Electromagnetic vibration table control method and system considering multiple non-linear factors

Abstract

The present invention provides a control method and system for an electromagnetic vibration table considering multiple non-linear factors, including: establishing a lumped parameter model of the non-linear motion of the vibration table by utilizing the similarity in mathematical form between the mechanical system and the circuit system; then, according to the characteristics of the model at different excitation frequencies, identifying the parameters of each mechanical component to obtain the control equation of the vibration table, and calculating the excitation current curve in the drive coil according to the control objective; finally, judging whether the tracking error meets the requirements through the simulation of the established non-linear model, and generating an excitation current waveform file or a real-time analog signal to be input into the power amplification device of the vibration table after meeting the requirements. The present invention considers the influence brought by the non-linear stiffness during the working process of the electro-dynamic vibration table, and uses a non-linear inductor to simulate the non-linear stiffness in the mechanical system. The drive current calculated by using the feed-forward control algorithm can reduce the harmonic distortion during the sine sweep test of the vibration table, and improve the control accuracy and test accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic vibration table control, and particularly to an electromagnetic vibration table control method and system considering multiple nonlinear factors. In particular, it relates to a precise control algorithm for the excitation frequency, amplitude, and waveform of a vibration table during a vibration test. Background Art

[0002] With the large-scale and complex working environment of aerospace service equipment, aerospace satellites and aero-engines usually need to work in an environment with periodic vibrations for a long time. In order to analyze the response of a satellite's entire body and an engine's entire body under vibration excitation, vibration tests need to be carried out on them. According to the test results, the inherent vibration characteristics and structural defects of the spacecraft are found, so as to optimize the design of the spacecraft.

[0003] During the vibration test, a large-scale electrodynamic vibration table is the core experimental equipment for simulating the adaptability and reliability of the actual dynamic environment. The design indicators of the vibration table mainly include the maximum thrust, the working frequency range, and the vibration amplitude. The power system of the vibration table mainly consists of a moving coil, a suspension spring, an air spring, an excitation coil, a drive coil, etc. (as Figure 1 )). During the control process of the vibration table, the dynamic model is usually simplified to a linear spring oscillator (as Figure 2 ), and under the action of the electromagnetic force, the moving coil drives the device under test to perform a vibration test. However, due to the non-uniformity of the magnetic field generated by the excitation coil of the electrodynamic vibration table, the traditional linear model is difficult to capture the nonlinear relationship between the displacement and the external excitation when the amplitude is large. Its output response will show harmonic distortion under a pure sine input, and it is impossible to identify the system response under the presence of harmonics and DC bias in the external excitation, and it is impossible to capture the creep effect of the vibration support system. The creep effect refers to a phenomenon that when the frequency of the vibration table becomes higher, the stiffness of its suspension system gradually becomes harder. This will cause great interference to the vibration test and is not conducive to accurately measuring the modal characteristics of the device under test.

[0004] Currently, the control strategies of the vibration table mainly focus on controlling the frequency and amplitude of the vibration table. The vibration table is often regarded as a linear system, ignoring the harmonic response and frequency interference caused by nonlinear effects, and lacking waveform control during the test process. And the current waveform control algorithms are mainly based on feedback control strategies, comparing the sampling results with the control target, and adjusting the external excitation according to the error between the two. The control effect often has hysteresis.

[0005] Therefore, how to avoid nonlinear phenomena such as harmonic distortion caused by nonlinear effects in the system under large amplitudes has become the focus of improving the performance of the vibration table. Summary of the Invention

[0006] Aiming at the defects in the prior art, the purpose of the present invention is to provide a control method and system for an electromagnetic vibration table considering multiple non - linear factors.

