Compensation method for vibration table-eccentric load interaction considering exciter coupling

Abstract

The present invention relates to a vibration table-eccentric load interaction compensation method that takes into account the coupling effect of the exciters. After adopting this compensation strategy, the coupling effect between the two exciters is completely eliminated, and the waveform correlation coefficients of the two exciters reproducing the seismic records are increased by 14.75% and 5.48%, respectively. The present invention also establishes a transfer function matrix for the vibration table and the eccentric load. Based on the transfer function matrix, an in-depth study is conducted on the control-structure interaction (CSI) of the vibration table under different load eccentricity (ER) conditions, revealing the influence of CSI. Due to the influence of CSI, the coupling effect between the two exciters is amplified by at least 22 times.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration testing, and in particular relates to a vibration table-eccentric load interaction compensation method for considering the coupling effect of an exciter. Background Art

[0002] Electro-hydraulic shakers are essential testing equipment in fields such as engineering seismic research, automotive road simulation, and aerospace vibration testing. Controlled-structure interaction (CSI) between the shaker and eccentric loads is a major factor in reducing shaker test accuracy. Currently, load eccentricity (ER) and exciter coupling pose challenges to studying CSI between the shaker and eccentric loads. The interaction becomes more pronounced when the load's center of gravity deviates from the shaker's surface. Research into the mechanisms of interaction between shakers and eccentric loads has made significant progress in compensating for this interaction. However, research into the effects of this interaction is still in its infancy. The impact of key load characteristics such as mass, moment of inertia, and eccentricity remains unclear. Furthermore, the impact of this interaction on the exciter and its coupling requires further investigation. In particular, a compensation strategy that not only compensates for the interaction between the shaker and the eccentric load but also for the coupling between the two exciters is urgently needed to further improve shaker test accuracy. Summary of the Invention

[0003] To address the above issues, this application discloses a real-time compensation method (strategy) that takes into account the coupling effect of the exciter, and verifies the effectiveness of this strategy in the frequency domain and time domain respectively. In addition, this application also uses a biaxial vibration table and eccentric load as research objects, establishes a system transfer function matrix, analyzes the impact of CSI, and compensates for CSI. Based on the transfer function matrix, an in-depth study is conducted on the impact of CSI under different load eccentricity (ER) conditions, thus exploring the influence of CSI on the transfer function matrix.

[0004] Specifically, the present invention provides a method for compensating for the interaction between a vibration table and an eccentric load, taking into account the coupling effect of the exciter. The eccentric load is eccentrically arranged on the surface of the vibration table. The vibration table is driven in a single horizontal direction by exciters 1 and 2 driven by a hydraulic drive system. The method is characterized in that the control error signal of exciter 1 and the control error signal of exciter 2 are calculated according to Equation 16:

[0005]

[0006] Among them, u1 is the control error signal of exciter 1; u2 is the control error signal of exciter 2; x is the control signal; G3 is the three-parameter generator and feedforward, G4 is the three-parameter feedback; Ga is the transfer function of the sensor; x1 is the displacement of exciter 1; x2 is the displacement of exciter 2; C xφ 、C 12 、C φx 、C 21 are the compensation transfer functions respectively.

[0007] A further vibration table-eccentric load interaction compensation method considering the exciter coupling effect is proposed, where the compensation transfer function C xφ 、C 12 、C φx 、C 22 Calculate according to formula 19:

[0008]

[0009] Where G2 is calculated according to formula 8; A p is the effective pressure-bearing area of ​​the piston; l is the distance from the exciter to the center of the vibration table; G q k q0 is the transfer function of the servo valve; I T is the moment of inertia of the vibration table; I E is the equivalent moment of inertia of the vibration table and the load; M T is the mass of the vibration table surface; M E is the equivalent mass of the vibration table and the load; s is the Laplace operator; a is the eccentric distance of the equivalent mass;

[0010]

[0011] Where V is the equivalent cylinder volume; β is the bulk elastic modulus of the oil; A p is the effective pressure-bearing area of ​​the piston; K c is the pressure flow coefficient of the servo valve; C C is the cylinder leakage coefficient; s is the Laplace operator.

