Electromagnetic vibration table control method and system considering multiple nonlinear factors

Abstract

The invention provides an electromagnetic vibration table control method and system considering various nonlinear factors, and the method comprises the steps: building a lumped parameter model of the nonlinear motion of a vibration table through the similarity of a mechanical system and a circuit system in a mathematical form; then, according to the characteristics of the model under different excitation frequencies, identifying parameters of each mechanical element to obtain a control equation of a vibration table, and calculating an excitation current curve in a driving coil according to a control target; and finally, judging whether the tracking error meets the requirement or not through simulation of the established nonlinear model, and generating an excitation current waveform file or a real-time analog signal after the requirement is met, and inputting the excitation current waveform file or the real-time analog signal into vibration table power amplification equipment. According to the method, the influence caused by the non-linear rigidity in the working process of the electric vibration table is considered, the non-linear rigidity in a mechanical system is simulated by using the non-linear inductor, the harmonic distortion of the vibration table in the sine frequency sweeping test process can be reduced by using the driving current calculated by using the feedforward control algorithm, and the control precision and the test precision are improved.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic vibration table control technology, and in particular, to a method and system for controlling an electromagnetic vibration table taking into account multiple nonlinear factors, and more particularly to a precise control algorithm for the excitation frequency, amplitude and waveform of a vibration table during a vibration test. Background Art

[0002] As aerospace equipment becomes larger and the working environment becomes more complex, space satellites and aircraft engines usually need to work for a long time in an environment with periodic vibration. In order to analyze the response of the entire satellite and engine under vibration excitation, vibration testing is required. Based on the test results, the inherent vibration characteristics and structural defects of the spacecraft are discovered, so as to optimize the design of the spacecraft.

[0003] In the process of vibration testing, a large electric 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, operating frequency range, and vibration amplitude. The power system of the vibration table is mainly composed of the moving coil, suspension spring, air spring, excitation coil, drive coil, etc. (such as Figure 1 In the control process of the vibration table, the dynamic model is usually simplified to a linear spring oscillator (such as Figure 2 ), under the action of electromagnetic force, the moving coil drives the device under test to perform vibration test. However, due to the non-uniformity of the magnetic field generated by the excitation coil of the electric 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. The output response will have harmonic distortion in the case of pure sinusoidal 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 in which the stiffness of the suspension system gradually becomes harder when the frequency of the vibration table becomes higher. 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] At present, the control strategy of the vibration table mainly focuses 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 lacks waveform control during the test. In addition, the current waveform control algorithm is mainly based on the feedback control strategy, comparing the sampling results with the control target, adjusting the external excitation according to the error between the two, and the control effect often has a lag.

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

[0006] In view of the defects in the prior art, an object of the present invention is to provide an electromagnetic vibration table control method and system taking into account multiple nonlinear factors.

[0007] According to the present invention, a control method for an electromagnetic vibration table taking into account multiple nonlinear factors is provided, comprising:

[0008] 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;

[0009] 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;

[0010] Step S3: obtaining a control equation of the vibration table according to the mechatronics 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 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;

[0012] Step S5: calculating the external control excitation and the excitation current curve in the driving coil;

[0013] 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.

[0014] Preferably, the mechatronic model includes nonlinear inductors, resistors and nonlinear transformers;

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

[0016] 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;

[0017] The nonlinear relationship between the driving current and the electromagnetic force is simulated by the nonlinear transformer.

[0018] Preferably, 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.

[0019] Preferably, step S3 includes 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 to obtain the control equation of the system.

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

[0021] 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.

[0022] According to the present invention, an electromagnetic vibration table control system considering multiple nonlinear factors includes:

[0023] Module M1: Based on the circuit-mechanical analogy, a concentrated mass model of the nonlinear motion of the vibration table is established, which is recorded as a mechatronics model;

[0024] 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;

[0025] Module M3: obtaining 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 external control excitation and the excitation current curve in the driving coil;

[0028] Module M6: 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 module M3 until the control target is met.

[0029] Preferably, the mechatronic model includes nonlinear inductors, resistors and nonlinear transformers;

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

[0031] 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;

[0032] The nonlinear relationship between the driving current and the electromagnetic force is simulated by the nonlinear transformer.

[0033] Preferably, 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.

[0034] Preferably, 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.

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

[0036] 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.