[0007] A control method for an electromagnetic vibration table considering multiple non - linear factors provided by the present invention includes:

[0008] Step S1: Based on the circuit - mechanical analogy method, establish a lumped mass model of the non - linear motion of the vibration table, denoted as the mechatronic model;

[0009] Step S2: According to the characteristics of the mechatronic model at different excitation frequencies, identify the parameters of each mechanical element of the vibration table;

[0010] Step S3: Obtain the control equation of the vibration table according to the mechatronic model and the identified parameters;

[0011] Step S4: Determine whether the control equation is an autonomous equation. If so, use the autonomous equation and the control objective to calculate the time - domain response of all state variables, and execute Step S5; if not, use the non - autonomous equation combined with the time - domain response of the state variables, and execute Step S5;

[0012] Step S5: Calculate the applied control excitation and calculate the excitation current curve in the drive coil;

[0013] Step S6: Judge whether the tracking error meets the requirements through the established mechatronic model simulation. If so, generate an excitation current waveform file or input a real - time analog signal into the vibration table power amplification device; if not, return to Step S3 until the control objective is met.

[0014] Preferably, the mechatronic model includes a non - linear inductor, a resistor, and a non - linear transformer;

[0015] The non - linear inductor is used to simulate the non - linear stiffness of the vibration table suspension system;

[0016] The non - linear inductor and the resistor are connected in parallel to form a non - linear unit, which is used to simulate the creep effect of the vibration system caused by the non - linear stiffness of the vibration table under low - frequency excitation and medium - frequency excitation;

[0017] Through the non - linear transformer, simulate the non - linear relationship between the drive current and the electromagnetic force.

[0018] Preferably, the method for identifying the parameters of each mechanical element of the vibration table includes using the impedance changes of each electrical component at different frequencies and the linearized system under low - amplitude conditions to estimate the system stiffness parameters and force coefficient parameters at different positions.

[0019] Preferably, step S3 includes controlling the impedance of each electronic component by adjusting the excitation frequency of the applied current, identifying the parameters of the electronic components in the system, and converting the circuit system into a mechanical system to obtain the control equation of the system.

[0020] Preferably, the autonomous equation and the non - autonomous equation are obtained by classifying the control equation according to whether it is autonomous;

[0021] Among multiple control equations, first use the autonomous equation combined with the ideal change situation of the control target to obtain the time - domain change situation of all control variables, and then combine the non - autonomous equation according to the time - domain change situation of all state variables to inversely deduce the applied control excitation.

[0022] According to an electromagnetic vibration table control system considering multiple non - linear factors provided by the present invention, it includes:

[0023] Module M1: Based on the circuit - mechanical analogy method, establish a lumped mass model of the non - linear motion of the vibration table, denoted as the mechatronics model;

[0024] Module M2: Identify the parameters of each mechanical component of the vibration table according to the characteristics of the mechatronics model at different excitation frequencies;

[0025] Module M3: Obtain the control equation of the vibration table according to the mechatronics model and the identified parameters;

[0026] Module M4: Determine whether the control equation is an autonomous equation. If so, use the autonomous equation and the control target to calculate the time - domain response of all state variables, and trigger Module M5; if not, use the non - autonomous equation combined with the time - domain response of the state variables to trigger Module M5;

[0027] Module M5: Calculate the applied control excitation and calculate the excitation current curve in the drive coil;

[0028] Module M6: Judge whether the tracking error meets the requirements through the established mechatronics model simulation. If so, generate an excitation current waveform file or input the real - time analog signal into the vibration table power amplification device; if not, return to Module M3 until the control target is met.

[0029] Preferably, the mechatronics model includes a non - linear inductor, a resistor, and a non - linear transformer;

[0030] The non - linear inductor is used to simulate the non - linear stiffness of the vibration table suspension system;

[0031] The non - linear inductor and the resistor are connected in parallel to form a non - linear unit, which is used to simulate the creep effect of the vibration system caused by the non - linear stiffness of the vibration table under low - frequency excitation and medium - frequency excitation;

[0032] Through the non-linear transformer, the non-linear relationship between the simulated driving current and the electromagnetic force is obtained.

