Thermal-mechanical-electrical coupled dynamic hysteresis modeling method for piezoelectric fast mirrors

Abstract

The present invention relates to a method for modeling a thermal-mechanical-electric coupled dynamic hysteresis of a piezoelectric fast reflector, comprising the steps of obtaining input and output data of the piezoelectric fast reflector at a current temperature; modeling a driving amplifier portion of the piezoelectric fast reflector using a series circuit of a resistor and a gain according to the obtained input and output data; modeling a hysteresis effect of the piezoelectric fast reflector using a series and parallel circuit; obtaining a variation law of an input and output characteristic curve of the piezoelectric fast reflector at different temperatures; modeling the electromechanical dynamic characteristics of the piezoelectric fast reflector using a mass-damping-spring model; modeling the output position and angle of the piezoelectric fast reflector using a strain bridge circuit according to the relationship between the position and angle of the piezoelectric fast reflector; and establishing a thermal-mechanical-electric coupled dynamic hysteresis nonlinear model of the piezoelectric fast reflector. The present invention can improve the modeling accuracy of the piezoelectric fast reflector and broaden its application field.

Description

Technical Field

[0001] The invention relates to a thermal-mechanical-electrical coupling dynamic hysteresis modeling method for a piezoelectric fast reflecting mirror. Background Art

[0002] Piezoelectric fast mirrors, as devices for precisely controlling beam direction, effectively address issues such as image motion and line-of-sight instability, and are widely used in various optoelectronic imaging systems. However, factors such as hysteresis, nonlinearity, and external temperature fluctuations and disturbances severely impact the control accuracy and response speed of piezoelectric fast mirrors.

[0003] Establishing a complex dynamic model for a high-precision piezoelectric fast mirror is a prerequisite for designing high-precision control methods. Currently, existing technologies for modeling piezoelectric fast mirrors only consider hysteresis, nonlinearity, and mechanical characteristics, but fail to model the mirror's temperature characteristics. This results in low modeling accuracy in environments with fluctuating external temperatures. Summary of the Invention

[0004] In view of this, it is necessary to provide a thermal-mechanical-electrical coupled dynamic hysteresis modeling method for piezoelectric fast mirrors.

[0005] The present invention provides a thermal-mechanical-electrical coupled dynamic hysteresis modeling method for a piezoelectric fast reflection mirror, which comprises the following steps: a. sending a signal to the piezoelectric fast reflection mirror through a control board, driving the piezoelectric fast reflection mirror through a high-voltage amplifier, measuring the position angle of the piezoelectric fast reflection mirror at the current moment through a displacement sensor and returning the result to the control board, thereby obtaining input and output data of the piezoelectric fast reflection mirror at the current temperature; b. modeling the driving and amplifying part of the piezoelectric fast reflection mirror using a series circuit of a resistor and a gain according to the obtained input and output data; c. modeling the hysteresis effect of the piezoelectric fast reflection mirror using a series and parallel circuit according to the obtained input and output data; d. sending a signal to the power amplifier through the control board to make the thermal resistance wire work, and modeling the piezoelectric fast reflection mirror through a series circuit of a resistor and a gain; The temperature sensor measures the temperature at this time and records the input and output signals of the piezoelectric fast reflection mirror at the same time to obtain the change law of the input-output characteristic curve of the piezoelectric fast reflection mirror at different temperatures; e. adopts the mass-damping-spring model to model the electromechanical dynamic characteristics of the piezoelectric fast reflection mirror; f. according to the relationship between the position and angle of the piezoelectric fast reflection mirror, adopts the strain bridge circuit to model the output position and angle of the piezoelectric fast reflection mirror; g. according to the modeled series circuit of resistance and gain, series and parallel circuits of hysteresis effect, the change law of the input-output characteristic curve of the piezoelectric fast reflection mirror at different temperatures, the mass-damping-spring model, and the strain bridge circuit, a thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast reflection mirror is established.

