Method for compensating temperature dependence of ultrasonic motor based on search current minimum value

Abstract

The invention relates to a method for compensating temperature dependence of an ultrasonic motor, in particular to a method for compensating temperature dependence of the ultrasonic motor based on a search current minimum value. The invention aims to solve the problem that the output performance of the ultrasonic motor becomes poor due to the fact that the working frequency of the ultrasonic motor drifts when the temperature of a machine body rises after the ultrasonic motor operates for a long time. The method comprises the following steps: step 1, establishing an ultrasonic motor mathematical model; 2, deriving a maximum efficiency-current minimum value-optimal excitation frequency relation; and step 3, designing and optimizing a search current minimum value algorithm. The invention belongs to the technical field of ultrasonic motor temperature dependence compensation.

Description

Technical Field

[0001] The present invention relates to a method for compensating the temperature dependence of an ultrasonic motor, and belongs to the technical field of temperature dependence compensation of ultrasonic motors. Background Art

[0002] Precision engineering is a widely involved discipline and plays a key role in promoting innovation in machines, instruments, and various systems. The Ultrasonic Motor (USM) stands out with its unique advantages. Compared with traditional motors, it has an extremely high power density, strong output torque, and does not generate electromagnetic interference. The noise during positioning is almost zero. These remarkable characteristics make it an ideal alternative with great potential in the field of precision motion systems. In addition, it can also adapt to harsh environments such as extreme temperatures, high vacuum, and strong radiation. Therefore, ultrasonic motors are also widely used in military fields such as aerospace.

[0003] Since there is contact friction between the stator and the rotor, once the ultrasonic motor enters a continuous and long-term working state, the energy loss generated during the friction process will continue to accumulate, resulting in a gradual increase in the temperature of the body. However, the increase in temperature will cause changes in the material properties of the piezoelectric ceramics. The change in the material property parameters of the piezoelectric ceramics will cause the resonance frequency to shift, thereby causing the working frequency of the motor to drift, making it difficult to maintain the stability of the motor operation, significantly increasing the mechanical loss, and even reducing the service life of the motor. Therefore, dynamically tracking the resonance frequency of the motor during operation and compensating for the temperature dependence can effectively stabilize the output performance of the motor. Previous methods such as compensating the motor speed by a single control variable or achieving speed and efficiency optimization by using a dual-variable control have not effectively alleviated the problem of rapid temperature rise of the motor and have not considered the influence of temperature increase on the drift of the efficiency curve. Summary of the Invention

[0004] The present invention aims to solve the problem that after the ultrasonic motor operates for a long time, the temperature of the body rises, causing the working frequency of the ultrasonic motor to drift, thereby deteriorating the output performance of the ultrasonic motor. Furthermore, a method for compensating the temperature dependence of the ultrasonic motor based on searching for the minimum value of the current is proposed.

[0005] The technical solution adopted by the present invention to solve the above problems is as follows: The specific steps of the present invention include:

[0006] Step 1: Establish a mathematical model of the ultrasonic motor;

[0007] Step 2: Deduce the relationship among the maximum efficiency - minimum current value - optimal excitation frequency;

[0008] Step 3: Design and optimize the algorithm for searching the minimum value of the current.

[0009] Further, the specific process of establishing the mathematical model of the ultrasonic motor in Step 1 is as follows:

[0010] Step 101: Establish the ultrasonic motor model;

[0011] Based on Hamilton's principle, the complex stress and strain problems of piezoelectric ceramics and stator metal elastomers are converted into solving energy equations; through the analysis of the kinetic energy, potential energy, and electrical energy of the stator, and by introducing modal assumptions, the expressions of the stator modal mass, modal stiffness, and modal force are deduced, and then the vibration equation of the stator is derived and the relationship between the amplitude at steady state and the amplitude of the driving voltage is clarified;

[0012] Step 102: Establish the AC conduction characteristic model of the ultrasonic motor;

[0013] Based on the theory of the change in Gibbs free energy of thermodynamics, it is sorted out how temperature affects piezoelectric constants, dielectric constants, and elastic coefficients; on this basis, an equivalent circuit model of piezoelectric ceramics is built, and the AC conduction characteristic expression is obtained. After further solving, it is clarified that the temperature rise directly affects the AC conduction characteristics of piezoelectric ceramics, and the output characteristics of the ultrasonic motor will also change accordingly.

[0014] Further, Step 2 specifically includes:

[0015] Starting from the AC conduction characteristic expression of the ultrasonic motor, the expression is converted into a form represented by the driving voltage and current. On the premise of ensuring that the input voltage remains constant all the time, the converted expression is simplified, modulus calculated, and derivative calculated to prove that there are extreme points in the current, but the characteristics such as the magnitude and occurrence position of the extreme points need to be further verified through subsequent experiments.

