CN116256133A - Synchronous control method for vertical vibrating table - Google Patents
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Abstract
The invention provides a synchronous control method of a vertical vibrating table, which aims at the problem that the synchronous control technology of an electrohydraulic earthquake simulation vibrating table is difficult to meet the test requirement, a single vibrating table with nine sub-tables is taken as a research object, a synchronous control strategy of the motion of the vibrating table is deduced, a three-parameter fuzzy controller of the displacement, the speed and the acceleration of the vibrating table is established on the basis of a fuzzy control algorithm, and the synchronous control performance of the vibrating table and the stability of a system are improved.
Description
Technical Field
The invention belongs to the field of engineering such as rock soil and geology, and particularly relates to a synchronous control method for a vertical vibrating table, a vibrating table and a vibrating table array.
Background
The electrohydraulic earthquake simulation vibrating table is widely applied to aspects of researching dynamic characteristics, earthquake response and the like of a structure. The vibration test of the slender structures such as large-scale space structures, pipelines, multi-span bridges and the like not only requires that the vibration table array system can accurately track expected signals, but also requires that synchronous control can be realized among the vibration exciters. Due to the influence of factors such as nonlinearity and friction of the system, synchronous control between each vibrating table and the vibration exciter has become one of the difficulties to be solved in the control of the vibrating table. The research of expert scholars at home and abroad on synchronous control is mainly developed from three aspects of control technology, control algorithm and control parameters: karen in 1980 proposed cross-coupling control technology and was widely used and in industry. In 2003 Perez, a deviation coupling control technology with stronger synchronization performance and expansibility is proposed, and the advantages and disadvantages of the synchronization control technology such as master-slave control, cross coupling, virtual electronic total axis and the like are compared in detail. And the Cheng adopts a fuzzy control algorithm to improve the synchronous control performance of the double-vibration exciter system interfered by eccentric load and the system. The Kazuhiro Tsuruta considers time lag, motor torsion, displacement, speed and acceleration control parameters, and provides a synchronous control prediction algorithm, so that the stability and synchronous control precision of the system are improved. Zhang Lianpeng the displacement, speed and acceleration parameter errors of the earthquake simulation vibrating table array are considered, and the synchronous performance of the system is improved by adopting a fuzzy control algorithm and a cross coupling control technology. However, the synchronous control technology related to the electrohydraulic earthquake simulation vibrating table is difficult to meet the test requirement, and the synchronous control strategy of the vertical vibrating table and the three-parameter fuzzy synchronous controller are still necessary to be improved.
Disclosure of Invention
In view of the above technical problems, a first aspect of the present invention provides a synchronous control method for a vertical vibration table, where the vertical vibration table 1 includes a table top 2 and 3 vibration exciters 3 that generate vertical vibration for the table top 2, the 3 vibration exciters are arranged at a geometric center of the table top 2, and the synchronous control method for a vertical vibration table includes an error processing step and an error coupling step that synchronize the 3 vibration exciters 3:
the error processing step obtains e according to 16 z Error signal e R Error signal e p The error signal is provided to the controller by the error signal,
wherein e z Is the z-direction motion error of the vibrating table; e, e R The rotation error of the vibrating table around the y axis is obtained; e, e p The rotation error of the vibrating table around the x axis is obtained; u (u) z Inputting a signal for the z direction of the vibrating table; u (u) R Rotating the input signal for the oscillating table about the y-axis; u (u) p Rotating the input signal for the oscillating table about the x-axis; z 1 、z 2 、z 3 Calculated according to equation 11:
wherein z is 1 、z 2 、z 3 Output signals of the three vibration exciters respectively; l (L) x The distance from the geometric center of the vibrating table to the vibration exciter 3; z is the z-direction movement of the vibrating table; r is the rotation angle of the y axis of the vibrating table; p is the x-axis rotation angle of the vibrating table;
the error coupling step obtains E according to 14 1 Error coupled signal, E 2 Error coupled signal, E 3 The error is coupled to the signal and,
wherein E is 1 The control error signal is corresponding to the vibration exciter 1; e (E) 2 The control error signal is corresponding to the vibration exciter 2; e (E) 3 Is a control error signal corresponding to the vibration exciter 3.
The second aspect of the invention provides a vertical vibration table 1, which comprises a table top 2 and 3 vibration exciters 3 for enabling the table top 2 to generate vertical vibration, wherein the 3 vibration exciters are arranged at the geometric center of the table top 2, and the vertical vibration table further comprises a three-parameter fuzzy synchronous controller which is configured according to the synchronous control method;
the third aspect of the invention provides a vibrating table array system composed of the vertical vibrating tables 1, wherein the number of the vertical vibrating tables 1 is several; preferably 4 to 9; it is further preferred that the vertical vibration table 1 is built up as a modular array system.