[0006] Preferably, step a includes: first, giving the piezoelectric fast reflection mirror a sinusoidal signal through the D / A module of the control board, and driving the piezoelectric fast reflection mirror through a high-voltage amplifier; at the same time, using a displacement sensor to measure the position angle of the piezoelectric fast reflection mirror at the current moment, and returning it to the control module of the control board through the A / D module of the control board to obtain the input and output data of the piezoelectric fast reflection mirror at the current temperature.

[0007] Preferably, the step b comprises:

[0008] According to the driving circuit principle of the piezoelectric fast mirror, the series circuit of the resistor and gain in the piezoelectric fast mirror is equivalent to a general proportional link for modeling. The mathematical expression of this part is:

[0009]

[0010] Among them, k v is the gain constant, R0 is the circuit resistance, is the charge in the circuit, u v (t) and u c (t) are the voltage of the hysteresis part and the voltage of the capacitance part respectively.

[0011] Preferably, the step c comprises:

[0012] The piezoelectric fast mirror is partially characterized by the hysteresis effect H(q), capacitance C and the thermal-mechanical-electrical coupling conversion factor G em The hysteresis effect H(q) is described by the PI model, and its mathematical expression is:

[0013]

[0014] Among them, w represents the play operator weight, R is the upper limit of the integral interval, P n [u] represents the play operator, and its mathematical expression is:

[0015]

[0016] Here, r represents the threshold of the play operator.

[0017] Preferably, the step c further comprises:

[0018] According to the characteristics of piezoelectric ceramic materials, the coupling conversion factor G in the PI hysteresis model is converted to em Characterized by:

[0019]

[0020] Among them, s 33 is the mechanical compliance coefficient, A and tp is the cross section of the piezoelectric material and the thickness of the stack, d 33 is the dielectric constant of the piezoelectric material, and its value is related to the ambient temperature.

[0021] Preferably, the step c further comprises

[0022] According to Kirchhoff's law, the circuit model expression is:

[0023]

[0024] At this time, the thermal-mechanical-electrical coupling conversion factor satisfies the equation:

[0025]

[0026] Where, is the derivative of the output displacement of the piezoelectric fast mirror.

[0027] Preferably, step d comprises:

[0028] The D / A module of the control board sends a signal to the power amplifier to start the thermal resistance wire and measure the temperature at this time through the temperature sensor; at the same time, the input and output signals of the piezoelectric fast reflection mirror are recorded, and then the recorded temperature data is substituted into the G in step c. em (T) function, the variation law of the input-output characteristic curve of the piezoelectric fast reflection mirror at different temperatures is obtained.

[0029] Preferably, the step e comprises:

[0030] The mechanical characteristics of the flexible hinge of the piezoelectric fast reflector are equivalent to a mass-damper-spring model. The mathematical expression of the mass-damper-spring model is:

[0031]

[0032] Among them, m, b and k are the mass, damping and stiffness of the piezoelectric fast reflection mirror, respectively. Reasonable parameter values ​​are selected according to the specific material of the piezoelectric fast reflection mirror.

[0033] Preferably, the step f comprises:

[0034] The angle sensing part and the mechanical strain part of the piezoelectric fast reflector are equivalent to a strain bridge circuit and expressed as a proportional link. That is, the mathematical expression between the rotation angle θ(t) of the piezoelectric deflection mirror and the strain x(t) is:

[0035] θ(t)=k sg x(t) (17)

[0036] Among them, k sgis the proportional coefficient of the sensor.

[0037] Preferably, the step g comprises:

[0038] According to the sub-models of each part of the piezoelectric fast mirror, a thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast mirror is established with electrical energy, charge potential energy, thermodynamics and mechanical dynamics as the conversion link. The mathematical expression of the thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast mirror is:

[0039]

[0040] According to the above steps, a thermal-mechanical-electrical coupled dynamic hysteresis model of the piezoelectric fast mirror is established.