[0016] Further, the steps of designing and optimizing the search algorithm for the minimum current in Step 3 include:

[0017] Step 301: Algorithm principle: Using the driving frequency as the control basis, a sine excitation signal is superimposed on the original signal to dynamically scan the frequency. By observing the response of the current to the applied signal, an index called "current gradient" is specifically defined. According to the information of this index, the driving frequency is adjusted to achieve the positioning of the minimum current and the tracking of the optimal frequency;

[0018] Step 302: First, determine the starting center control frequency, then superimpose the sine excitation. After high-pass filtering the sine perturbation excitation, the filtered current value is multiplied by a sine signal with the same frequency and Π phase to obtain the gradient information for frequency search; the obtained gradient information is added to the prior value of the center driving frequency in the previous step to obtain the frequency value corresponding to the current step. The above process is continuously looped until the obtained gradient value is 0. At this time, the current frequency value is output and maintained;

[0019] Step 303: Add a compensator for eliminating steady-state oscillation after the demodulator. By using the method of combining a low-pass filter with relevant gain adjustment, make the amplitude of the sine disturbance gradually tend to 0 as the algorithm converges, so as to eliminate the steady-state oscillation and improve the stability and reliability of the algorithm.

[0020] The beneficial effects of the present invention are as follows:

[0021] 1. The present invention solves the problems of frequency operating point drift, speed and efficiency drift of ultrasonic motors caused by temperature rise during operation, and designs a search current minimum value algorithm to compensate for the influence of temperature drift.

[0022] 2. The present invention deeply studies the overall machine model of the ultrasonic motor and the AC conduction characteristic model of the ultrasonic motor, and reveals the internal mechanism of the motor operation from the theoretical root. The present invention comprehensively considers the influence of temperature on the characteristics of piezoelectric ceramics, accurately grasps the key connection between temperature and motor performance, and provides a scientific and accurate theoretical basis for the design of the temperature drift compensation method.

[0023] 3. The search current minimum value algorithm designed by the present invention superimposes a sine excitation signal on the driving frequency, and combines a series of complex and orderly operation steps such as strict high-pass filtering, precise phase adjustment, and efficient gradient calculation, which can quickly and accurately locate the current minimum value in a complex motor operation environment.

[0024] 4. For the possible steady-state oscillation problem, the present invention innovatively introduces a compensator, so that the sine disturbance amplitude copy can smoothly converge to 0 during the algorithm convergence process.

[0025] 5. The present invention can accurately and quickly locate the current minimum value, and then realize the efficient tracking of the optimal frequency, effectively compensate the temperature drift characteristics of the ultrasonic motor, significantly improve the operation stability and driving efficiency of the motor, and has important significance for promoting the wide application of ultrasonic motors in the fields of aerospace, precision manufacturing, etc. Description of the Drawings

[0026] Figure 1 is the flow chart of the search current minimum value algorithm;

[0027] Figure 2 is the schematic diagram of the principle of the search current minimum value algorithm without steady-state oscillation. Detailed Embodiments

[0028] Detailed Embodiment 1: As Figure 1 shown, the method for compensating the temperature dependence of the ultrasonic motor based on the search current minimum value specifically includes the following steps:

[0029] Step 1: Establish a mathematical model of the ultrasonic motor;

[0030] Step 101, Stator motor coupling model;

[0031] Based on Hamilton's principle, analyze the kinetic energy, potential energy, and electrical energy of the stator, combine Kirchhoff's plate theory, and use the modal hypothesis method to derive the relationship between the vibration amplitude of the motor and the amplitude of the driving voltage under steady-state conditions:

[0032]

[0033] In formula (1), W 0 represents the vibration amplitude of the ultrasonic motor stator at steady state, Θ represents the electromechanical coupling coefficient, U 0 is the amplitude of the driving voltage, K s represents the modal stiffness of the stator, M s is the modal mass corresponding to the modal coordinate of the stator, ω represents the angular frequency, C s is the modal damping coefficient of the stator;

[0034] Step 102, Ultrasonic motor admittance model;

[0035] Based on the theory of the change in Gibbs free energy in thermodynamics, deeply analyze the internal relationship between temperature and these parameters, determine the specific influence mechanism of temperature on the characteristics of piezoelectric ceramics, and obtain its admittance expression as:

[0036]

[0037] In formula (2), G represents conductance, B represents susceptance, G d represents the static branch admittance, C d represents the static clamping capacitance, C m represents the dynamic branch capacitance, L m represents the dynamic branch capacitance, R m represents the dynamic branch resistance;

[0038] Step 2, Establish a frequency-current model;

[0039] Further expand and deeply derive formula (2) to establish the mathematical relationship between the current of the ultrasonic motor and the driving frequency:

[0040] 2ω[ADω 8 -2AEω 6 +(3A - BE - CD)ω 4 +2C] = 0 (3),

[0041] In formula (3), and By using the MATLAB zero analysis function for the above formula, it is obtained that there are multiple zeros in the above formula, one zero is ω = 0, and the magnitudes of the other zeros depend on Cm , L m , and R m specific numerical values;

