6, the reverse input port is grounded through the varistor R4, the parameter a in the chaotic system is realized through the resistor R6 and the varistor R4 in the circuit system, and the output of the output port is x+ay; therefore, when the pressure in the application scenario changes, the varistor R4 also changes accordingly, that is, the parameter a of the chaotic oscillator changes, thereby realizing the switching between the period window and the chaotic oscillation.

[0045] This embodiment utilizes the special periodic window phenomenon of the chaotic system and adopts the characteristics of the varistor to change the resistance value of the varistor R4 in the circuit structure, thereby realizing the regulation of the parameter a in the dynamic system, and further transforming the subtle pressure changes into obvious and easily observable chaotic phenomena through the change of the phase track emitted by the physical chaotic circuit signal.

[0046] Since the initial value of the chaotic system cannot be reflected in the circuit and the interference of the environment on the pressure stability monitoring circuit must be considered in practical applications, the adjustable resistor R5 is retained. In specific application scenarios, the chaotic state and periodic state can be set by simply fine-tuning the adjustable resistor R5. When the pressure stability monitoring circuit based on the periodic window of the chaotic system is applied to actual monitoring, changes in pressure will change the resistance of the varistor R4, thereby changing the value of parameter a in the dynamic system, and realizing the switching between chaotic oscillations and periodic phenomena.

[0047] like Figure 4 As shown, it is the chaotic phase trajectory diagram in the experimental simulation of the pressure stability monitoring circuit based on the periodic window of the chaotic system. Figure 4 (a) is the xy plane phase trajectory diagram when a=0.9, Figure 4 (b) is the xz plane phase trajectory diagram when a=0.9, which shows that the pressure stability monitoring circuit based on the chaotic system period window can realize chaotic oscillation.

[0048] like Figure 5 As shown, it is the period window phase trajectory diagram in the experimental simulation of the pressure stability monitoring circuit based on the period window of the chaotic system, where Figure 5 (a) is the xy plane phase trajectory diagram when a=0.87, Figure 5 (b) is the xy plane phase trajectory diagram when a=0.96. Since the actual circuit cannot represent the initial conditions of the chaotic system, the phase trajectory in the actual circuit will be slightly different from the simulation. However, it can be seen from the simulation diagram that the circuit system still maintains the periodic characteristics of the periodic window.

[0049] In reality, the conversion between periodic window and chaos can be easily achieved by changing the resistance values ​​of varistor R4 and adjustable resistor R5. The clear periodic window phenomenon in the actual circuit can be achieved by controlling the resistance value of varistor R4, thereby converting subtle pressure changes into obvious and easily observable chaos-periodic switching phenomenon through a simple detection circuit structure.

[0050] Therefore, the special periodic window phenomenon of the selected chaotic system (that is, the existence of multiple periodic small intervals in a large chaotic interval) is utilized, and the resistance value of some resistors in the circuit structure is changed by using varistors, so as to realize the regulation of parameter a in the dynamic system; and further through the change of the phase track emitted by the actual chaotic circuit signal, the subtle pressure changes are converted into obvious and easy-to-observe chaotic phenomena; the detection system manufactured based on this principle has high sensitivity and the effect is very significant, and it will be widely used in intelligent manufacturing, disaster prevention and mitigation and other fields with excellent reliability.

[0051] In addition to the above embodiments, the present invention may also have other implementation modes. Any technical solution formed by equivalent replacement or equivalent transformation falls within the protection scope required by the present invention.