The invention has the beneficial effects that a single vertical vibration table of the Jiuzi table of Beijing industrial university is taken as a research object, a synchronous control compensation strategy of the motion of the vibration table is deduced, a three-parameter fuzzy controller of the displacement, the speed and the acceleration of the vibration table is established based on a fuzzy control algorithm, and the synchronous control performance of the vibration table and the stability of a system are improved. The vibration table system is excited by adopting step signals and random signals, and the maximum synchronization error between the vibration exciters is reduced from 1.1089mm to 0.1353mm. e, e R And e p The control error is also greatly improved. The test result shows that the control strategy and the three-parameter fuzzy synchronous controller are effective.
Drawings
FIG. 1 vertical vibration table;
FIG. 2 vertical three-exciter vibration model;
FIG. 3 is a control block diagram;
FIG. 4a three vibration exciter synchronous control Simulink model-error processing and error coupling;
in the figure, inu-input u, inz 1-input z 1 Inz 2-input z 2 Inz 3-input z 3 Ez represents e Z Ep represents e p Er represents e R Error processing and Error coupling;
FIG. 4b three vibration exciter synchronous control Simulink model-error processing model;
in the figure, gain represents Gain; otherwise as in fig. 4a;
FIG. 4c three vibration exciter synchronous control Simulink model-error coupling model;
in the figure, gain represents Gain;
FIG. 5 three-parameter fuzzy controller;
in the figure, displacement; velocity-speed; an acceleration of the acceleration; 2-D fuzzy controller-two-dimensional fuzzy controller;
the membership function of fig. 6a E;
FIG. 6b membership function of EC;
FIG. 7U membership function;
degree of membership-membership in the figure;
FIG. 8 control a surface;
FIG. 9 displacement control system model;
in the figure, a PID Controller;
FIG. 10 is a synchronous control system;
FIG. 11a step signal response-no synchronization control is employed;
in the figure, displacement; time-Time; reference-Reference signal; the Exciter 1-vibration Exciter 1; the Exciter 2-vibration Exciter 2; the Exciter 3-vibration Exciter 3;
FIG. 11b step signal response-employing synchronous control;
FIG. 11c step signal response-with synchronous fuzzy control;
FIG. 12a random signal response-no synchronization control is employed;
FIG. 12b random signal response-employing synchronous control;
FIG. 12c random signal response-employing synchronous fuzzy control;
FIG. 13 synchronization error of vibration exciter1 and 2;
in the figure, displacement; time-Time; without synchronous control-synchronous control is not employed; with synchronous control-synchronous control is adopted; with fuzzy synchronous control-synchronous fuzzy control is adopted;
FIG. 14e Z Is a synchronous control error of (1);
FIG. 15e P Is a synchronous control error of (1);
FIG. 16e R Is used for controlling errors in synchronization.
Reference numerals: 1-earthquake simulation shaking table (vertical shaking table); 2-a table top; 3-vibration exciter; 4-a hydraulic cylinder; 5-servo valve; 6, a base; 7-supporting the guide; 8-connecting rod.
Detailed Description
The following examples further illustrate the invention but are not to be construed as limiting the invention. Modifications and substitutions to methods, procedures, or conditions of the present invention without departing from the spirit and nature of the invention are intended to be within the scope of the present invention.
In some embodiments of the synchronization control method for a vertical vibration table of the present invention, as shown in fig. 1, the vertical vibration table 1 includes a table top 2 and 3 vibration exciters 3 for generating vertical vibration on the table top 2, as shown in fig. 2, the 3 vibration exciters are arranged at the geometric center of the table top 2, and the synchronization control method for a vertical vibration table includes an error processing step and an error coupling step for synchronizing the 3 vibration exciters 3:
the error processing step obtains e according to 16 z Error signal e R Error signal e p The error signal is provided to the controller by the error signal,
wherein e z Is the z-direction motion error of the vibrating table; e, e R The rotation error of the vibrating table around the y axis is obtained; e, e p The rotation error of the vibrating table around the x axis is obtained; u (u) z Inputting a signal for the z direction of the vibrating table; u (u) R Rotating the input signal for the oscillating table about the y-axis; u (u) p Rotating the input signal for the oscillating table about the x-axis; z 1 、z 2 、z 3 Calculated according to equation 11:
wherein z is 1 、z 2 、z 3 Output signals of the three vibration exciters respectively; l (L) x The distance from the geometric center of the vibrating table to the vibration exciter 3; z is the z-direction movement of the vibrating table; r is the rotation angle of the y axis of the vibrating table; p is the x-axis rotation angle of the vibrating table;
the error coupling step obtains E according to 14 1 Error coupled signal, E 2 Error coupled signal, E 3 The error is coupled to the signal and,
wherein E is 1 The control error signal is corresponding to the vibration exciter 1; e (E) 2 The control error signal is corresponding to the vibration exciter 2; e (E) 3 Is a control error signal corresponding to the vibration exciter 3.