[0012] A further vibration table-eccentric load interaction compensation method considering the exciter coupling effect is proposed, where the transfer function of exciter 1 and exciter 2 is shown in Equation 20:

[0013]

[0014] Where G2 is calculated according to Formula 8; l is the distance from the exciter to the center of the vibration table; a is the eccentric distance of the equivalent mass; J t is the moment of inertia of the vibration table; s is the Laplace operator; x1 is the displacement of exciter 1; x2 is the displacement of exciter 2; G3 is the transfer function of the three-parameter input device; A p is the effective pressure-bearing area of ​​the piston; G q kq0 is the transfer function of the servo valve; u 01 is the control signal of vibration table 1; u 02 is the control signal of vibration table 2.

[0015] A vibration table-eccentric load interaction compensation method is further provided that takes into account the coupling effect of the exciter, wherein the vibration table includes a servo valve, a hydraulic cylinder, a vibration table surface, and an exciter.

[0016] A vibration table-eccentric load interaction compensation method is further proposed that considers the exciter coupling effect, in which the system model of the vibration table and the eccentric load is constructed based on the dynamic system model, the hydraulic drive model and the TVC model.

[0017] A vibration table-eccentric load interaction compensation method is further considered with the exciter coupling effect, where the dynamic system model is shown in Equation 2:

[0018]

[0019] Among them, M E and I E The calculation is shown in Equation 1; s is the Laplace operator; x is the displacement of the equivalent mass; φ is the motion angle of the equivalent moment of inertia; A p p L1 and A p p L2 are the outputs of the two exciters respectively; a is the eccentric distance of the equivalent mass; l is the distance from the exciter to the center of the vibration table; A p is the effective area of ​​the hydraulic cylinder; p L1 is the load pressure; p L2 is the load pressure.

[0020]

[0021] Among them, I T +I TA and I L +I LA are the moments of inertia of the vibration table and the eccentric load relative to the x-axis, respectively.

[0022] A vibration table-eccentric load interaction compensation method is further considered with the exciter coupling effect, where the hydraulic drive model is shown in Equation 4:

[0023]

[0024] Among them, Q L Indicates load flow; G q k q0 is the transfer function of the servo valve; u is the control error signal; K Cis the flow pressure parameter near the steady-state operating point; p L is the load pressure; A P is the effective area of ​​the hydraulic cylinder; M is the total mass of the piston and the load; x p is the piston displacement, V is the total capacity of the two hydraulic cylinders; β is the effective bulk modulus; C tc is the total leakage coefficient of the hydraulic cylinder.

[0025] A vibration table-eccentric load interaction compensation method is further proposed that takes into account the exciter coupling effect. The control error signal of the TVC model is shown in Equation 5:

[0026] u=G3u0-G4G a x T (5)

[0027] Where u is the control error signal; u0 is the control signal; G3 is the three-parameter generator and feedforward; G4 is the three-parameter feedback; x T is the displacement of the vibration table; G a is the transfer function of the sensor; G a The expression is:

[0028]

[0029] Among them, n a Sensor frequency; D a is the sensor damping ratio.

[0030] A vibration table-eccentric load interaction compensation method is further proposed that takes into account the exciter coupling effect. The transfer function of the vibration table and eccentric load system is shown in Equation 12:

[0031]

[0032] Where x1 is the displacement of exciter 1; x2 is the displacement of exciter 2; G3 is the three-parameter generator and feedforward, G5, G6, and G7 are shown in Equation 10; u 01 is the control signal of vibration table 1; u 01 is the control signal of vibration table 2; G q k q0 is the transfer function of the servo valve; A P is the effective area of ​​the hydraulic cylinder;

[0033]

[0034] Preferably, Equation 12 is converted into a transfer function matrix as shown in Equation 13:

[0035]

[0036] Among them, H11 and H22 are the transfer functions of the two exciters affected by CSI; H12 and H21 are the transfer functions of the coupling between the two exciters.

[0037] Another aspect of the present invention relates to a vibration table-eccentric load interaction compensation system that takes into account the exciter coupling effect. The system includes at least one processor and a memory storing instructions that, when executed by the at least one processor, implement the steps of the aforementioned method.