[0041] This application can comprehensively consider the working temperature change, hysteresis nonlinearity, mechanical dynamics and other characteristics of the piezoelectric fast reflection mirror, and has important engineering practical significance for improving the modeling accuracy of the piezoelectric fast reflection mirror and broadening its application field. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a flow chart of the thermal-mechanical-electrical coupled dynamic hysteresis modeling method for the piezoelectric fast mirror of the present invention;

[0043] Figure 2 A logic diagram for implementing a thermal-mechanical-electrical coupled dynamic hysteresis modeling method for a piezoelectric fast mirror provided in an embodiment of the present invention;

[0044] Figure 3 A schematic diagram of the hardware implementation environment of the thermal-mechanical-electrical coupled dynamic hysteresis modeling method for a piezoelectric fast mirror provided by an embodiment of the present invention;

[0045] Figure 4 A schematic diagram of input and output data using a piezoelectric fast reflection mirror under different temperature conditions provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] See Figure 1 1 is a flowchart of a preferred embodiment of the thermal-mechanical-electrical coupled dynamic hysteresis modeling method for a piezoelectric fast reflection mirror according to the present invention.

[0048] Step S1: The control board sends a signal to the piezoelectric fast reflection mirror, which is driven by a high-voltage amplifier. The displacement sensor measures the current position angle of the piezoelectric fast reflection mirror and returns it to the control board, thereby obtaining the input and output data of the piezoelectric fast reflection mirror at the current temperature. Specifically:

[0049] Please combine Figure 2-3 As shown, first, a sinusoidal signal is given to the piezoelectric fast reflection mirror through the D / A module of the control board, and the piezoelectric fast reflection mirror is driven by the high-voltage amplifier; at the same time, a displacement sensor is used to measure the current position angle of the piezoelectric fast reflection mirror, and the position angle is returned to the control module of the control board through the A / D module of the control board to obtain the input and output data of the piezoelectric fast reflection mirror at the current temperature.

[0050] Step S2: Based on the obtained input and output data, a series circuit of resistance and gain is used to model the driving amplifier part of the piezoelectric fast reflection mirror. Specifically:

[0051] In this embodiment, based on the driving circuit principle of the piezoelectric fast reflection mirror, part (A) is regarded as a series circuit of resistance and gain, which is equivalent to a general proportional link for modeling. The mathematical expression of this part is:

[0052]

[0053] Among them, k v is the gain constant, R0 is the circuit resistance, is the charge in the circuit, u v (t) and u c (t) are the voltage of the hysteresis part and the voltage of the capacitance part respectively.

[0054] Step S3: Based on the input and output data obtained, a series and parallel circuit is used to model the hysteresis effect of the piezoelectric fast reflection mirror. Specifically:

[0055] In this embodiment, part (B) is characterized by the hysteresis effect H(q), capacitance C and thermal-mechanical-electrical coupling conversion factor G em The hysteresis effect H(q) is described by the PI model, and its mathematical expression is:

[0056]

[0057] Among them, w represents the play operator weight, R is the upper limit of the integral interval, P n [u] represents the play operator, and its mathematical expression is:

[0058]

[0059] Where r represents the threshold of the play operator; assuming that the number of play operators n in the present invention is 10, the operator threshold is r i=i / 10; z(t) is the boundary value of the play operator. According to the input and output data of the piezoelectric fast reflection mirror obtained in step S1, the weight w of the PI hysteresis model is calculated. According to the characteristics of the piezoelectric ceramic material, the coupling conversion factor G in the PI hysteresis model is converted to em Characterized by:

[0060]

[0061] Among them, s 33 is the mechanical compliance coefficient, A and t p is the cross section of the piezoelectric material and the thickness of the stack, d 33 is the dielectric constant of the piezoelectric material, and its value is related to the ambient temperature. According to Kirchhoff's law, the circuit model expression is:

[0062]

[0063] At this time, the thermal-mechanical-electrical coupling conversion factor satisfies the equation:

[0064]

[0065] Where, is the derivative of the output displacement of the piezoelectric fast mirror.