[0033] Preferably, the method for identifying the parameters of each mechanical element of the identification vibration table includes estimating the system stiffness parameters and force coefficient parameters at different positions by using the impedance changes of each electrical component at different frequencies and the linearized system in the case of low amplitude.

[0034] Preferably, module M3 includes controlling the impedance of each electronic component by adjusting the excitation frequency of the applied current, identifying the parameters of the electronic components in the system, and converting the circuit system into a mechanical system to obtain the control equation of the system.

[0035] Preferably, the autonomous equation and the non-autonomous equation are obtained by distinguishing according to whether the control equation is autonomous;

[0036] Among multiple control equations, first, the time-domain variation of all control variables is obtained by using the autonomous equation in combination with the ideal variation of the control target, and then the applied control excitation is deduced by combining the time-domain variation of all state variables with the non-autonomous equation.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. The present invention takes into account the influence of non-linear stiffness during the operation of the electrodynamic vibration table, uses a non-linear inductor to simulate the non-linear stiffness in the mechanical system, and the driving current calculated by the feed-forward control algorithm can reduce the harmonic distortion during the sine sweep test of the vibration table, which helps to improve the control accuracy and test accuracy.

[0039] 2. The present invention obtains parameters such as the stiffness and damping of the vibration system through parameter identification, and based on these parameters, the curve for controlling the vibration table is deduced, thereby compensating for the interference of non-linear factors during the operation of the vibration table, which helps to improve the control accuracy and test accuracy.

[0040] 3. The control structure of the present invention is simple, and it is applicable to the feed-forward precise tracking control of parameters such as the moving coil motion waveform, amplitude, and frequency of the vibration table. For any controlled target in the state variables, tracking control can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] By reading the following detailed description of the non-limiting embodiments with reference to the accompanying drawings, other features, objects, and advantages of the present invention will become more apparent:

[0042] Figure 1 It is a schematic diagram of the main component structure of the vibration table system in the present invention;

[0043] Figure 2 It is a simplified model and force diagram of the vibration table;

[0044] Figure 3 It is a schematic diagram of the traditional linear model of the vibration table in the present invention;

[0045] Figure 4 It is a mechatronic model diagram of the present invention considering the nonlinear effect of the vibration table;

[0046] Figure 5 It is a simplified diagram of the vibration system when the excitation frequency exceeds 10 times the natural frequency of the system, and is used to measure the drive current - electromagnetic force coefficient of the vibration table at different positions;

[0047] Figure 6 It is a schematic diagram of the working method flow of the present invention. Specific embodiments

[0048] The present invention will be described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0049] The present invention first uses the similarity between the mechanical system and the circuit system in mathematical form to establish a lumped mass model of the nonlinear motion of the vibration table; then, according to the characteristics of the model at different excitation frequencies, the parameters of each mechanical element are identified; subsequently, the control equation of the vibration table is obtained based on the established model and the identified parameters, and the excitation current curve in the drive coil is calculated according to the control objective; finally, it is judged whether the tracking error meets the requirements through the established nonlinear model simulation, and after meeting the requirements, an excitation current waveform file or a real-time analog signal is generated and input into the vibration table power amplification device.

[0050] Embodiment 1

[0051] According to a control method for an electromagnetic vibration table considering multiple nonlinear factors provided by the present invention, as Figure 6 shown, it includes:

[0052] Step S1: Based on the circuit - mechanical analogy method, establish a lumped mass model of the nonlinear motion of the vibration table, denoted as a mechatronic model considering the nonlinear effect of the vibration table. The mechatronic model includes a nonlinear inductor, a resistor, and a nonlinear transformer, as Figure 4As shown, a mechatronic model of a vibration table is constructed by means of circuit-mechanical analogy using non-linear electronic components, and a non-linear inductor is used to simulate the non-linear stiffness of the suspension system of the vibration table. Based on the traditional linear model, the system stiffness is changed by adding a non-linear unit composed of an inductor and a resistor to simulate phenomena such as harmonic distortion, DC offset, and creep effect that occur during the operation of the vibration table; that is, a non-linear unit composed of a parallel connection of a non-linear inductor and a resistor is used to simulate the creep effect that occurs in the vibration system under low-frequency excitation and medium-frequency excitation due to the non-linear stiffness of the vibration table. The non-linear relationship between the driving current and the electromagnetic force is simulated by a non-linear transformer.

