CN107687925B - Control method of earthquake simulation vibration table - Google Patents
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Abstract
The invention relates to a control method of an earthquake simulation vibration table, and belongs to the technical field of structural experiments. The control method comprises the steps of obtaining a differential signal of an acceleration instruction signal and a differential signal of an acceleration feedback signal through differentiation, obtaining a displacement error integral signal through integrating a difference value of displacement feedforward and displacement feedback, and summing the acceleration instruction differential signal, the acceleration feedback differential signal and the displacement error integral signal with the existing three-parameter instruction signal to obtain a composite multi-parameter control signal. Compared with the existing three-parameter control method, the acceleration feedback differential signal in the multi-parameter control algorithm can reduce the influence of the resonance frequency of the system and expand the bandwidth of the system; the acceleration instruction differential signal can widen the system frequency band and improve the high-frequency performance of the system; the displacement error integral signal can reduce the displacement static error of the multi-vibration table system and improve the low-frequency control performance of the system.
Description
Technical Field
The invention relates to a control method of an earthquake simulation vibration table, and belongs to the technical field of structural experiments.
Background
The earthquake simulation shaking table is the most direct and effective test research tool in the field of engineering earthquake resistance, and hundreds of earthquake simulation shaking tables with various scales are built in the world on behalf of the United states, Japan, China and British. With the rapid development of the fields of hydraulic pressure, electronics, sensors, signal processing, control and the like, the earthquake simulation shaking table realizes the conversion from analog control to digital control and from displacement PID control to acceleration feedback control, and then the control of three parameters of displacement, speed and acceleration becomes a basic algorithm for shaking table control. At present, PID control, three-parameter control and offline iterative control are adopted by most electro-hydraulic servo earthquake simulation vibration tables at home and abroad. The three-parameter control of the vibration table adopts displacement, acceleration feedback and velocity signal feedback synthesized by acceleration integral and displacement differential to realize lower computer closed loop: the actuator is positioned and the low-frequency control performance is ensured through displacement feedback, the speed feedback is used for expanding the using frequency range, and the acceleration feedback is used for improving the stability of the system. However, for the vibration table system with the servo valve 90 ° phase shift frequency close to the system hydraulic resonance frequency, the system characteristics are easily affected by the servo valve characteristics, and the bandwidth of the system is difficult to meet the use requirements. In the existing three-parameter control system, only a proportion link (P control) and a displacement differential link (D control) corresponding to speed feedforward and feedback exist on displacement components, and for a vibration table array system consisting of a plurality of vibration tables, the displacement motion of each vibration table is inconsistent due to displacement errors under the three-parameter control, so that additional internal force of a test piece is caused, and the test piece is damaged unexpectedly.
Disclosure of Invention
In order to overcome the defects of poor low-frequency displacement control precision and insufficient high-frequency acceleration control precision of the existing three-parameter control method, the invention introduces displacement error integral and acceleration differential physical quantities into a closed-loop control link of the earthquake simulation vibrating table, thereby forming the earthquake simulation vibrating table control method.
In order to achieve the purpose, the design scheme of the invention is as follows:
a control method for earthquake simulation vibration table comprises an acceleration feedback link, a displacement feedback link and a speed synthesis link, and comprises a control parameter synthesis link for generating speed signals and displacement signals through acceleration command signals.
The control gains of the acceleration instruction differential signal, the acceleration feedback differential signal and the displacement error integral signal are obtained by considering the frequency domain analysis of a hydraulic system model with the high-order characteristics of a servo valve and a sensor link.
The acceleration signal is integrated to generate a speed signal, the speed signal is integrated to obtain a displacement signal, the displacement signal is integrated to obtain a displacement integral signal, and the acceleration signal is incompletely differentiated to obtain an acceleration differential signal. And eliminating integral saturation phenomenon by an integral separation method in a displacement error integral link.
The hydraulic system model frequency domain analysis comprises the following steps:
and 3, substituting the transfer function of the multi-parameter generator obtained in the step 2 into the transfer function of the vibration table system with multi-parameter feedback obtained in the step 1 to obtain the whole transfer function of the vibration table control system.
The step 1 specifically comprises the following steps: the three continuous equations of the hydraulic system are transformed by Laplace:
wherein M is the load mass; x is the piston displacement; a. thepIs the effective bearing area of the piston; p is a radical ofLIs the load drop; qLLoad flow, control cavity volume, β oil elastic modulus, CcIs the leakage coefficient; k is a radical ofqIs the flow gain of the spool valve near the steady state operating point; kcIs the flow pressure coefficient of the slide valve near the steady-state action point; s is a Laplace change factor; and E is the spool displacement of the spool valve.