Further embodiments of the method for synchronously controlling the vertical vibrating tables according to the invention, E 1 、E 2 、E 3 And e z 、e R 、e p Satisfying the requirement of 15,
wherein, E 1 The control error signal is corresponding to the vibration exciter 1; e (E) 2 The control error signal is corresponding to the vibration exciter 2; e (E) 3 A control error signal corresponding to the vibration exciter 3; e, e z Is the z-direction motion error of the vibrating table; e, e R The rotation error of the vibrating table around the y axis is obtained; e, e p Is the error of rotation of the vibrating table about the x-axis. In some further embodiments of the synchronous control method for the vertical vibration table of the present invention, the force balance equation of the 3 vibration exciters 3 is shown in formula 4:
wherein M is load mass; s is the Laplace operator; p is p L1 、p L2 、p L3 Load pressures corresponding to the vibration exciters 1, 2 and 3 respectively; j (J) R The moment of inertia of the vibration table around the y axis; j (J) p Moment of inertia for the table to move about the x-axis; l (L) x The distance from the geometric center of the vibrating table to the vibration exciter 3; l (L) y Is the distance from the vibration exciter1 to the vibration exciter2 of the vibrating table.
In further embodiments of the method for synchronously controlling the vertical vibration table according to the present invention, as shown in fig. 1, each of the 3 vibration exciters 3 includes a hydraulic cylinder 4 and a servo valve 5, and when the parameters of the 3 vibration exciters 3 are selected to be consistent, the output flow of the servo valve 5 is calculated according to equation 5:
wherein Q is 1 、Q 2 、Q 3 The flow rates corresponding to the vibration exciters 1, 2 and 3 are respectively; e (E) 1 、E 2 、E 3 Control error signals corresponding to the vibration exciters 1, 2 and 3 respectively; l (L) q Gain for flow of the spool valve near steady state operating point; k (K) c Is the flow pressure coefficient of the spool valve near the steady state operating point.
The flow rate required by the 3 vibration exciters (3) is calculated according to the formula 6:
wherein Q is 1 、Q 2 、Q 3 The flow rates corresponding to the vibration exciters 1, 2 and 3 are respectively; p is p L1 、p L2 、p L3 Load pressures corresponding to the vibration exciters 1, 2 and 3 respectively; a is that P The effective bearing area of the piston; s is the Laplace operator; z 1 、z 2 、z 3 The motion sizes of the vibration exciters 1, 2 and 3 in the z direction are respectively; v is the volume of the hydraulic cylinder chamber; beta is the elastic modulus of oil; c (C) c Is the leakage coefficient of the oil cylinder.
In some further embodiments of the synchronous control method for the vertical vibration table of the present invention, the force balance equation of the 3 vibration exciters 3 is shown in formula 10:
in some further embodiments of the synchronous control method for the vertical vibration table of the present invention, the force balance equation of the 3 vibration exciters 3 is shown in formula 13:
wherein G is 2 Calculated according to equation 8:
wherein A is P The effective bearing area of the piston; s is the Laplace operator; v is the volume of the hydraulic cylinder chamber; beta is the elastic modulus of oil; c (C) c Is the leakage coefficient of the oil cylinder; k (K) c Is the flow pressure coefficient of the spool valve near the steady state operating point.
Further embodiments of the method for synchronously controlling the vertical vibration table according to the present invention, Z, R, P are calculated according to formula 20;
G z 、G R 、G p calculated according to equation 19:
wherein M is load mass; s is the Laplace operator; k (k) q Gain for flow of the spool valve near steady state operating point; a is that P The effective bearing area of the piston; j (J) R The moment of inertia of the vibration table around the y axis; j (J) p Is the moment of inertia of the table about the x-axis.