[0066] Step S4: The control board sends a signal to the power amplifier to activate the thermal resistor, and the temperature at that time is measured by the temperature sensor. At the same time, the input and output signals of the piezoelectric fast reflector are recorded to obtain the change pattern of the input and output characteristic curve of the piezoelectric fast reflector at different temperatures. Specifically:

[0067] The D / A module of the control board sends a signal to the power amplifier to start the thermal resistance wire and measure the temperature at that time through the temperature sensor; at the same time, the input and output signals of the piezoelectric fast reflection mirror are recorded, and the recorded data is as follows: Figure 4 Then substitute the recorded temperature data into G in step S3. em (T) function, the variation law of the input-output characteristic curve of the piezoelectric fast reflection mirror at different temperatures is obtained.

[0068] Step S5: Modeling the electromechanical dynamic characteristics of the piezoelectric fast reflection mirror using a mass-damper-spring model. Specifically:

[0069] In this embodiment, as shown in part (C), the mechanical characteristics of the flexible hinge of the piezoelectric fast reflection mirror are equivalent to a mass-damper-spring model. The mathematical expression of the mass-damper-spring model is:

[0070]

[0071] Among them, m, b and k are the mass, damping and stiffness of the piezoelectric fast reflection mirror, respectively. Reasonable parameter values ​​are selected according to the specific material of the piezoelectric fast reflection mirror.

[0072] Step S6: Based on the relationship between the position and angle of the piezoelectric fast reflection mirror, a strain bridge circuit is used to model the output position and angle of the piezoelectric fast reflection mirror. Specifically:

[0073] In this embodiment, as shown in (D), the angle sensing portion and the mechanical strain portion of the piezoelectric fast reflector are equivalent to a strain bridge circuit and expressed as a proportional link. That is, the mathematical expression between the rotation angle θ(t) of the piezoelectric deflection mirror and the strain x(t) is:

[0074] θ(t)=k sg x(t) (26)

[0075] Among them, k sg is the proportional coefficient of the sensor.

[0076] Step S7: Based on the modeled series circuit of resistance and gain, the series and parallel circuits of hysteresis effect, the variation law of the input and output characteristic curves of the piezoelectric fast reflector at different temperatures, the mass-damper-spring model, and the strain bridge circuit, a thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast reflector is established. Specifically:

[0077] According to the sub-models of each part of the piezoelectric fast mirror, a thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast mirror is established with electrical energy, charge potential energy, thermodynamics and mechanical dynamics as the conversion link. The mathematical expression of the thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast mirror is:

[0078]

[0079] According to the above steps, a thermal-mechanical-electrical coupled dynamic hysteresis model of the piezoelectric fast mirror is established.

[0080] This application fully considers the modeling of the thermal-mechanical-electrical coupled hysteresis dynamic characteristics of the piezoelectric fast reflector, which has important engineering practical significance for improving its modeling accuracy and broadening its application field.

[0081] Although the present invention has been described with reference to the current preferred embodiments, those skilled in the art should understand that the above-mentioned preferred embodiments are only used to illustrate the present invention and are not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A thermal-mechanical-electrical coupled dynamic hysteresis modeling method for a piezoelectric fast mirror, characterized in that: The method comprises the following steps: a. The control board sends a signal to the piezoelectric fast reflector, which is driven by a high-voltage amplifier. The displacement sensor measures the current position angle of the piezoelectric fast reflector and returns it to the control board, thereby obtaining the input and output data of the piezoelectric fast reflector at the current temperature. b. Modeling the driving amplifier portion of the piezoelectric fast mirror using a series circuit of a resistor and a gain according to the obtained input and output data; c. Modeling the hysteresis effect of the piezoelectric fast mirror using series and parallel circuits based on the input and output data obtained; d. The control board sends a signal to the power amplifier to activate the thermal resistor wire, and the temperature at this time is measured by the temperature sensor. At the same time, the input and output signals of the piezoelectric fast reflector are recorded to obtain the change pattern of the input and output characteristic curve of the piezoelectric fast reflector at different temperatures; e. Modeling the electromechanical dynamic characteristics of the piezoelectric fast mirror using a mass-damper-spring model; f. Based on the relationship between the position and angle of the piezoelectric fast mirror, a strain bridge circuit is used to model the output position and angle of the piezoelectric fast mirror; g. A thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast reflector is established based on the modeled series circuit of resistance and gain, the series and parallel circuits of hysteresis effect, the changing patterns of the input-output characteristic curves of the piezoelectric fast reflector at different temperatures, the mass-damper-spring model, and the strain bridge circuit.