[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 nonlinear stiffness during the operation of the electric vibration table, and uses nonlinear inductance to simulate the nonlinear stiffness in the mechanical system. The driving current calculated by the feedforward control algorithm can reduce the harmonic distortion of the vibration table during the sinusoidal sweep frequency test, which helps to improve the control accuracy and test accuracy.

[0039] 2. The present invention obtains the stiffness, damping and other parameters of the vibration system through parameter identification, and reversely obtains the curve for vibration table control based on these parameters, thereby compensating for the interference of nonlinear factors in the working process 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 is suitable for feedforward precise tracking control of parameters such as the waveform, amplitude and frequency of the dynamic coil of the vibration table. It can achieve tracking control for any controlled target in the state variable. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0043] Figure 2 Simplify the model and force diagram for the shaking table;

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

[0045] Figure 4 A diagram of a mechatronics model constructed for the present invention taking into account the nonlinear effects of the vibration table;

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

[0047] Figure 6 It is a schematic diagram of the working method of the present invention. DETAILED DESCRIPTION

[0048] The present invention is 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 are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0049] The present invention firstly utilizes the similarity between the mechanical system and the circuit system in mathematical form to establish a concentrated 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 component are identified; subsequently, the control equation of the vibration table is obtained according to the established model and the identified parameters, and the excitation current curve in the driving coil is calculated according to the control target; finally, the established nonlinear model is simulated to determine whether the tracking error meets the requirements, and if the requirements are met, an excitation current waveform file or a real-time analog signal is generated and input into the vibration table power amplifier device.

[0050] Embodiment 1

[0051] According to the present invention, a control method of an electromagnetic vibration table considering multiple nonlinear factors is provided, such as Figure 6 As shown, including:

[0052] Step S1: Based on the circuit-mechanical analogy, a concentrated mass model of the nonlinear motion of the vibration table is established, which is recorded as a mechatronics model considering the nonlinear effect of the vibration table. The mechatronics model includes nonlinear inductance, resistance and nonlinear transformer, such as Figure 4As shown in the figure, the mechatronics model of the vibration table is constructed by circuit-mechanical analogy using nonlinear electronic components, and the nonlinear inductance is used to simulate the nonlinear stiffness of the vibration table suspension system. The system stiffness is changed on the basis of the traditional linear model, and a nonlinear unit composed of an inductor and a resistor is added to simulate the harmonic distortion, DC bias, creep effect and other phenomena that occur during the operation of the vibration table; that is, the nonlinear unit composed of a nonlinear inductor and a resistor in parallel 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 a nonlinear transformer.

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

[0054] The mechanical model of the electric vibration table is converted into a circuit model by using mechatronics modeling. Based on the mathematical similarity between circuit elements and mechanical elements, the current I and voltage V in the circuit system are compared with the force F and velocity u in the mechanical system, as shown in Table 1. The inductance, resistance and capacitance in the circuit elements are compared with mechanical elements such as springs, damping and mass to construct the traditional linear model of the vibration table, as shown in Table 1. Figure 3 As shown. Where M1 represents the mass of the vibration table's dynamic coil, K1 represents the stiffness of the vibration table's suspension system, C1 represents the vibration table's mechanical damping, and Bl represents the ratio of the electromagnetic force on the drive coil to the current in the drive coil. Since the speeds corresponding to all mechanical components are equal to the speed of the dynamic coil, the corresponding inductors, capacitors, and resistors are connected in parallel with each other, and the sum of the inertial force f1, restoring force f2, and damping force f3 on the three components is equal to the electromagnetic force f on the drive coil. According to the current-force analogy and Kirchhoff's node current law, the three components and the transformer can be regarded as forming a series circuit.

[0055] Table 1 Analogy relationship between mechanical components and electrical components migration

[0056]

[0057]

[0058] Step S2: Identify the parameters of each mechanical component of the vibration table according to the characteristics of the mechatronics model at different excitation frequencies. 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 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 according to the mechatronics 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) will increase with the increase of displacement. The present invention simulates the nonlinear effect of the vibration table support suspension system by adding nonlinear units on the basis of the traditional linear model, and simulates the non-uniformity of the magnetic field generated by the vibration table excitation coil through a nonlinear transformer, such as Figure 4 As shown, an algorithm for identifying parameters such as nonlinear stiffness and nonlinear force coefficient of a large vibration table is established.

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

[0062] First, the stiffness K1 is defined as position-dependent. A DC signal is used to make the vibration table's dynamic coil produce a static displacement x.

[0063] In such a static equilibrium position, the vibration table is swept with a small amplitude signal to measure the local resonance frequency f1 near the static displacement state under DC excitation.