[0053] The main components of the vibration table system are as Figure 1 shown. The vibration table system includes a driving circuit system and a mechanical vibration system. As Figure 2 shown, the simplified model and force diagram of the vibration table.

[0054] Using mechatronic modeling, the mechanical model of the electrodynamic vibration table is transformed into a circuit model. According to the similar mathematical relationship between circuit components and mechanical components, the current I and voltage V in the circuit system are respectively analogized to the force F and velocity u in the mechanical system. As shown in Table 1, the inductor, resistor, and capacitor in the circuit components are analogized to mechanical components such as springs, dampers, and masses to construct a traditional linear model of the vibration table, as Figure 3 shown. Where M 1 represents the mass of the moving coil of the vibration table, K 1 represents the stiffness of the suspension system of the vibration table, C 1 represents the mechanical damping of the vibration table, and Bl represents the ratio of the electromagnetic force on the driving coil to the current in the driving coil. Since the velocities corresponding to all mechanical components are equal to the velocity of the moving coil, the corresponding inductor, capacitor, and resistor components are connected in parallel to each other, and the inertial force f 1 , restoring force f 2 , and damping force f 3 sum up to be equal to the electromagnetic force f on the driving coil. According to the current-force analogy relationship and Kirchhoff's nodal current law, it can be regarded as a series circuit composed of three components and a transformer.

[0055] Table 1 Migration analogy relationship table between mechanical components and electrical components

[0056]

[0057]

[0058] Step S2: Identify the parameters of each mechanical component of the vibration table according to the characteristics of the mechatronic model at different excitation frequencies. The method for identifying the parameters of each mechanical component of the vibration table includes estimating the system stiffness parameters and force coefficient parameters at different positions by using the impedance changes of each electrical component at different frequencies and the linearized system under low-amplitude conditions.

[0059] Step S3: Obtain the control equation of the vibration table based on the mechatronic model and the identified parameters. By adjusting the excitation frequency of the applied current, controlling the impedance of each electronic component, identifying the parameters of the electronic components in the system, and converting the circuit system into a mechanical system, the control equation of the system is obtained.

[0060] The stiffness of the vibration table suspension system (suspension spring and air spring) increases with the increase of displacement. In the present invention, a nonlinear unit is added to the traditional linear model to simulate the nonlinear effect of the vibration table support suspension system, and a nonlinear transformer is used to simulate the non-uniformity of the magnetic field generated by the vibration table excitation coil, as Figure 4 shown, and an algorithm for identifying parameters such as the nonlinear stiffness and nonlinear force coefficient of a large vibration table is established.

[0061] (1) System mass and nonlinear stiffness identification

[0062] First, define the stiffness K 1 as position-dependent. Use a direct current signal to make the moving coil of the vibration table generate a static displacement x.

[0063] At such a static equilibrium position, use a small-amplitude signal to sweep the frequency of the vibration table. Measure the local resonance frequency f 1 .

[0064] Then, change the mass of the system so that the mass changes from the original M to M + m, change the magnitude of the current, keep the suspension position unchanged, and perform a small-amplitude frequency sweep on the system again to determine the local resonance frequency f 2 of the system in the same displacement state.

[0065] The mechanical impedance at the resonance of the system satisfies equations (1) and (2)

[0066]

[0067] By combining, the system stiffness and mass are obtained as equations (3) and (4) respectively:

[0068]

[0069]

[0070] From the measured values of these two resonance frequencies, the mass M of the system and the stiffness K at the current position can be determined.