[0038] The beneficial effects of the present invention are as follows: The present invention establishes a transfer function matrix for the vibration table and eccentric load. Based on this transfer function matrix, an in-depth study of the CSI impact under different ER conditions is conducted. This analysis reveals that the CSI impact is amplified by at least 22 times due to the coupling effect between the exciters. Furthermore, the present invention discloses a real-time CSI compensation strategy that considers the coupling effect of the exciters. With this strategy, the coupling effect between the two exciters is completely eliminated, and the correlation coefficients of the earthquake records reproduced by the two exciters are improved by 14.75% and 5.48%, respectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 .Simplified diagram of the vibration table and eccentric load system;

[0040] Figure 2 Schematic diagram of the three sub-models of the shaking table and eccentric load system;

[0041] Figure 3 .Schematic diagram of the dynamic system model;

[0042] Figure 4 .Schematic diagram of the hydraulic drive system model;

[0043] Figure 5 .TVC model diagram;

[0044] Figure 6 . Schematic diagram of the effect of interaction on the transfer function matrix under different eccentric load conditions;

[0045] Figure 7 .Control strategy block diagram;

[0046] Figure 8 .Schematic diagram of system performance improvement in the frequency domain;

[0047] Figure 9 .Schematic diagram of waveform reproduction accuracy;

[0048] Figure 10 .Schematic diagram of synchronization and tracking control errors;

[0049] Figure 11 .Simplified diagram of the vibration table and eccentric load system. DETAILED DESCRIPTION

[0050] The following examples further illustrate the present invention, but should not be construed as limiting the present invention. Without departing from the spirit and substance of the present invention, modifications or substitutions made to the methods, steps or conditions of the present invention are within the scope of the present invention.

[0051] Electro-hydraulic shakers are important experimental equipment in fields such as earthquake engineering testing, aerospace vibration testing, and vehicle road simulation. In shaker testing, CSI (Constant Separation Inertia) refers to the dynamic coupling between the shaker and the load. CSI not only affects the shaker's control accuracy but also introduces errors into the load response. Relevant technologies have demonstrated that the CSI between the shaker and the eccentric load increases significantly under certain operating conditions. Extensive research has been conducted on the mechanisms of CSI between shakers and loads, focusing on the CSI effect and CSI compensation strategies.

[0052] CSI impact analysis is to study the impact trend and degree of CSI under different system characteristics. In the existing CSI impact analysis, the relevant technology takes the vibration table and the central symmetric load as the research objects and establishes the vibration table and load system model. CSI impact analysis is mainly carried out from two aspects: vibration table characteristics and load characteristics. From the perspective of vibration table characteristics, the relevant technology analyzes the influence of control parameters (proportional integral differential parameters and three variable control (TVC) parameters), time lag, servo valve bias, hinge stiffness, hydraulic cylinder mass, table deformation, and the coupling between the two vibration tables on the vibration table and load system. From the perspective of load characteristics, the relevant technology analyzes the influence of mass, damping ratio, frequency, stiffness and flexibility, the physical construction method of damping, the physical construction method of stiffness, and structural vibration mode characteristics on the vibration table and load system.

[0053] In order to compensate for CSI, related technologies have proposed a series of offline and real-time compensation control strategies. By adopting multiple offline iterations, Twitchell and Fletcher mitigated the impact of CSI. However, multiple offline iterations may cause irreversible damage to the load, which may affect the test results. Many related technologies have shown that real-time compensation control strategies are effective methods to compensate for CSI. Related technologies have proposed different methods to calculate CSI and then compensate for the interaction. Related technologies use adaptive inverse control strategies to identify CSI and compensate for CSI based on the identification. Related technologies propose strategies to compensate for CSI based on modal control strategies. In addition, many strategies to compensate for CSI have been proposed, such as acceleration trajectory tracking control methods, attitude synchronization tracking control strategies, and differential motion synchronization tracking control strategies.

[0054] In summary, a series of studies have been conducted to explore the mechanisms of CSI. However, load eccentricity (ER) is a key system characteristic that has not been addressed in previous CSI research, and the impact of CSI on inter-exciter coupling requires further investigation. Furthermore, the effectiveness and practicality of compensation strategies in related technologies are severely hampered by inter-exciter coupling.

[0055] The following describes in detail the embodiments of the present invention.

[0056] 1. System Modeling

[0057] The schematic diagram of the vibration table and eccentric load system is shown in Figure 1 As shown. Figure 1 It can be seen that the system mainly consists of a control computer, a servo valve, a hydraulic cylinder, a vibration table, exciter 1 and exciter 2, and a load. The performance indicators of the vibration table are shown in Table 1. The central symmetrical load is eccentrically arranged on the vibration table. This arrangement can largely simulate the working condition of the eccentric load structure on the vibration table. Figure 1 As shown, the system is driven horizontally by exciter 1 and exciter 2. Therefore, the system model established in some embodiments of the present invention is a multi-input multi-output model, and the two exciters are coupled to each other.