Further embodiments of the synchronous control method for the vertical vibrating table of the invention, the error processing step obtains e as follows z 、e R 、e p ：
Calculating displacement error d, speed error d/dt and acceleration error d of vibration exciter2 and vibration exciter1 2 /dt 2 Then the e is obtained through the operation of the two-dimensional fuzzy controller p The method comprises the steps of carrying out a first treatment on the surface of the Wherein u is p When d=0, d=1/2 (z 2 -z 1 )；
Calculated displacement error d, velocity error d/dt, acceleration error d 2 /dt 2 Then the e is obtained through the operation of the two-dimensional fuzzy controller z The method comprises the steps of carrying out a first treatment on the surface of the Wherein d=u z -1/3(z 1 +z 2 +z 3 )；
Calculated displacement error d, velocity error d/dt, acceleration error d 2 /dt 2 Then the e is obtained through the operation of the two-dimensional fuzzy controller R The method comprises the steps of carrying out a first treatment on the surface of the Wherein u is R When d=0, d=1/3 (2 z 3 -z 1 -z 2 )。
Further embodiments of the synchronous control method for the vertical vibration table of the present invention include that the two-dimensional fuzzy controller includes a first two-dimensional fuzzy controller and a second two-dimensional fuzzy controller, and e p For example, the calculation process of (1) is as follows:
the first two-dimensional fuzzy controller calculates displacement error d and speed error d/dt to obtain output quantity U 1 (e p1 )；
The second two-dimensional fuzzy controller calculates the speed error d/dt and the acceleration error d 2 /dt 2 Output U is obtained 2 (e p2 )；
From U 1 (e p1 ) U and U 2 (e p2 ) Calculating to obtain e p ，e z 、e R The same applies to the calculation process.
According to further embodiments of the synchronous control method for the vertical vibrating table, the two-dimensional fuzzy controller is a mamdani type fuzzy controller, wherein:
defining a fuzzy subset of fuzzy variables E, EC as { negative large, negative small, zero, positive small, positive large }, and noted { NB, NS, Z, PS, PB }; the fuzzy subset of outputs U1, U2 is set to { negative large, negative medium, negative small, zero, positive small, median, positive large }, and is denoted { NVB, NB, NM, NS, Z, PS, PM, PB, PVB }, E, EC, and U (U 1 、U 2 ) Is quantized to [ -1,1 [ -1 ]]Between them; the membership function of the input and output variables is triangular wave;
further embodiments of the synchronous control method of the vertical vibrating table of the invention obtain e p The fuzzy rule table of (2) is as follows:
wherein E, EC is a fuzzy variable.
The following describes the embodiments of the present invention further with reference to the drawings.
1. System description
1.1 System introduction
The nine-station earthquake simulation vibration table array system consists of 9 single stations with the size of 1m multiplied by 1m, and can realize earthquake simulation vibration table array tests with various forms and different position layouts. Each sub-table (vertical vibration table 1) shown in fig. 1 consists of a rigid table top 2, a supporting and guiding device 6, a connecting rod 7, a vibration exciter and a base 5, wherein the vibration exciter comprises a hydraulic cylinder 3 and a servo valve 4. However, the present invention is not limited specifically and entirely to the above features of the vertical vibrating table and the vibrating table array system.
1.2 model building
The hydraulic system (hydraulic cylinder 3) mainly comprises a power mechanism, an electrohydraulic servo valve (sometimes called a servo valve), a pressure sensor, an accumulator and the like. The dynamic model of the vibrating table can be represented by a series of differential equations. The electrohydraulic servo valve is a core component in the earthquake simulation vibrating table, and the performance of the electrohydraulic servo valve plays a decisive role in the working of the vibrating table.
1) Servo valves can be modeled generally in terms of a second order oscillation link:
wherein: g sv (s) is a transfer function of the servo valve, s is a Laplacian; omega v Is the natural frequency of the servo valve, xi v K being the damping ratio of the servo valve v Is the flow gain of the servo valve.
2) Hydraulic cylinder continuity equation:
in which Q is L For load flow, define
p L For load pressure, p L ＝p 1 -p 2 ；k q Gain for flow of the spool valve near steady state operating point; k (K) c A flow pressure coefficient for the spool valve near the steady state operating point; x is x v Is the displacement of the spool valve. A is that P The effective bearing area of the piston; x is x p Is piston displacement; m is M t The total mass converted to the piston and from the load; v (V) t Is the total volume of two chambers of the hydraulic cylinder, V t ＝V 1 +V 2 The method comprises the steps of carrying out a first treatment on the surface of the Beta is the elastic modulus of oil; />
Is the total leakage coefficient; c (C) ic Is the leakage coefficient of the hydraulic cylinder, C ec Is the leakage coefficient of the hydraulic cylinder.