[0071] Repeat this process for different values of x to obtain the stiffnesses at different positions. Use Equation (5) to fit the stiffness-displacement curve of the shaker based on the stiffnesses at different positions.

[0072] K 1 (x) = K 1 (0)(1 + a 1 x + a 2 x 2 + a 3 x 3 + a 4 x 4 + a 5 x 5 + a 6 x 6 )(5)

[0073] where a 1 -a 6 are all parameters to be fitted.

[0074] (2) Identification of Nonlinear Force Coefficient

[0075] First, define the force coefficient Bl as position-dependent. Apply a DC electrical signal to cause the shaker to have a static displacement x.

[0076] Apply a high-frequency excitation, which is 10 times higher than the resonance frequency. The electromagnetic force can be considered to act completely on the mass of the shaker, and the equivalent circuit is as Figure 5 shown. Measure the amplitude of the shaker voice coil acceleration and denote it as A.

[0077] Change the system mass so that the mass changes from the original M to M + m, and measure the amplitude of the shaker voice coil acceleration A'.

[0078] Obtain the equations:

[0079] IBl = MA (6)

[0080] I'Bl = (M + m)A' (7)

[0081] By combining these equations, we get:

[0082]

[0083] Change the DC component to make the voice coil float at different positions, and obtain the relationship between the current and the electromagnetic force at different positions.

[0084] Based on the force coefficients at different positions, use Equation (8) to fit the stiffness-displacement curve of the shaker.

[0085]

[0086] where b 1 and b 2 and c 1 and c 2 and d 1 and d 2 are all parameters to be fitted.

[0087] (3) Linear damping parameter identification

[0088] Measure K 2 and K 3 (0), R 1 and R 2 and R 3 using the iterative method. Pass a small direct current through the drive coil and measure the step response of the moving coil of the vibration table. Since the current amplitude is low and the displacement of the moving coil is small, the whole process can be regarded as linear vibration. Assume the initial values of K 2 and K 3 (0), R 1 and R 2 and R 3 . Predict the response of the system for the same step input. Fix R 1 and change K 2 and K 3 (0), R 2 and R 3 to minimize the error of the predicted response. Fix K 2 and K 3 (0), R 2 and R 3 and recalculate R 1 . Repeat this process. Calculate the non-linear stiffness using the scaling relationship

[0089] Step S4: Determine whether the control equation is an autonomous equation. If so, calculate the time-domain responses of all state variables using the autonomous equation and the control objective, and execute Step S5; if not, use the non-autonomous equation combined with the time-domain responses of the state variables and execute Step S5. The autonomous equation and the non-autonomous equation are obtained by classifying the control equation according to whether it is autonomous. That is to say, the control equation of the system is divided into an autonomous equation and a non-autonomous equation according to whether it is autonomous.

[0090] Among multiple control equations, first use the autonomous equation combined with the ideal change situation of the control objective to obtain the time-domain change situation of all control variables, and then, based on the time-domain change situation of all state variables and combined with the non-autonomous equation, inversely deduce the externally applied control excitation. This is a feedforward control method.

[0091] Step S5: Calculate the externally applied control excitation and calculate the excitation current curve in the drive coil.

[0092] Step S6: Determine whether the tracking error meets the requirements through the established mechatronics model simulation. If so, generate an excitation current waveform file or input the real-time analog signal into the vibration table power amplification device; if not, return to Step S3 until the control target is met.

[0093] The feedforward control algorithm based on the backstepping control theory is the key to the present invention. Assume that the displacements of three nodes are x 1 , x 2 , x 3 . According to the above-mentioned mechatronic system modeling, the motion equation of the dynamic system can be expressed as:

[0094]

[0095] where K 1 and K 3 are both functions of x 1 . The state variable x 1 and its variation are the control objectives. Assume that the tracking value of x 1 is x 1d . The tracking values of its velocity and acceleration can be obtained as and Substitute the tracking target into the control equations (2)-(3), and the state equations can be obtained:

[0096]

[0097] Using the Runge-Kutta method, calculate the time-domain variations of x 2 , x 3 , and , denoted as x 2d , x 3d , and Substitute the obtained state change laws into Equation (14) to calculate the excitation current i(t) required for feedforward control.