[0058] Table 1. Basic parameters of the vibration table

[0059]

[0060] In some embodiments, according to Figure 2 The modular approach shown is used to model the system. Figure 2 It can be seen that the system can be divided into three main sub-models, including dynamic system model, hydraulic drive model and TVC model. They are the motion mechanism part, hydraulic drive part and control part of the system respectively. The working principle block diagram of these three parts is as follows Figure 11 To establish the transfer function matrix model, Figure 11 The system composition and physical characteristics are comprehensively considered. The parameter values ​​are shown in Table 2.

[0061] Table 2. Vibration table parameters.

[0062]

[0063] according to Figure 11 ,The specific modeling process of some embodiments is as follows.

[0064] 1.1 Dynamic System Modeling

[0065] Consider the vibration table and eccentric load as a whole, and then make the dynamic model equivalent accordingly, as shown in the schematic diagram. Figure 3 shown. Figure 3(a) gives the equivalent model of the dynamic system model, Figure 3 (b) The equivalent model is analyzed. T is the mass of the vibration table surface; M L is the load mass; M E is the equivalent mass of the vibration table and the load; A p p L1 (F1) and A p p L2 (F2) are the outputs of the two exciters respectively; x1 is the displacement of exciter 1; x2 is the displacement of exciter 2; x is the displacement of the equivalent mass; I T is the moment of inertia of the vibration table; I L is the load moment of inertia; I E is the equivalent moment of inertia of the vibration table and the load; φ is the motion angle of the equivalent moment of inertia; a is the eccentric distance of the equivalent mass; l is the distance from the exciter to the center of the vibration table surface.

[0066] According to the parallel axis theorem, the equivalent model can be expressed as:

[0067]

[0068] Among them, I T +I TA and I L +I LA The vibration table and eccentric load are relative to Figure 3 (b) The moment of inertia about the x-axis.

[0069] Based on equation (1), the dynamic model of the shaking table and eccentric load was established using Newton's second law. The obtained dynamic model is:

[0070]

[0071] The following is an example of calculating the moment of inertia. The center of the platform is used as the coordinate origin, and the center of mass formula is used to calculate the center of mass position. The center of mass of the vibration table and the eccentric load are:

[0072]

[0073] Where a is the distance from the center of gravity of the equivalent mass to the center of gravity of the vibration platform; A is the distance from the center of gravity of the load to the center of gravity of the vibration platform.

[0074] Based on the parallel axis theorem and formula 1, I T ,I TA ,I L , and I LA The expression is

[0075]

[0076] Where m and n are the length and width of the vibration table, respectively; c and k are the length and width of the load, respectively.

[0077] According to equations (1), (21) and (22), Table 3 lists the moments of inertia under different loading conditions.

[0078] Table 3. System inertia moment under different working conditions

[0079]

[0080] 2.2. Hydraulic drive model modeling

[0081] The hydraulic drive system of the system is as follows Figure 4 As shown. Figure 4 It can be seen that the hydraulic drive system is mainly composed of servo valves and hydraulic cylinders. The hydraulic drive system can be expressed by a series of continuity equations.

[0082] Assuming that the servo valve is a second-order oscillation model, the servo valve model is:

[0083]

[0084] Among them, w v is the servo valve frequency; v is the servo valve damping ratio.

[0085] Reference (Wang JK, Li XJ, Li FF, et al. Effect and compensation of the interaction between a unidirectional twin-axis shaking table and the tested structure. J Vib Shock 2021; 40(10): 140-149. [In Chinese]), through Laplace transform processing, the three continuity equations of the hydraulic drive model can be obtained. The continuity equations are shown in (4):

[0086]

[0087] Among them, Q L Indicates load flow; G q k q0 is the transfer function of the servo valve; u is the control error signal; K C is the flow pressure parameter near the steady-state operating point; p L is the load pressure; A P is the effective area of ​​the hydraulic cylinder; M is the total mass of the piston and the load; x pis the piston displacement; V is the total capacity of the two hydraulic cylinders; β is the effective bulk modulus; C tc is the total leakage coefficient of the hydraulic cylinder.

[0088] 2.3. Three-parameter system modeling

[0089] Three-parameter feedback, feedforward and generator are the three core parts of the TVC model. The block diagram of the TVC model is as follows: Figure 5 shown.