2. The method according to claim 1, wherein The step a comprises: First, a sinusoidal signal is given to the piezoelectric fast reflection mirror through the D / A module of the control board, and the piezoelectric fast reflection mirror is driven by a high-voltage amplifier; at the same time, a displacement sensor is used to measure the current position angle of the piezoelectric fast reflection mirror, and the signal is returned to the control module of the control board through the A / D module of the control board to obtain the input and output data of the piezoelectric fast reflection mirror at the current temperature.

3. The method according to claim 2, wherein The step b comprises: According to the driving circuit principle of the piezoelectric fast mirror, the series circuit of the resistor and gain in the piezoelectric fast mirror is equivalent to a general proportional link for modeling. The mathematical expression of this part is: Among them, k v is the gain constant, R0 is the circuit resistance, is the charge in the circuit, u v (t) and u c (t) are the voltage of the hysteresis part and the voltage of the capacitance part respectively.

4. The method according to claim 3, wherein The step c comprises: The piezoelectric fast mirror is partially characterized by the hysteresis effect H(q), capacitance C and the thermal-mechanical-electrical coupling conversion factor G em The hysteresis effect H(q) is described by the PI model, and its mathematical expression is: Among them, w represents the play operator weight, R is the upper limit of the integral interval, P n [u] represents the play operator, and its mathematical expression is: Here, r represents the threshold of the play operator.

5. The method according to claim 4, wherein The step c also includes: According to the characteristics of piezoelectric ceramic materials, the coupling conversion factor G in the PI hysteresis model is converted to em Characterized by: Among them, s 33 is the mechanical compliance coefficient, A and t p is the cross section of the piezoelectric material and the thickness of the stack, d 33 is the dielectric constant of the piezoelectric material, and its value is related to the ambient temperature.

6. The method according to claim 5, wherein The step c also includes According to Kirchhoff's law, the circuit model expression is: At this time, the thermal-mechanical-electrical coupling conversion factor satisfies the equation: Where, is the derivative of the output displacement of the piezoelectric fast mirror.

7. The method according to claim 6, wherein Step d includes: The D / A module of the control board sends a signal to the power amplifier to start the thermal resistance wire and measure the temperature at this time through the temperature sensor; at the same time, the input and output signals of the piezoelectric fast reflection mirror are recorded, and then the recorded temperature data is substituted into the G in step c. em (T) function, the variation law of the input-output characteristic curve of the piezoelectric fast reflection mirror at different temperatures is obtained.

8. The method according to claim 7, wherein The step e comprises: The mechanical characteristics of the flexible hinge of the piezoelectric fast reflector are equivalent to a mass-damper-spring model. The mathematical expression of the mass-damper-spring model is: Among them, m, b and k are the mass, damping and stiffness of the piezoelectric fast reflection mirror, respectively. Reasonable parameter values ​​are selected according to the specific material of the piezoelectric fast reflection mirror.

9. The method according to claim 8, wherein Described step f comprises: The angle sensing part and the mechanical strain part of the piezoelectric fast reflector are equivalent to a strain bridge circuit and expressed as a proportional link. That is, the mathematical expression between the rotation angle θ(t) of the piezoelectric deflection mirror and the strain x(t) is: θ(t)=k sg x(t) (8) Among them, k sg is the proportional coefficient of the sensor.

10. The method according to claim 9, wherein Described step g comprises: According to the sub-models of each part of the piezoelectric fast mirror, a thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast mirror is established with electrical energy, charge potential energy, thermodynamics and mechanical dynamics as the conversion link. The mathematical expression of the thermal-mechanical-electrical coupled dynamic hysteresis nonlinear model of the piezoelectric fast mirror is: According to the above steps, a thermal-mechanical-electrical coupled dynamic hysteresis model of the piezoelectric fast mirror is established.

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