[0098]

[0099] Input the calculated excitation current into the drive coil of the vibration table, and the interference of the nonlinear effect on the vibration waveform can be eliminated, and the motion waveform of the moving coil of the vibration table under ideal conditions can be obtained.

[0100] Substitute the excitation current into the state equation (15), and use the fourth-order Runge-Kutta algorithm to simulate and calculate the motion curve x 1 (t) of the moving coil of the vibration table, and compare it with the control target x 1dCompare with (t) to determine whether the tracking control error meets the requirements. If the control result meets the error requirements, generate a waveform file of the exciting current or input the obtained real-time analog model value into the vibration table power amplification device.

[0101]

[0102] Furthermore, the electromagnetic vibration table control method considering multiple non-linear factors of the present invention will be specifically described below in conjunction with the accompanying drawings and embodiments:

[0103] Step 1: Estimate parameters such as the non-linear stiffness of the vibration table suspension support system. Apply direct current to the drive coil to cause a certain displacement of the moving coil of the vibration table. Based on the DC signal, perform linear frequency sweeping using a small-amplitude signal, measure the amplitude of the moving coil of the vibration table using a laser sensor, and measure the resonance frequency f of the system. 1 Change the system mass and measure the resonance frequency f again. 2 Combine the resonance frequencies measured twice to calculate the mass of the moving coil of the vibration table and the stiffness at this position.

[0104] Step 2: Change the magnitude of the DC signal, repeat Step 1, measure the system stiffness at different positions, and use the least squares method to fit the stiffness-displacement curve of the system.

[0105] Step 3: Apply a small-amplitude step excitation to the system and measure the step response. Use the iterative method, K 2 , K 3 (0), R 1 , R 2 and R 3 , and obtain the control equation of the mechanical system according to the circuit system.

[0106] Step 4: Set the control target. For example, control the acceleration waveform of the moving coil of the vibration table to be a pure sine excitation, that is, require Integrate to obtain the velocity and displacement of the moving coil as and x 1 =-A(2πf) 2 sin(2πft). Where A and f are the amplitude and frequency of the moving coil of the vibration table under control respectively; if the acceleration of the vibration table is controlled to perform linear sine frequency sweeping motion, then it is required that where f 0 , f t are the start frequency and stop frequency of the frequency sweep respectively, and c 1 and c 2 are parameters used to eliminate the DC component of the signal respectively.

[0107] Step 5: Use the autonomous equation in the control equation set and the control target to solve for the time-domain variation of all state variables.

[0108] Step Six: Substitute the state variables into the non-autonomous equations in the control equations to solve for the time-domain variation of the applied control excitation.

[0109] Step Seven: Apply the calculated applied excitation to the established non-linear system model, use the Runge-Kutta method to simulate the motion of the moving coil of the shaking table after applying the feedforward control, and determine whether the tracking error meets the requirements based on it. If the requirements are met, generate an excitation current waveform file or input the real-time analog signal into the power amplification device of the shaking table.

[0110] The present invention aims to provide a method for identifying parameters such as the non-linear stiffness and force coefficient of a shaking table, and performing feedforward control on the vibration waveform of the moving coil during its operation according to the identification results, so as to overcome the waveform distortion phenomenon caused by non-linear effects in the case of low-frequency and large-amplitude of a large shaking table.

[0111] Embodiment Two

[0112] The present invention also provides an electromagnetic shaking table control system considering multiple non-linear factors. The electromagnetic shaking table control system considering multiple non-linear factors can be implemented by executing the process steps of the electromagnetic shaking table control method considering multiple non-linear factors. That is, those skilled in the art can understand the electromagnetic shaking table control method considering multiple non-linear factors as a preferred implementation manner of the electromagnetic shaking table control system considering multiple non-linear factors.