[0090] According to the detailed TVC system modeling process in the literature (Wang JK, Li XJ, Li FF, et al. Analysis of the interaction effects between double shaking tables and test structure. J Vib Control 2021; 27(11-12): 1407-1419.), the control error signal is

[0091] u=G3u0-G4G a x T (5)

[0092] Where u is the control error signal; u0 is the control signal; G3 is the three-parameter generator and feedforward; G4 is the three-parameter feedback; x T is the displacement of the vibration table; G a is the transfer function of the sensor, G a The expression is:

[0093]

[0094] Among them, n a Sensor frequency; D a is the sensor damping ratio.

[0095] 2.4. Transfer function matrix modeling

[0096] Based on the above three sub-models, the transfer function matrix is ​​established. In the modeling process, it is assumed that the parameters of actuators 1 and 2 are consistent with each other. Then the transfer function can be derived as

[0097]

[0098] Among them, u1 and u2 are the control error signals of the two exciters; G q k q0 is the transfer function of the servo valve, and the expression of G2 is:

[0099]

[0100] Substituting equation (5) into equation (7), the transfer function of the system model is as follows:

[0101]

[0102] assumed:

[0103]

[0104] We can get:

[0105]

[0106] Finally, the transfer function of the shaker and eccentric load system is:

[0107]

[0108] Converting Equation 12 into the form of a transfer function matrix, we can obtain:

[0109]

[0110] Where H11 and H22 are the transfer functions of the two exciters affected by CSI; H12 and H21 are the transfer functions of the coupling between the two actuators. The expressions of H11, H12, H12 and H22 are:

[0111]

[0112] Assume u 01 =u 02 =u, then the transfer function of the two exciters is:

[0113]

[0114] Where A1 is the transfer function of exciter 1; A2 is the transfer function of exciter 2.

[0115] Interaction impact analysis

[0116] Based on the established transfer function matrix, some embodiments tested the effects of load eccentricity (ER) and revealed the impact of CSI. The experiments were conducted under different ER conditions. The research conditions were designed based on the load characteristics shown in Table 4. In Table 4, ER is expressed as ER = a / l, where l is 1.2 m. See Table 3 for the moments of inertia under different ER conditions.

[0117] Table 4. Test conditions at different load eccentricity levels

[0118]

[0119] To compare and analyze the impact of the CSI on the transfer function matrix, the shaker's empty operating condition is defined as the reference condition. The amplitude-frequency characteristics of the transfer function matrix are a key metric in this analysis. If the CSI value is within the range of 0.71 absolute values ​​(abs) to 1.41 abs, the shaker operates within its effective frequency range (-3.00 dB to +3.00 dB).

[0120] Figure 6 The influence of CSI under different ER conditions is given. Figure 6 As shown in (a), when ER = 0.6, the H11 value at 16.70 Hz is 1.36 abs; when ER = 0.4, the H11 value at 16.20 Hz is 1.50 abs; when ER = 0.6, the H11 value at 16.00 Hz is 1.65 abs; and when ER = 0.6, the H11 value at 11.40 Hz is 1.41 abs. Simultaneously, when ER = 0.2, the H22 value at 40.90 Hz is 0.71 abs; when ER = 0.4, the H22 value at 45.30 Hz is 0.71 abs; and when ER = 0.6, the H22 value at 48.20 Hz is 0.71 abs. Analysis of the above data indicates that within the oil injection resonance frequency and its surrounding frequency band, the effect of CSI on H11 increases with increasing ER, while the effect of CSI on H22 decreases with increasing ER. At the same time, the frequency of the H11 oil injection resonance peak decreases with increasing ER, while the amplitude of the H11 oil injection resonance peak increases with increasing ER. In addition, the effective frequency band of H22 increases to a certain extent, but does not exceed the effective frequency band under no-load conditions (53.70Hz).

[0121] from Figure 6 (b) As can be seen, at 20.00 Hz, the values ​​of H12 and H21 are 0.22 abs when ER = 0.2, 0.33 abs when ER = 0.4, and -0.40 abs when ER = 0.6. These data indicate that the coupling between the two exciters increases with increasing ER, amplifying the coupling by at least a factor of 22.

[0122] The following conclusion can be drawn from the embodiment of the present invention: the load eccentricity ER will affect the transfer function matrix of the oil injection frequency resonance peak and its surrounding frequency bands.

[0123] 2. Real-time compensation strategy considering exciter interaction

[0124] Based on the aforementioned CSI impact analysis and the shortcomings of previous CSI compensation strategies, the following embodiments relate to a real-time CSI compensation method (strategy) that considers the coupling effect between exciters.