[0064] Then, the mass of the system is changed from the original M to M+m, the current is changed, the suspension position is kept unchanged, and the system is swept again with a small amplitude to determine the local resonance frequency f2 of the system under the same displacement state.

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

[0066]

[0067] The system stiffness and mass are obtained by combining equations (3) and (4), respectively:

[0068]

[0069]

[0070] From the measured values ​​of the two resonant frequencies, the mass M of the system and the stiffness K in the current position can be determined.

[0071] For different x values, this process is repeated to obtain the stiffness at different positions. According to the stiffness at different positions, the stiffness-displacement curve of the vibration table is fitted using formula (5).

[0072] K1(x)=K1(0)(1+a1x+a2x 2 +a3x 3+a4x 4 +a5x 5 +a6x 6 ) (5)

[0073] Among them, a1-a6 are parameters to be fitted.

[0074] (2) Identification of nonlinear force coefficients

[0075] First, the force coefficient Bl is defined as position-dependent. A DC signal is applied to cause the vibration table to produce a static displacement x.

[0076] Applying high-frequency excitation, 10 times higher than the resonance frequency, the electromagnetic force can be considered to act entirely on the mass of the vibration table. The equivalent circuit is as follows: Figure 5 Measure the acceleration amplitude of the vibration table moving coil, denoted as A.

[0077] Change the mass of the system so that the mass changes from the original M to M+m, and measure the acceleration amplitude A′ of the moving coil of the vibration table.

[0078] We get the equation:

[0079] IBl=MA(6)

[0080] I′Bl=(M+m)A′ (7)

[0081] Combined, we get:

[0082]

[0083] By changing the DC component, the moving coil is suspended at different positions, and the relationship between the current and the electromagnetic force at different positions is obtained.

[0084] According to the force coefficients at different positions, the stiffness-displacement curve of the vibration table is fitted using formula (8).

[0085]

[0086] Among them, b1, b2, c1, c2, d1, and d2 are all parameters to be fitted.

[0087] (3) Identification of linear damping parameters

[0088] Use the iterative method to measure K2, K3(0), R1, R2, and R3. Pass a small DC current through the drive coil and measure the step response of the vibration table's dynamic coil. Because the current amplitude is low and the displacement of the dynamic coil is small, the entire process can be regarded as a linear vibration. Assuming the initial values ​​of K2, K3(0), R1, R2, and R3, predict the response of the system for the same step input. Fix R1 and change K2, K3(0), R2, and R3 to minimize the error in the predicted response. Fix K2, K3(0), R2, and R3, recalculate R1, and repeat the process. Calculate nonlinear stiffness using scaling relationships

[0089] 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. The autonomous equation and the non-autonomous equation are obtained by dividing the control equation according to whether it is autonomous, that is, the control equation of the system is divided into autonomous equation and non-autonomous equation according to whether it is autonomous.

[0090] Among 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, based on the time domain changes of all state variables and combined with the non-autonomous equations, the external control excitation is obtained by reverse deduction. This is a feedforward control method.

[0091] Step S5: Calculate the external control excitation and the excitation current curve in the driving 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 to the vibration table power amplifier 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 the three nodes are x1, x2, and x3 respectively. According to the above electromechanical system modeling, the motion equation of the dynamic system can be expressed as:

[0094]

[0095] Where K1 and K3 are functions of x1. The state variable x1 and its changes are the control targets. Assume that the tracking value of x1 is x 1d , we can get the tracking values ​​of its velocity and acceleration respectively and Substituting the tracking target into the control equations (2)-(3), we can obtain the state equation:

[0096]

[0097] Using the Runge-Kutta method, we can calculate x2, x3, and The time domain variation of 2d 、x 3d , and Substitute the obtained state change rules into equation (14) to calculate the excitation current i(t) required for feedforward control.

[0098]

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

[0100] Substitute the excitation current into the state equation (15), use the fourth-order Runge-Kutta algorithm to simulate and calculate the motion curve x1(t) of the vibration table moving coil, and compare it with the control target x 1d (t) Compare and judge whether the tracking control error meets the requirements. If the control result meets the error requirements, generate the waveform file of the excitation current or input the obtained real-time simulation model into the vibration table power amplifier device.