Assuming that the table top and the test piece are regarded as a whole, and the load property is inertial load, the three continuous equations can be written as follows after Laplacian transformation:
wherein M is load mass; s is the Laplace operator; a is that P The effective bearing area of the piston; p is p L For load pressure, p L ＝p 1 -p 2 ；Q L For load flow, define
x is the displacement of the piston; v is the volume of the hydraulic cylinder chamber; beta is the elastic modulus of oil; c (C) c Is the leakage coefficient of the oil cylinder; k (k) q Gain for flow of the spool valve near steady state operating point; e is a control signal；K c Is the flow pressure coefficient of the spool valve near the steady state operating point.
2. Synchronous control strategy for vertical vibration of vibrating table
2.1 synchronization control strategy derivation
The size of a single table top of the nine-table is 1m multiplied by 1m. In the vertical vibration mode, three vibration exciters are arranged at the geometric center of the table top. A specific arrangement is shown in figure 2.
Its force balance equation is:
wherein M is load mass; s is the Laplace operator; p is p L1 、p L2 、p L3 Load pressures corresponding to the vibration exciters 1, 2 and 3 respectively; j (J) R The moment of inertia of the vibration table around the y axis; j (J) p Moment of inertia for the table to move about the x-axis; l (L) x The distance from the geometric center of the vibrating table to the vibration exciter 3; l (L) y Is the distance from the vibration exciter1 to the vibration exciter2 of the vibrating table.
Assuming that the parameters of the three vibration exciters are selected consistently, the output flow of the servo valve is as follows:
wherein Q is 1 、Q 2 、Q 3 The flow rates corresponding to the vibration exciters 1, 2 and 3 are respectively; e (E) 1 、E 2 、E 3 Control error signals corresponding to the vibration exciters 1, 2 and 3 respectively; k (k) p Gain for flow of the spool valve near steady state operating point; k (K) c Is the flow pressure coefficient of the spool valve near the steady state operating point.
The flow required by the vibration exciter is as follows:
wherein Q is 1 、Q 2 、Q 3 The flow rates corresponding to the vibration exciters 1, 2 and 3 are respectively; p is p L1 、p L2 、p L3 Load pressures corresponding to the vibration exciters 1, 2 and 3 respectively; a is that P The effective bearing area of the piston; s is the Laplace operator; z 1 、z 2 、z 3 The motion sizes of the vibration exciters 1, 2 and 3 in the z direction are respectively; v is the volume of the hydraulic cylinder chamber; beta is the elastic modulus of oil; c (C) c Is the leakage coefficient of the oil cylinder.
Equaling formulas (5) and (6) can be obtained:
and (3) making:
then:
(9) Substitution (4) can be obtained:
from fig. 2, the geometric method can be found:
wherein z is 1 、z 2 、z 3 Output signals of the three vibration exciters respectively; l (L) x The distance from the geometric center of the vibrating table to the vibration exciter 3; z is the z-direction movement of the vibrating table; r is the rotation angle of the y axis of the vibrating table; p is the x-axis rotation angle of the vibrating table;
this can be achieved by:
(12) Substituting the formula (10) to obtain:
assume that the control block diagram is as shown in fig. 3:
it can be seen that:
thus, it is possible to obtain:
(12) Substituted into (16)
Substituting (17) into (15) and substituting (13). The method comprises the following steps:
and (3) making:
(18) The formula can be obtained:
from equation (20), the vertical translation and the two rotations are independent degrees of freedom and are not coupled. Other parameter calculations can be analyzed entirely in a single exciter drive. For the convenience of comparison analysis, let u r 、u p Equal to zero. The above-mentioned synchronous control strategy is divided into an error processing portion and an error coupling portion. The Simulink model is shown in fig. 4a, fig. 4b and fig. 4 c:
2.2 three parameter fuzzy controller design
The fuzzy control is widely applied in the control field of a nonlinear system because of the advantages of independence of an accurate model, good robustness and the like, and the fuzzy control is also widely applied in the design of a synchronous controller.
Some embodiments of the invention use a fuzzy control algorithm to solve e during error processing Z 、e p 、e R . If the method shown in FIG. 4b is used to find e Z 、e p 、e R I.e. the error is calculated according to equation 21. Only the displacement is used as a synchronous control parameter, and the synchronous control precision is low. In order to obtain better synchronous control precision, three parameters of displacement, speed and acceleration can be used as control quantities, and the three-dimensional fuzzy controller can meet the requirements, however, the three-dimensional fuzzy controller has a complex structure, large operation quantity and little application, and does not meet the requirements.