[0125] 2.1 Compensation Strategy

[0126] The control block diagram of the compensation strategy is as follows: Figure 7 The control strategy consists of two parts. The first part (C1) is used to compensate for the interaction between the exciter and the load, and the second part (C2) is used to compensate for the coupling between the two exciters.

[0127] according to Figure 7 , assuming u φ =0, then the control error signals of the two actuators are

[0128]

[0129] assumed

[0130] u x =u 01 =u 02 (17)

[0131] Substituting equations (16) and (17) into equation (9), we can obtain:

[0132]

[0133] Then C xφ ,C φx ,C 12 , and C 21 The expression is:

[0134]

[0135] Finally, after adopting the compensation strategy of the embodiment, the transfer function of the system is:

[0136]

[0137] Analyzing Equation (20), we can see that the CSI effect and the coupling effect between the two exciters are completely eliminated. To verify the effectiveness of this strategy, a comprehensive study was conducted in both the frequency and time domains. During the verification process, Condition 2 in Table 2 was selected as the load condition.

[0138] 2.2 Frequency Domain Verification

[0139] Figure 8 The improvement of the system in the frequency domain after adopting the compensation strategy of the embodiment is given. Figure 8 (a) It can be seen that due to the influence of CSI, the value of H11 at 16.20Hz is 1.50abs, and the value of H22 at 45.30Hz is 0.71abs. Figure 8 (b) It can be seen that at 20.00 Hz, the values ​​of H12 and H21 are 0.01 abs under the reference working condition and 0.33 abs under the influence of CSI. Figure 8 (c) shows that the value of A1 is 1.71abs at 16.50Hz and the value of A2 is 0.71abs at 32.60Hz. Figure 8 (d) shows that the value of A1 is 1.47 abs at 15.70 Hz. The values ​​of H12 and H21 increase from 0.01 abs to 0.33 abs, indicating that the coupling between the two exciters has been amplified by a factor of 33. Based on the above data, we can see that due to the interaction, the operating frequency band of the shaker has dropped dramatically, and the coupling between the two exciters has increased significantly.

[0140] observe Figure 8 (a) It can be seen that after adopting the compensation strategy of the embodiment, the values ​​of CH11 and CH22 are equal to the values ​​under the reference working condition. Figure 8 (b) shows that the coupling between the two exciters is reduced to 0.00abs. Figure 8 (c) It can be seen that the values ​​of CA1 and CA2 at 53.60Hz are 0.71abs, and the values ​​under the reference working condition at 53.70Hz are also 0.71abs. Figure 8 (d) As can be seen, at 53.00 Hz, the CST value is 0.80 abs, and at 50.00 Hz, the value under the reference working condition is 0.83 abs. These data show that the compensation strategy of the embodiment eliminates the coupling effect between the two exciters and effectively compensates for the interaction.

[0141] 2.3 Time Domain Verification

[0142] A 3x compressed El-centro earthquake record is used as the excitation signal input into the system. The accuracy of earthquake record reproduction, synchronization control, and tracking control errors are used to evaluate the effectiveness of the embodiment strategy.

[0143] Figure 9 The recurrence of earthquake motion records and their evaluation indicators are given. In order to facilitate observation and comparison, the recurrence of the 6.2s-6.3s period is magnified. Figure 9 (a) It can be seen that at 6.28 seconds, the replication results of A1 and A2 are 143.6 cm / s 2 and 107.4 cm / s 2 , the result under the reference working condition is 76.99cm / s 2 , the recurrence values ​​of C-A1, A2, and ST are all 75.14 cm / s 2 These data demonstrate that the compensation strategy of the embodiment can effectively compensate for the interaction between the vibration table and the eccentric load at the time point of 6.28 s.

[0144] To further verify the effectiveness of the proposed strategy, the reproduction accuracy of ground motion records was analyzed. Figure 9 (b) shows the reproducibility evaluation indicators before and after compensation. Figure 9 (b) As can be seen, before compensation, the waveform correlation coefficients for exciters 1 and 2 were 75.05% and 84.32%, respectively. After compensation, actuators 1 and 2 moved synchronously, and the correlation coefficient of the reproduced waveforms was 89.80%. The maximum waveform reproduction error for exciters 1 and 2 after compensation was 82.28 dm, compared to 142.48 dm and 102.95 dm before compensation, respectively. The RMS value of the waveform reproduction error for exciters 1 and 2 after compensation was 32.35 dm, compared to 79.72 dm and 45.20 dm before compensation. Analysis of the above data indicates that after compensation, the waveform correlation coefficients of the two exciters increased by 14.75% and 5.48%, respectively, the maximum error decreased by 42.25% and 20.08%, and the RMS error decreased by 59.42% and 28.43%, respectively. Furthermore, the difference between the reference and compensated operating conditions does not exceed ±2%, which is an acceptable range (these differences arise from the three-parameter control parameters, which can be corrected by fine-tuning them). The improved accuracy of the ground motion recording reproduction demonstrates that the compensation strategy of the embodiment is effective.