The system open loop transfer function is simplified by three continuous equations as follows:
in the formula, n0The oil column resonance frequency, commonly referred to as the moving cylinder; d0Is the damping ratio.
Introducing displacement feedback, speed feedback, acceleration feedback, jerk feedback and displacement integral feedback on the basis of a system open-loop transfer function, wherein the spool displacement E of the spool valve is as follows:
substituting the formula into a system open-loop transfer function to obtain a system transfer function of the vibration table with multi-parameter feedback, wherein the system transfer function is as follows:
setting:
u＝Adu0
Ka＝Aa'Ka0
Kv＝Av'Kv0
Kd＝A'dKd0
KI＝AI'KI0
Kj＝A'jKj0
in the formula u0Is a control command signal; u is a control signal; a. thedInputting a gain for the displacement; a'dIs the displacement feedback gain; a. thev' is the velocity feedback gain; a'aIs the acceleration feedback gain; a. theI' is the displacement integral feedback gain; a'jA gain is added to the acceleration feedback; kdIs a displacement feedback coefficient; kd0The sensitivity is normalized for displacement feedback; kvIs a velocity feedback coefficient; kv0Normalizing the sensitivity for velocity feedback; kaAs a feedback coefficient of acceleration；Ka0Normalizing the sensitivity for acceleration feedback; kIIs a displacement integral feedback coefficient; kI0Feeding back the normalized sensitivity for displacement integration; kjIs a jerk feedback coefficient; kj0The sensitivity is normalized for jerk feedback.
The system transfer function is simplified as follows:
the step 2 specifically comprises the following steps: generating a speed signal by primary integration of an input acceleration signal, integrating the obtained speed signal to obtain a displacement signal, integrating the obtained displacement signal to obtain a displacement integral signal, and carrying out incomplete differentiation on the acceleration signal to obtain an acceleration signal, wherein the acceleration, speed, displacement integral and acceleration signal of the acceleration sensor have the following corresponding equations:
wherein,
in the formula, gainA, gainB and gainC are integral gains; gjIs a transfer function corresponding to an acceleration differentiator, TDIs a differential time constant; gfTransfer function, T, for low-pass filter of acceleration signalfIs the filter coefficient; e.g. of the typeaIs an acceleration control signal; e.g. of the typevIs a speed control signal; e.g. of the typedIs a displacement control signal; e.g. of the typeIIntegrating the control signal for the displacement; e.g. of the typejIs a jerk control signal; k is a radical ofaAn acceleration gain in the multi-parameter generator; k is a radical ofdFeedback coefficients for the displacements in the multi-parameter generator; k is a radical ofvFeedback coefficients for the velocity in the multi-parameter generator; k is a radical ofIThe feedback coefficients are integrated for the displacement in the multi-parameter generator.
Then:
synthesizing five signals output by the multi-parameter generator into a control signal, wherein the formula is as follows:
u＝Aaea+Avev+Aded+AIeI+Ajej
the step 3 specifically comprises the following steps: and substituting the synthesized control signal in the acceleration control mode into a system transfer function with multi-parameter feedback control, and simultaneously considering the second-order characteristics of a servo valve and a sensor to obtain the system transfer function under the multi-parameter control.
Consider a servo valve as a second order system:
Ksv＝Gqkq
wherein,
in the formula, KsvIs the transfer function of the electro-hydraulic servo valve; gqIs k q1 is the transfer function of the servo valve; n isqIs the natural frequency of the second-order system of the servo valve; dqIs the second order system inherent damping ratio of the servo valve.
Considering the sensor as a second order system, the transfer function of the feedback signal is
Wherein,
in the formula, GaIs the transfer function of the sensor; n isaThe natural frequency of a second-order system of the sensor; daIs the inherent damping ratio of the second-order system of the sensor.
The multi-parameter control system transfer function considering the second-order characteristics of the servo valve and the sensor is as follows:
in the step 1: in the case of separate introduction of jerk feedback on the basis of the system open loop transfer function, i.e. when A'a＝Av'＝A'd＝AIWhen the value is equal to 0, the mark is,
wherein,
in the formula, njFor the hydraulic resonance frequency of the system under jerk feedback, DjIs the damping ratio of the system under the feedback of the jerk.
When jerk feedback is negative feedback: a'jKj0＞0，nj＜n0，Dj＜D0The hydraulic resonance frequency and the damping ratio of the system are reduced.