[0113] An electromagnetic shaking table control system considering multiple non-linear factors provided according to the present invention includes:

[0114] Module M1: Based on the circuit-mechanical analogy method, establish a lumped mass model of the non-linear motion of the shaking table, denoted as the mechatronic model. The mechatronic model includes a non-linear inductor, a resistor, and a non-linear transformer. The non-linear inductor is used to simulate the non-linear stiffness of the shaking table suspension system. The non-linear inductor and the resistor are connected in parallel to form a non-linear unit, which is used to simulate the creep effect of the vibration system caused by the non-linear stiffness of the shaking table under low-frequency excitation and medium-frequency excitation. Through the non-linear transformer, the non-linear relationship between the drive current and the electromagnetic force is simulated.

[0115] Module M2: According to the characteristics of the mechatronic model at different excitation frequencies, identify the parameters of each mechanical component of the shaking table. The method of identifying the parameters of each mechanical component of the shaking table includes using the impedance changes of each electrical component at different frequencies and the linearized system under low-amplitude conditions to estimate the system stiffness parameters and force coefficient parameters at different positions.

[0116] Module M3: Obtain the control equation of the shaking table based on the mechatronics model and the identified parameters. Module M3 includes controlling the impedance of each electronic component by adjusting the excitation frequency of the applied current, identifying the parameters of the electronic components in the system, and converting the circuit system into a mechanical system to obtain the control equation of the system.

[0117] Module M4: Determine whether the control equation is an autonomous equation. If so, calculate the time-domain response of all state variables using the autonomous equation and the control objective, and trigger Module M5. If not, use the non-autonomous equation combined with the time-domain response of the state variables to trigger Module M5. The autonomous equation and the non-autonomous equation are obtained by classifying the control equation according to whether it is autonomous. Among multiple control equations, first use the autonomous equation combined with the ideal change of the control objective to obtain the time-domain change of all control variables, and then, based on the time-domain change of all state variables combined with the non-autonomous equation, inversely deduce the applied control excitation.

[0118] Module M5: Calculate the applied control excitation and calculate the excitation current curve in the drive coil.

[0119] Module M6: Determine whether the tracking error meets the requirements through simulation using the established mechatronics model. If so, generate an excitation current waveform file or input the real-time simulation signal into the power amplification device of the shaking table. If not, return to Module M3 until the control objective is met.

[0120] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc., to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structure within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as either software modules for implementing the method or the structure within the hardware component.

[0121] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined arbitrarily with each other.

Claims

1. A control method for an electromagnetic vibration table taking into account multiple nonlinear factors, characterized in that: include: Step S1: Based on the circuit-mechanical analogy method, a concentrated mass model of the nonlinear motion of the vibration table is established, which is recorded as a mechatronics model; Step S2: identifying the parameters of each mechanical component of the vibration table according to the characteristics of the mechatronics model at different excitation frequencies; Step S3: obtaining a control equation of the vibration table according to the mechatronics model and the identified parameters; Step S4: Determine whether the control equation is an autonomous equation. If so, use the autonomous equation and the control target to calculate the time domain response of all state variables and execute step S5; if not, use the non-autonomous equation combined with the time domain response of the state variables and execute step S5; Step S5: calculating the external control excitation and the excitation current curve in the driving coil; Step S6: Determine whether the tracking error meets the requirements through the established mechatronics model simulation. If so, generate an excitation current waveform file or input the real-time analog signal to the vibration table power amplifier device; if not, return to step S3 until the control target is met.

2. The electromagnetic vibration table control method considering multiple nonlinear factors according to claim 1, characterized in that: The mechatronics model includes nonlinear inductors, resistors and nonlinear transformers; The nonlinear inductor is used to simulate the nonlinear stiffness of the vibration table suspension system; The nonlinear inductor and resistor are connected in parallel to form a nonlinear unit, which is used to simulate the creep effect of the vibration system caused by the nonlinear stiffness of the vibration table under low-frequency excitation and medium-frequency excitation; The nonlinear relationship between the driving current and the electromagnetic force is simulated by the nonlinear transformer.