[0145] Synchronous control error and tracking control error are as follows Figure 10 As shown. Observe Figure 10 (a) It can be seen that at 6.28s, the synchronization control error between the two exciters is 33.65cm / s 2 After adopting the compensation strategy of the embodiment, the synchronization controller error between the two exciters is 0.00 cm / s 2 .Depend on Figure 10 (b) It can be seen that at 6.28s, the tracking control errors of the two exciters are -149.9cm / s 2 and -113.7 cm / s 2 After adopting the compensation strategy, the tracking control error of the two exciters is 83.29cm / s 2 The above results show that the tracking error is reduced by at least 26.74% at 6.28s. Figure 10 It can be determined that the control strategy of the embodiment can significantly reduce synchronization error and tracking error.

[0146] Through time domain and frequency domain verification, it can be seen that the strategy of the embodiment can not only improve the waveform reproduction accuracy of the system, but also effectively improve the synchronization and tracking control performance of the system. The above verification proves that this strategy can improve the accuracy of the shaking table test.

[0147] In summary, the present invention establishes a transfer function matrix to study the CSI between the vibration table and the eccentric load. Based on this transfer function matrix, an in-depth study of performance under different ER operating conditions was conducted, and the impact trends and extent of CSI were determined. Furthermore, a real-time control strategy that considers the coupling between the exciters is disclosed. Consequently, the present invention achieves at least the following technical benefits:

[0148] 1. The load eccentricity (ER) affects the transfer function matrix of the oil injection frequency resonance peak and its surrounding frequency bands.

[0149] 2. The effects of CSI on H11 and H22 are different. The effect of CSI on H21 increases with the increase of ER, while the effect on H22 decreases with the increase of ER.

[0150] 3. CSI leads to a significant increase in the coupling between the two exciters, which is amplified by at least 22 times. At the same time, the coupling between the two exciters increases with the increase of ER.

[0151] 4. The control strategy of the embodiment can compensate for the interaction between the vibration table and the eccentric load and the coupling between the two exciters, which can effectively improve the accuracy of the vibration table test.

[0152] The embodiments and functional operations of the subject matter described in this specification may be implemented in digital electronic circuitry, tangibly implemented computer software or firmware, computer hardware including the structures disclosed in this specification and their structural equivalents, or a combination of one or more of the foregoing. The embodiments of the subject matter described in this specification may be implemented as one or more computer programs, i.e., as one or more modules of computer program instructions encoded on one or more tangible, non-transitory program carriers, for execution by, or to control the operation of, a data processing device.

[0153] Alternatively or additionally, the program instructions may be encoded on an artificially generated propagated signal, such as a machine-generated electrical, optical, or electromagnetic signal, which is generated to encode information for transmission to an appropriate receiver device for execution by a data processing device. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of the foregoing.