Some embodiments of the present invention provide a fuzzy controller that is a two-dimensional fuzzy controller added to a two-dimensional fuzzy controller. As shown in fig. 5, at e p For example, d is the displacement error of the exciter2 and the exciter1, d/dt is the velocity error of the two, d 2 /dt 2 The acceleration error is calculated by fuzzy operation to obtain e p . Thereby realizing the same displacement, speed and accelerationAnd (5) step control.
Some embodiments of the present invention employ a mamdani type fuzzy controller that defines the fuzzy subset of the fuzzy variable E, EC as { negative large, negative small, zero, positive small, positive large }, and is denoted { NB, NS, Z, PS, PB }. The fuzzy subset of the outputs U1, U2 is set to { negative large, negative medium, negative small, zero, positive small, median, positive large }, and is denoted { NVB, NB, NM, NS, Z, PS, PM, PB, PVB }, E, EC and U (U 1 、U 2 ) Is quantized to [ -1,1 [ -1 ]]Between them. The membership function of the input and output variables is triangular wave. The membership function is shown in fig. 7 and 8.
Determination of fuzzy rule by e p The process of the calculation of (a) is as an example: when the error is negative and large, i.e. the vibration exciter No. 1 moves faster than the vibration exciter No. 2, if the error changes to be negative, the error tends to increase, so that ep should be large in order to eliminate the existing negative and large error as soon as possible and suppress the error from becoming large. When the error is negative and the error change is positive, the system itself has a tendency to reduce the error, and ep should be small in order to eliminate the error as soon as possible without causing overshoot.
The fuzzy rule table shown in table 1 is determined according to the fuzzy rule, and the input-output relationship is shown in fig. 8.
TABLE 1 control rules
2.3 synchronous control system for vibrating table
2.3.1 Displacement control System transfer function
According to the hydraulic system model established in 1.1, the displacement control system consists of 2 second-order links and 1 first-order link, so that the displacement control system model of the vibrating table is 5-order. The method of changing the parameters of the PID controller is adopted to realize the condition that the three vibration exciters are not synchronous in operation due to the nonlinearity and friction of the system, and the established model is shown in figure 9. Table 2 shows PID control parameters of the three vibration exciters.
Table 2 PID parameters of each exciter of the vibrating table
2.3.2 synchronous control System
In summary, the above embodiment is derived and modeled, and a synchronous control model of the vibrating table as shown in fig. 10 is built in Matlab/Simulink according to the parameters of table 3. When the switch is in an open state, the three-exciter system does not adopt synchronous control. When the switch is closed, the algorithm shown in fig. 4b and the proposed three-parameter fuzzy controller can be adopted to realize synchronous control on the system.
Table 3 table shaking table displacement closed loop control model parameters
3. Test and discussion
3.1 step Signal test
Step signals with the amplitude of 1mm are respectively input into the vibrating table system, and step responses without synchronous control, with synchronous control and with fuzzy synchronous control strategies are compared. As shown in fig. 11a, 11b, and 11c, the detail of each figure is exaggerated for comparison.
3.2 random wave test
Generating random wave with the maximum amplitude of 0.4Hz-5 Hz plus or minus 2mm, and inputting the random wave into a vibrating table system. Fig. 12a, 12b, and 12c are output curves of a three-exciter of a vibrating table of the three-exciter. From fig. 11a, 11b, 11c, 12a, 12b and 12c, it can be seen that the proposed synchronization control strategy can effectively improve the synchronization control accuracy of waveforms, and select a group of analysis with the largest difference between the vibration exciters, and the synchronization error between the vibration exciter1 and the vibration exciter2 is shown as fig. 13, and from table 4, it can be seen that the synchronization error is reduced from 1.1089mm to 0.1353mm. It can be seen from FIGS. 14, 15 and 16 that the overall synchronization accuracy of the vibrating table is improved, and that e is affected by the phase synchronization accuracy as shown in Table 5 Z The same control effect is not obvious. From Table 6, it can be seen that e P The control error is reduced by 0.5545mmTo 0.0676mm. From Table 7, it can be seen that e R The control error is reduced from 0.0619mm to 0.0054mm.