[0042] Step 3: Design an algorithm for searching the minimum value of the search current; the steps of the algorithm for searching the minimum value of the search current include:

[0043] Step 301: Determine the starting center control frequency;

[0044] Step 302: Superimpose a sinusoidal perturbation excitation;

[0045] Step 303: Perform high-pass filtering;

[0046] Step 304: Multiply the in-phase phase at the same frequency by the filtered current value to obtain the gradient message for frequency search;

[0047] Step 305: Add the gradient to the prior value of the center drive frequency in the (n - 1)th step to obtain the frequency value in the nth step;

[0048] Step 306: Determine whether the gradient is 0. If it is, execute Step 307. If not, return to Step 302;

[0049] Step 307: Output and hold the current frequency value.

[0050] As Figure 2 shown, optimize the algorithm for searching the minimum value of the search current without steady-state oscillation; where in the formula, θ represents the actual input of the system, θ * represents the unknown optimal input (extreme point) of the system, f″ represents the second derivative of the objective function, f * represents the optimal output (extreme value) of the system, and f(θ) represents the output objective function of the system.

[0051] The above is only a preferred embodiment of the present invention, and does not impose any form of limitation on the present invention. Although the present invention has been disclosed above with a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to make equivalent embodiments with equivalent changes within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent replacement, and improvement made to the above embodiments within the spirit and principle of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for compensating the temperature dependence of an ultrasonic motor based on searching for a current minimum, characterized in that: The specific steps include: Step 1, establishing a mathematical model of ultrasonic motor; Step 2: derive the relationship between maximum efficiency, current minimum and optimal excitation frequency; Step 3: Design and optimize the algorithm for searching the current minimum.

2. The method for compensating the temperature dependence of an ultrasonic motor based on searching for a current minimum according to claim 1, characterized in that: The specific process of establishing the mathematical model of the ultrasonic motor in step 1 is: Step 101, establishing an ultrasonic motor model; Based on Hamilton's principle, the complex stress and strain problems of piezoelectric ceramics and stator metal elastic bodies are converted into energy equations for solution; by analyzing the stator's kinetic energy, potential energy and electric energy, and introducing modal assumptions, the expressions of the stator's modal mass, modal stiffness and modal force are derived, and then the vibration equation of the stator is deduced, and the relationship between the amplitude and the driving voltage amplitude in the steady state is clarified; Step 102, establishing an AC conduction characteristic model of an ultrasonic motor; Based on the Gibbs free energy change theory of thermodynamics, we sorted out how temperature affects the piezoelectric constant, dielectric constant and elastic coefficient; on this basis, we built an equivalent circuit model of piezoelectric ceramics and obtained the expression of the AC conduction characteristics. After further solving and clarifying that temperature rise directly affects the AC conduction characteristics of piezoelectric ceramics, the output characteristics of the ultrasonic motor will also change accordingly.

3. The method for compensating the temperature dependence of an ultrasonic motor based on searching for a current minimum according to claim 1, characterized in that: Step 2 specifically includes: Starting from the expression of the ultrasonic motor's AC conduction characteristic, the expression is converted into a form expressed in terms of driving voltage and current. On the premise of ensuring that the input voltage always remains constant, the converted expression is simplified, modulo-calculated, and differentiated to prove that there are extreme points in the current. However, the size of the extreme points, their location, and other characteristics need to be further verified through subsequent experiments.

4. The method for compensating the temperature dependence of an ultrasonic motor based on searching for a current minimum according to claim 1, characterized in that: The steps of designing and optimizing the algorithm for searching the current minimum in step 3 include: Step 301, algorithm principle: taking the driving frequency as the control basis, the frequency is dynamically scanned by superimposing a sinusoidal excitation signal on the original signal. By observing the response of the current to the applied signal, an indicator called "current gradient" is specially defined. The driving frequency is adjusted according to the information of this indicator, thereby locating the current minimum and tracking the optimal frequency; Step 302: First determine the starting center control frequency, then superimpose the sinusoidal excitation, perform high-pass filtering on the sinusoidal disturbance excitation, and multiply the filtered current value by the same frequency π phase sinusoidal signal to obtain the gradient information of the frequency search; add the obtained gradient information to the prior value of the center drive frequency in the previous step to obtain the frequency value corresponding to the current step. Repeat the above process until the obtained gradient value is 0, at which time the current frequency value is output and maintained; Step 303: add a compensator to eliminate steady-state oscillation after the demodulator, and use a low-pass filter combined with a related gain adjustment method to make the amplitude of the sinusoidal disturbance gradually approach 0 as the algorithm converges, thereby eliminating steady-state oscillation and improving the stability and reliability of the algorithm.

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