In the case of jerk feedback introduced on the basis of three-parameter feedback, i.e. when AIWhen the value is equal to 0, the mark is,
the above formula is simplified as follows:
wherein,
in the formula, n is the hydraulic resonance frequency of the multi-parameter feedback system based on the jerk feedback, and D is the damping ratio of the multi-parameter feedback system based on the jerk feedback.
Thus:
namely:
i. when in use
When n is equal to n0At the moment, the introduction of speed feedback and jerk feedback has no influence on the hydraulic resonance frequency;
ii when
When n is more than n0The hydraulic resonance frequency is improved;
iii when
When n is less than n0The hydraulic resonance frequency is reduced.
For systems in which the servo valve 90 ° phase shift frequency is relatively close to the system hydraulic resonance frequency, the hydraulic resonance frequency of the system can be reduced by introducing jerk feedback, thereby reducing the effect of the servo valve characteristics on system performance.
In the step 2: when gainC is 0, TfWhen 0, i.e. without the displacement-integrated signal and without taking filtering into account, addUnder the action of the acceleration feedforward signal and the three-parameter feedback control, the transfer function of the driving signal synthesized by the multi-parameter generator is as follows:
wherein,
from the above analysis, it can be seen that:
the above formula is converted into a first order link and a second order link:
wherein,
utilizing the following relationships
The resultant control signal can be expressed as:
the system transfer function controlled by three-parameter feedback is:
order:
then there are:
and substituting a drive signal transfer function synthesized by a multi-parameter device with the participation of jerk feedforward into the following steps:
in the acceleration control mode, under a multi-parameter control algorithm with jerk feedforward participating, the transfer function of the system is as follows:
due to the multi-parameter control with the participation of jerk feedforward, G is introduced into the transfer function of the systemboGcoCan be paired with GbGcThe characteristics are compensated, thereby achieving the purpose of expanding the used frequency band.
In the step 1, a static error exists in the electro-hydraulic servo system, and a displacement difference exists between each two of the array systems, so that the displacement of the array systems is asynchronous. When A'a＝Av'＝A'j0, and said step 2 is aa＝Av＝AjIn the case of 0, namely the system is under the displacement closed loop and displacement error integral control, the static error of the system can be eliminated due to the existence of the integral link. The error transfer function of the system is:
but the control performance of the system is reduced due to the phenomenon of possible integral saturation, and in order to avoid the influence of the integral saturation on the control performance, an integral separation multi-parameter control algorithm is introduced in a displacement error integral link.
On the basis of three-parameter control, the invention introduces jerk feedback, jerk feedforward and displacement error integral signals to form a control method of the earthquake simulation shaking table. The acceleration feedback can reduce the hydraulic resonance frequency and reduce the influence of the characteristics of the servo valve on the system performance, thereby widening the system frequency band; the acceleration feedforward can achieve the effect of widening the system frequency band and improve the high-frequency response of the system; the displacement error integral signal can eliminate the steady state error of the system, improve the zero-difference degree of the system, can be used for solving the problem of asynchronous displacement of the seismic simulation vibration table array system, and avoids the additional internal force generated by the test piece due to asynchronous displacement.
Drawings
FIG. 1 is a schematic diagram of a method for controlling a seismic modeling vibration table according to the present invention;
FIG. 2 is a block diagram of a transfer function of a system with multi-parameter feedback according to the present invention;
FIG. 3 is a schematic diagram of an incomplete differential multi-parametric signal generator according to the present invention;
FIG. 4 is a schematic diagram of a multi-parameter signal synthesis proposed by the present invention;
FIG. 5 is a graph illustrating the effect of jerk feedback on the system performance of a vibrating table under multi-parameter control according to the present invention;
FIG. 6 is a graph illustrating the effect of jerk feedforward on the system performance of a vibrating table under multi-parameter control according to the present invention;
FIG. 7 shows the system static error under three parameter control;
FIG. 8 is a flow chart of an integral separation multi-parameter control algorithm proposed by the present invention;
FIG. 9 illustrates the effect of a unique error integral signal on the system static error of a vibration table under a multi-parameter control proposed by the present invention.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
The implementation steps of the invention are as follows:
(1) and three continuous equations of the hydraulic system are transformed by Laplace transform:
wherein M is the load mass; x is a displacement; a. thepIs the effective bearing area of the piston; p is a radical ofLIs the load drop; qLLoad flow, control cavity volume, β oil elastic modulus, CcIs the leakage coefficient; k is a radical ofqIs the flow gain of the spool valve near the steady state operating point; kcIs the flow pressure coefficient of the slide valve near the steady-state action point; s is a Laplace change factor; and E is the spool displacement of the spool valve.
The system open loop transfer function is simplified by three continuous equations as follows:
wherein,
in the formula, n0Is the hydraulic resonance frequency; d0Is the damping ratio.