Claims

1. A pressure stability monitoring circuit based on a chaotic system period window, characterized in that: The chaotic oscillation circuit includes a first branch, a second branch and a third branch. A current feedback operational amplifier U4 is connected between the first branch and the second branch. The first branch includes a multiplier U1, a resistor R1, an adjustable resistor R5 and a capacitor C1. The multiplier U1 is powered by an external power supply V p Through its own VS+ port, external power supply V n It is driven by its own VS-port; the two ends of the resistor R1 are respectively connected to the W output port and the Z output port of the multiplier U1; the X1 port and the Y1 port of the multiplier U1 are both connected to the input signal y, the X2 port is grounded, and the Y2 port is connected to the input signal z through the adjustable resistor R5; the multiplier U1 is connected to the input signal x through the resistor R1, and the output of the multiplication term is transmitted to the input signal x; one end of the capacitor C1 is connected to the input signal x, and the other end is grounded, so as to realize the x-dimensional differential operation of the chaotic oscillation circuit; The second branch includes a multiplier U2, a resistor R2 and a capacitor C2. The multiplier U2 is powered by an external power supply V p Through its own VS+ port, external power supply V n Driven by its own VS-port, the two ends of the resistor R2 are respectively connected to the W output port and the Z output port of the multiplier U2; the X1 port of the multiplier U2 is connected to the input signal y, the X2 port and the Y1 port are both connected to the input signal z, and the Y2 port is grounded; the multiplier U2 is connected to the input signal y through the resistor R2, and the output of the multiplication term is transmitted to the input signal y; one end of the capacitor C2 is connected to the input signal y, and the other end is grounded, so as to realize the y-dimensional differential operation of the chaotic oscillation circuit; The third branch includes a multiplier U3, a resistor R3 and a capacitor C3. The multiplier U3 is powered by an external power supply V p Through its own VS+ port, external power supply V n Driven by its own VS-port, the two ends of the resistor R3 are respectively connected to the W output port and the Z output port of the multiplier U3; the X1 port of the multiplier U3 is connected to the input signal x, the X2 port is connected to the control voltage Vcc, the Y1 port is connected to the input signal y, and the Y2 port is grounded; the multiplier U3 is connected to the input signal z through the resistor R3, and the output of the multiplication term is transmitted to the input signal z; one end of the capacitor C3 is connected to the input signal z, and the other end is grounded, so as to realize the z-dimensional differential operation of the chaotic oscillation circuit; The current feedback operational amplifier U4 is powered by an external power supply V p and V n Drive, its positive input port is connected to the input signal y, the TZ port is connected to the input signal x through the resistor R6, the reverse input port is grounded through the varistor R4, and the output of the output port is x+ay; the parameter a in the chaotic system is realized by the resistor R6 and the varistor R4, and the parameter a changes with the change of the varistor R4, so as to realize the switching between the period window and the chaotic oscillation.

2. The pressure stability monitoring circuit based on the chaotic system period window according to claim 1 is characterized in that: The expression of the chaotic system is: Among them, x, y, and z are state variables in three dimensions respectively; a and b are system parameters respectively.

3. The pressure stability monitoring circuit based on chaotic system period window according to claim 1 is characterized in that: The circuit equation is Among them, x, y, and z are state variables in three dimensions respectively.

4. The pressure stability monitoring circuit based on chaotic system period window according to claim 1 is characterized in that: The resistors R1 , R2 and R3 are all set to be equal, and the capacitors C1 , C2 and C3 are all set to be equal.

5. The pressure stability monitoring circuit based on chaotic system period window according to claim 2 is characterized in that: The resistors R1, R2 and R3 are all set to 1 kΩ, the resistor R6 is set to 0 Ω, the capacitors C1, C2 and C3 are all set to 10 nF, and the external power supply V p Set to 15V, external power supply V n Set to -15V, control voltage Vcc is set to 0V, and chaotic oscillation is achieved when varistor R4 is equal to 10kΩ and adjustable resistor R5 is equal to 1MΩ.

6. The pressure stability monitoring circuit based on chaotic system period window according to claim 1 is characterized in that: The models of the multiplier U1, the multiplier U2 and the multiplier U3 are all AD633.

7. The pressure stability monitoring circuit based on chaotic system period window according to claim 1 is characterized in that: The model of the current feedback operational amplifier U4 is AD844.

Images