Table 4 error of vibration exciter1 and 2
TABLE 5e Z Is controlled by the synchronization error of (a)
TABLE 6e P Is controlled by the synchronization error of (a)
TABLE 7e R Is controlled by the synchronization error of (a)
The embodiments and functional operations of the subject matter described in this specification can be implemented in the following: digital electronic circuitry, tangibly embodied computer software or firmware, computer hardware, including the structures disclosed in this specification and structural equivalents thereof, or a combination of one or more of the foregoing. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., 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, data processing apparatus.
While the invention has been described in detail in the foregoing general description, embodiments and experiments, it will be apparent to those skilled in the art that modifications and improvements can be made thereto. Accordingly, such modifications or improvements may be made without departing from the spirit of the invention and are intended to be within the scope of the invention as claimed.
Claims (10)
1. A method of synchronous control of a vertical vibrating table, the vertical vibrating table (1) comprising a table top (2) and 3 exciters (3) for generating vertical vibrations of the table top (2), characterized in that the 3 exciters are arranged at the geometric center of the table top (2), the method of synchronous control of a vertical vibrating table comprising an error processing step and an error coupling step for synchronizing the 3 exciters (3):
the error processing step obtains e according to 16 z Error signal e R Error signal e p The error signal is provided to the controller by the error signal,
wherein e z Is the z-direction motion error of the vibrating table; e, e R The rotation error of the vibrating table around the y axis is obtained; e, e p The rotation error of the vibrating table around the x axis is obtained; u (u) z Inputting a signal for the z direction of the vibrating table; u (u) R Rotating the input signal for the oscillating table about the y-axis; u (u) p Rotating the input signal for the oscillating table about the x-axis; z 1 、z 2 、z 3 Calculated according to equation 11:
wherein z is 1 、z 2 、z 3 Output signals of the three vibration exciters respectively; l (L) x The distance from the geometric center of the vibrating table to the vibration exciter 3; z is the z-direction movement of the vibrating table; r is the rotation angle of the y axis of the vibrating table; p is the x-axis rotation angle of the vibrating table;
the error coupling step obtains E according to 14 1 Error controlDifference signal, E 2 Control error signal, E 3 The control signal is used to control the error signal,
wherein E is 1 The control error signal is corresponding to the vibration exciter 1; e (E) 2 The control error signal is corresponding to the vibration exciter 2; e (E) 3 Is a control error signal corresponding to the vibration exciter 3.
2. The synchronous control method for vertical vibrating table as claimed in claim 1, wherein E 1 、E 2 、E 3 And e z 、e R 、e p Satisfying the requirement of 15,
wherein E is 1 The control error signal is corresponding to the vibration exciter 1; e (E) 2 The control error signal is corresponding to the vibration exciter 2; e (E) 3 A control error signal corresponding to the vibration exciter 3; e, e z Is the z-direction motion error of the vibrating table; e, e R The rotation error of the vibrating table around the y axis is obtained; e, e p Is the error of rotation of the vibrating table about the x-axis.
3. A method for synchronous control of a vertical vibrating table according to any of claims 1-2, characterized in that the force balance equation of 3 exciters (3) is shown in formula 4:
wherein M is load mass; s is the Laplace operator; p is p L1 、p L2 、p L3 Load pressures corresponding to the vibration exciters 1, 2 and 3 respectively; j (J) R The moment of inertia of the vibration table around the y axis; j (J) p For movement of the oscillating table about the x-axisIs a rotational inertia of (a); l (L) x The distance from the geometric center of the vibrating table to the vibration exciter 3; l (L) y Is the distance from the vibration exciter1 to the vibration exciter2 of the vibrating table.
4. A method for synchronous control of a vertical vibrating table according to any of claims 1-3, characterized in that the 3 vibration exciters (3) each comprise a hydraulic cylinder (4) and a servo valve (5), and when the parameters of the 3 vibration exciters (3) are selected to be consistent, the output flow of the servo valve (5) is calculated according to formula 5:
wherein Q is 1 、Q 2 、Q 3 The flow rates corresponding to the vibration exciters 1, 2 and 3 are respectively; e (E) 1 、E 2 、E 3 Control error signals corresponding to the vibration exciters 1, 2 and 3 respectively; k (k) q Gain for flow of the spool valve near steady state operating point; k (K) c Is the flow pressure coefficient of the spool valve near the steady state operating point.
The flow rate required by the 3 vibration exciters (3) is calculated according to the formula 6:
wherein Q is 1 、Q 2 、Q 3 The flow rates corresponding to the vibration exciters 1, 2 and 3 are respectively; p is p L1 、p L2 、p L3 Load pressures corresponding to the vibration exciters 1, 2 and 3 respectively; a is that P The effective bearing area of the piston; s is the Laplace operator; z 1 、z 2 、z 3 The motion sizes of the vibration exciters 1, 2 and 3 in the z direction are respectively; v is the volume of the hydraulic cylinder chamber; beta is the elastic modulus of oil; c (C) c Is the leakage coefficient of the oil cylinder.