[0101]

[0102] Furthermore, the electromagnetic vibration table control method considering various nonlinear factors of the present invention will be described in detail as follows in combination with the accompanying drawings and implementation examples:

[0103] Step 1: Estimate the nonlinear stiffness and other parameters of the vibration table suspension support system. Apply direct current to the drive coil to cause a certain displacement of the vibration table dynamic coil. Use a micro-amplitude signal to perform a linear frequency sweep based on the DC signal. Use a laser sensor to measure the amplitude of the vibration table dynamic coil and measure the system resonant frequency f1. Change the system mass and measure the resonant frequency f2 again. Combine the two measured resonant frequencies to calculate the mass of the vibration table dynamic coil and the stiffness at that position.

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

[0105] Step 3: Apply a small step excitation to the system and measure the step response. Using the iterative method, K2, K3 (0), R1, R2 and R3, and according to the circuit system, the control equation of the mechanical system is obtained.

[0106] Step 4: Set the control target. For example, to control the vibration table dynamic coil acceleration waveform to pure sine excitation, that is, The velocity and displacement of the moving coil are obtained by integration. and x1=-A(2πf) 2 sin(2πft). A and f are the amplitude and frequency of the dynamic coil of the controlled vibration table respectively; if the acceleration of the vibration table is controlled to perform a linear sinusoidal sweep motion, then where f0, f t are the start frequency and cut-off frequency of the frequency sweep, c1 and c2 are the parameters used to eliminate the DC component of the signal.

[0107] Step 5: Use the autonomous equations in the control equation group and the control objectives to solve the time domain changes of all state variables.

[0108] Step 6: Substitute the state variables into the non-autonomous equations in the control equation group to solve the time domain variation of the external control excitation.

[0109] Step 7: Apply the calculated external excitation to the constructed nonlinear system model, and use the Runge-Kutta method to simulate the motion of the vibration table's dynamic coil after feedforward control is applied. Based on this, determine whether the tracking error meets the requirements. If it does, generate an excitation current waveform file or input the real-time analog signal into the vibration table power amplifier.

[0110] The present invention aims to provide a method for identifying parameters such as nonlinear stiffness and force coefficient of a vibration table, and performing feedforward control on the vibration waveform of the dynamic coil when the vibration table is working according to the identification results, so as to overcome the waveform distortion phenomenon caused by nonlinear effects of large vibration tables under low frequency and large amplitude conditions.

[0111] Embodiment 2

[0112] The present invention also provides an electromagnetic vibration table control system that takes multiple nonlinear factors into consideration. The electromagnetic vibration table control system that takes multiple nonlinear factors into consideration can be realized by executing the process steps of the electromagnetic vibration table control method that takes multiple nonlinear factors into consideration, that is, those skilled in the art can understand the electromagnetic vibration table control method that takes multiple nonlinear factors into consideration as a preferred implementation of the electromagnetic vibration table control system that takes multiple nonlinear factors into consideration.

[0113] According to the present invention, an electromagnetic vibration table control system considering multiple nonlinear factors includes:

[0114] Module M1: Based on the circuit-mechanical analogy, a concentrated mass model of the nonlinear motion of the vibration table is established, which is recorded as a mechatronics model. 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 through the nonlinear transformer.

[0115] Module M2: Identify the parameters of each mechanical component of the vibration table based on the characteristics of the mechatronics model at different excitation frequencies. 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 using the impedance changes of each electrical component at different frequencies and the linearized system under low amplitude conditions.

[0116] Module M3: The control equation of the vibration table is obtained based on the mechatronics model and the identified parameters. Module M3 includes 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 to obtain the control equation of the system.

[0117] 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. Autonomous equations and non-autonomous equations are obtained by dividing the control equations according to whether they are autonomous. Among multiple control equations, first use the autonomous equation combined with the ideal change of the control target to obtain the time domain change of all control variables, and then combine the non-autonomous equation based on the time domain change of all state variables to reversely obtain the external control excitation.

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

[0119] Module M6: Determine whether the tracking error meets the requirements through the established mechatronics model simulation. If yes, generate an excitation current waveform file or input the real-time analog signal to the vibration table power amplifier. If not, return to module M3 until the control target is met.

[0120] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. 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 realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0121] The above describes the specific embodiments of the present invention. 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 does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

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: Establishing a lumped parameter model of the nonlinear motion of the vibration table based on the circuit-mechanical analogy method; Module M2: Identifying the parameters of each mechanical element of the vibration table according to the characteristics at different excitation frequencies; Module M3: obtaining the control equation of the vibration table according to 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: Said includes nonlinear inductance, resistance and nonlinear transformer; 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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