[0154] Although the present invention has been described in detail above using general explanations, specific embodiments, and experiments, it will be apparent to those skilled in the art that modifications and improvements may be made based on the present invention. Therefore, such modifications and improvements, which do not depart from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A method for compensating the interaction between a vibration table and an eccentric load, taking into account the coupling effect of an exciter, wherein the eccentric load is eccentrically arranged on the table surface of the vibration table, and the vibration table is driven in a single horizontal direction by an exciter 1 and an exciter 2 driven by a hydraulic drive system, characterized in that: The control error signal of exciter 1 and the control error signal of exciter 2 are calculated according to formula 16: Among them, u1 is the control error signal of exciter 1; u2 is the control error signal of exciter 2; u x is the control signal; G3 is the three-parameter (TVC) generator and feedforward, G4 is the three-parameter feedback; G a is the transfer function of the sensor; x1 is the displacement of exciter 1; x2 is the displacement of exciter 2; C xφ 、C 12 、C φx 、C 21 are the compensation transfer functions respectively; Compensation transfer function C xφ 、C 12 、C φx 、C 21 Calculate according to formula 19: Where G2 is calculated according to formula 8; A p is the effective pressure-bearing area of ​​the piston; l is the distance from the exciter to the center of the vibration table; G q k q0 is the transfer function of the servo valve; I T is the moment of inertia of the vibration table; I E is the equivalent moment of inertia of the vibration table and the load; M T is the mass of the vibration table surface; M E is the equivalent mass of the vibration table and the load; s is the Laplace operator; a is the eccentric distance of the equivalent mass; Where V is the equivalent cylinder volume; β is the bulk elastic modulus of the oil; A p is the effective pressure-bearing area of ​​the piston; K c is the pressure flow coefficient of the servo valve; C c is the cylinder leakage coefficient; s is the Laplace operator; The system model of the shaking table and eccentric load is constructed based on the dynamic system model, hydraulic drive model and TVC model; The dynamic system model is shown in Equation 2: Among them, M E and I E The calculation is shown in Equation 1; s is the Laplace operator; x is the displacement of the equivalent mass; φ is the motion angle of the equivalent moment of inertia; A p p L1 and A p p L2 are the outputs of the two exciters respectively; a is the eccentric distance of the equivalent mass; l is the distance from the exciter to the center of the vibration table; A p is the effective area of ​​the hydraulic cylinder; p L1 is the load pressure; p L2 is the load pressure; Among them, I T +I TA and I L +I LA are the moments of inertia of the vibration table and eccentric load relative to the x-axis, respectively; The transfer function of the vibration table and eccentric load system is shown in Equation 12: Where x1 is the displacement of exciter 1; x2 is the displacement of exciter 2; G3 is the three-parameter generator and feedforward, G5, G6, and G7 are shown in Equation 10; u 01 is the control signal of vibration table 1; u 02 is the control signal of vibration table 2; G q k q0 is the transfer function of the servo valve; A P is the effective area of ​​the hydraulic cylinder; 2. The vibration table-eccentric load interaction compensation method considering the exciter coupling effect as claimed in claim 1, wherein: The transfer function of exciter 1 and exciter 2 is shown in Equation 20: Where G2 is calculated according to Formula 8; l is the distance from the exciter to the center of the vibration table; a is the eccentric distance of the equivalent mass; I T is the moment of inertia of the vibration table; s is the Laplace operator; x1 is the displacement of exciter 1; x2 is the displacement of exciter 2; G3 is the transfer function of the three-parameter input device; A p is the effective pressure-bearing area of ​​the piston; G q k q0 is the transfer function of the servo valve; u 01 is the control signal of vibration table 1; u 02 is the control signal of vibration table 2.

3. The vibration table-eccentric load interaction compensation method considering the exciter coupling effect according to any one of claims 1 to 2, wherein: The vibration table includes a servo valve, a hydraulic cylinder, a vibration table surface, and a vibration exciter.

4. The vibration table-eccentric load interaction compensation method considering the exciter coupling effect as claimed in claim 3, wherein: The hydraulic drive model is shown in Equation 4: Among them, Q L Indicates load flow; G q k q0 is the transfer function of the servo valve; u is the control error signal; K C is the flow pressure parameter near the steady-state operating point; p L is the load pressure; A P is the effective area of ​​the hydraulic cylinder; M is the total mass of the piston and the load; x p is the piston displacement; V is the total capacity of the two hydraulic cylinders; β is the effective bulk modulus; C c is the total leakage coefficient of the hydraulic cylinder.

5. The vibration table-eccentric load interaction compensation method considering the exciter coupling effect as claimed in claim 4, wherein: The control error signal of the TVC model is shown in Equation 5: u=G3u0-G4G a x T (5) Where u is the control error signal; u0 is the control signal; G3 is the three-parameter generator and feedforward; G4 is the three-parameter feedback; x T is the displacement of the vibration table; G a is the transfer function of the sensor; G a The analytical expression is: Among them, n a Sensor frequency; D a is the sensor damping ratio.

6. The vibration table-eccentric load interaction compensation method considering the exciter coupling effect as claimed in claim 5, wherein: Converting Equation 12 into a transfer function matrix is ​​shown in Equation 13: Among them, H11 and H22 are the transfer functions of the two exciters affected by CSI; H12 and H21 are the transfer functions of the coupling between the two actuators.

7. A vibration table-eccentric load interaction compensation system considering the exciter coupling effect, characterized in that: The system comprises at least one processor and a memory storing instructions. When the instructions are executed by the at least one processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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