5. A method of synchronous control of a vertical vibrating table according to any of claims 1-4, characterized in that the force balance equation of 3 exciters (3) is shown in formula 10:
preferably, the force balance equation of the 3 vibration exciters (3) is shown in formula 13:
wherein G is 2 Calculated according to equation 8:
wherein A is P The effective bearing area of the piston; s is the Laplace operator; v is the volume of the hydraulic cylinder chamber; beta is the elastic modulus of oil; c (C) c Is the leakage coefficient of the oil cylinder; k (K) c Is the flow pressure coefficient of the spool valve near the steady state operating point.
6. A method of synchronous control of a vertical vibration table according to any one of claims 1 to 5, wherein Z, R, P is calculated according to equation 20;
G z 、G R 、G p calculated according to equation 19:
wherein M is load mass; s is the Laplace operator; k (k) q Gain for flow of the spool valve near steady state operating point; a is that P The effective bearing area of the piston; j (J) R For rotation of the oscillating table about the y-axisInertia; j (J) p Is the moment of inertia of the table about the x-axis.
7. The synchronous control method for a vertical vibration table according to any one of claims 1 to 6, wherein the error processing step obtains e as follows z 、e R 、e p ：
Calculating displacement error d, speed error d/dt and acceleration error d of vibration exciter2 and vibration exciter1 2 /dt 2 Then the e is obtained through the operation of the two-dimensional fuzzy controller p The method comprises the steps of carrying out a first treatment on the surface of the Wherein u is p When d=0, d=1/2 (z 2 -z 1 )；
Calculated displacement error d, velocity error d/dt, acceleration error d 2 /dt 2 Then the e is obtained through the operation of the two-dimensional fuzzy controller z The method comprises the steps of carrying out a first treatment on the surface of the Wherein d=u z -1/3(z 1 +z 2 +z 3 )；
Calculated displacement error d, velocity error d/dt, acceleration error d 2 /dt 2 Then the e is obtained through the operation of the two-dimensional fuzzy controller R The method comprises the steps of carrying out a first treatment on the surface of the Wherein u is R When d=0, d=1/3 (2 z 3 -z 1 -z 2 )。
8. The synchronous control method for a vertical vibration table according to any one of claims 1 to 7, wherein the two-dimensional fuzzy controller includes a first two-dimensional fuzzy controller and a second two-dimensional fuzzy controller, wherein e p The solving process of (1) is as follows:
the first two-dimensional fuzzy controller calculates displacement error d and speed error d/dt to obtain output quantity U 1 (e p1 )；
The second two-dimensional fuzzy controller calculates the speed error d/dt and the acceleration error d 2 /dt 2 Output U is obtained 2 (e p2 )；
From U 1 (e p1 ) U and U 2 (e p2 ) Calculating to obtain e p 。
9. The synchronized control method of a vertically oscillating table of any one of claims 1-8, wherein the two-dimensional fuzzy controller is a mamdani-type fuzzy controller, wherein:
defining a fuzzy subset of fuzzy variables E, EC as { negative large, negative small, zero, positive small, positive large }, and noted { NB, NS, Z, PS, PB }; set output U (U) 1 、U 2 ) Is { negative large, negative medium, negative small, zero, positive small, medium, positive large }, and is denoted { NVB, NB, NM, NS, Z, PS, PM, PB, PVB }; e, EC and U (U) 1 、U 2 ) Is quantized to [ -1,1 [ -1 ]]Between them; the membership function of the input and output variables is triangular wave;
preferably, e is obtained p The fuzzy rule table of (2) is as follows:
wherein E, EC is a fuzzy variable.
10. A vertical vibration table (1) comprising a table top (2) and 3 vibration exciters (3) for enabling the table top (2) to generate vertical vibration, characterized in that the 3 vibration exciters are arranged at the geometric center of the table top (2), the vertical vibration table further comprises a three-parameter fuzzy synchronous controller, and the three-parameter fuzzy synchronous controller is configured according to the synchronous control method of any one of claims 1-9;
preferably, the vibrating table array system composed of the vertical vibrating tables (1) according to any one of claims 1-9, wherein the number of the vertical vibrating tables (1) is several; preferably 4 to 9; it is further preferred that the vertical vibrating table (1) is built up as a modular array system.
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