3. The electromagnetic vibration table control method considering multiple nonlinear factors according to claim 1, characterized in that: The method of identifying the parameters of each mechanical component of the vibration table includes estimating the system stiffness parameters and force coefficient parameters at different positions by utilizing the impedance changes of each electrical component at different frequencies and the linearized system under low amplitude conditions.

4. The electromagnetic vibration table control method considering multiple nonlinear factors according to claim 1, characterized in that: Step S3 includes controlling the impedance of each electronic component by adjusting the excitation frequency of the external current, identifying the parameters of the electronic components in the system, and converting the circuit system into a mechanical system to obtain the control equation of the system.

5. The electromagnetic vibration table control method considering multiple nonlinear factors according to claim 1, characterized in that: The autonomous equation or non-autonomous equation is distinguished according to whether the differential equation explicitly contains a time-dependent driving current i(t); In multiple control equations, the autonomous equations are first used in combination with the ideal changes of the control objectives to obtain the time domain changes of all control variables. Then, the time domain changes of all state variables are combined with the non-autonomous equations to reversely obtain the external control excitation.

6. An electromagnetic vibration table control system considering multiple nonlinear factors, characterized in that: include: Module M1: Based on the circuit-mechanical analogy, a lumped parameter model of the nonlinear motion of the vibration table is established, which is denoted as the mechatronics model; Module M2: Identify the parameters of each mechanical element of the vibration table according to the characteristics of the mechatronics model at different excitation frequencies; Module M3: obtaining the control equation of the vibration table according to the mechatronics model and the identified parameters; Module M4: Determine whether the control equation is an autonomous equation. If so, use the autonomous equation and the control target to calculate the time domain response of all state variables, and trigger module M5; if not, use the non-autonomous equation combined with the time domain response of the state variables to trigger module M5; Module M5: Calculate the external control excitation and the excitation current curve in the driving coil; Module M6: Determine whether the tracking error meets the requirements through the established simulation. If so, generate an excitation current waveform file or input the real-time analog signal to the vibration table power amplifier device; if not, return to module M3 until the control target is met.

7. The electromagnetic vibration table control system considering multiple nonlinear factors according to claim 6, characterized in that: The mechatronics model includes nonlinear inductors, resistors and nonlinear transformers; The nonlinear inductor is used to simulate the nonlinear stiffness of the vibration table suspension system; The nonlinear inductor and resistor are connected in parallel to form a nonlinear unit, which is used to simulate the creep effect of the vibration system caused by the nonlinear stiffness of the vibration table under low-frequency excitation and medium-frequency excitation; The nonlinear relationship between the driving current and the electromagnetic force is simulated by the nonlinear transformer.

8. The electromagnetic vibration table control system considering multiple nonlinear factors according to claim 6, characterized in that: The method of identifying the parameters of each mechanical component of the vibration table includes estimating the system stiffness parameters and force coefficient parameters at different positions by utilizing the impedance changes of each electrical component at different frequencies and the linearized system under low amplitude conditions.

9. The electromagnetic vibration table control system considering multiple nonlinear factors according to claim 6, characterized in that: Module M3 includes controlling the impedance of each electronic component by adjusting the excitation frequency of the external current, identifying the parameters of the electronic components in the system, and converting the circuit system into a mechanical system to obtain the control equation of the system.

10. The electromagnetic vibration table control system considering multiple nonlinear factors according to claim 6, characterized in that: The autonomous equation and the non-autonomous equation are obtained by dividing the control equation according to whether it is autonomous or not; In multiple control equations, the autonomous equations are first used in combination with the ideal changes of the control objectives to obtain the time domain changes of all control variables. Then, the time domain changes of all state variables are combined with the non-autonomous equations to reversely obtain the external control excitation.

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