(2) Introducing displacement feedback, speed feedback, acceleration feedback and jerk feedback (as shown in figure 2) on the basis of the system open-loop transfer function, and obtaining the system transfer function of the vibration table with multi-parameter feedback, wherein the system transfer function is as follows:
setting:
u＝Adu0
Ka＝Aa'Ka0
Kv＝Av'Kv0
Kd＝A'dKd0
KI＝AI'KI0
Kj＝A'jKj0
in the formula u0Is a control command signal; u is a control signal; a. thedInputting a gain for the displacement; a'dIs the displacement feedback gain; a. thev' is the velocity feedback gain; a'aIs the acceleration feedback gain; a. theI' is the displacement integral feedback gain; a'jA gain is added to the acceleration feedback; kdIs a displacement feedback coefficient; kd0The sensitivity is normalized for displacement feedback; kvIs a velocity feedback coefficient; kv0Normalizing the sensitivity for velocity feedback; kaIs an acceleration feedback coefficient; ka0Normalizing the sensitivity for acceleration feedback; kIIs a displacement integral feedback coefficient; kI0Feeding back the normalized sensitivity for displacement integration; kjIs a jerk feedback coefficient; kj0The sensitivity is normalized for jerk feedback.
The system transfer function can be:
(3) generating a speed signal by integrating the input acceleration signal once, integrating the obtained speed signal to obtain a displacement signal, integrating the obtained displacement signal to obtain a displacement integral signal, and performing incomplete differentiation on the acceleration signal to obtain an jerk signal, wherein the acceleration, speed, displacement integral and jerk signal have the following corresponding equations as shown in fig. 3:
ea＝kau0-kvev-kded-kIeI
ej＝eaGj·Gf
wherein,
Gj＝TDs
in the formula, gainA, gainB and gainC are integral gains; gjIs a transfer function corresponding to an acceleration differentiator, TDIs a differential time constant; gfTransfer function, T, for low-pass filter of acceleration signalfIs the filter coefficient; e.g. of the typeaIs an acceleration control signal; e.g. of the typevIs a speed control signal; e.g. of the typedIs a displacement control signal; e.g. of the typeIIntegrating the control signal for the displacement; e.g. of the typejIs a jerk control signal; k is a radical ofaAn acceleration gain in the multi-parameter generator; k is a radical ofdFor bits in a multi-parameter generatorShifting a feedback coefficient; k is a radical ofvFeedback coefficients for the velocity in the multi-parameter generator; k is a radical ofIThe feedback coefficients are integrated for the displacement in the multi-parameter generator.
Then:
synthesizing five signals output by the multi-parameter generator into a control signal, wherein the formula is as follows:
u＝Aaea+Avev+Aded+AIeI+Ajej
(4) and substituting the synthesized control signal in the acceleration control mode into a system transfer function with multi-parameter feedback control, and simultaneously considering the second-order characteristics of a servo valve and a sensor to obtain the system transfer function under the multi-parameter control.
Consider a servo valve as a second order system:
Ksv＝Gqkq
wherein,
in the formula, KsvIs the transfer function of the electro-hydraulic servo valve; gqIs k q1 is the transfer function of the servo valve; n isqIs the natural frequency of the second-order system of the servo valve; dqIs the second order system inherent damping ratio of the servo valve.
Considering the sensor as a second order system, the transfer function of the feedback signal is
Wherein,
in the formula,Gais the transfer function of the sensor; n isaThe natural frequency of a second-order system of the sensor; daIs the inherent damping ratio of the second-order system of the sensor.
The multi-parameter control system transfer function considering the second-order characteristics of the servo valve and the sensor is as follows:
(5) when A'a＝Av'＝A'd＝AIWhen' is 0, in the case that the system open loop transfer function in (1) alone introduces jerk feedback:
wherein,
in the formula, njFor the hydraulic resonance frequency of the system under jerk feedback, DjIs the damping ratio of the system under the feedback of the jerk.
When jerk feedback is negative feedback: a'jKj0＞0，nj＜n0，Dj＜D0The hydraulic resonance frequency and the damping ratio of the system are reduced.
In the case of jerk feedback introduced on the basis of three-parameter feedback, i.e. when AIWhen the value is equal to 0, the mark is,
the above equation can be simplified as:
wherein,
in the formula, n is the hydraulic resonance frequency of the multi-parameter feedback system based on the jerk feedback, and D is the damping ratio of the multi-parameter feedback system based on the jerk feedback.
Thus:
namely:
i. when in use
When n is equal to n0The introduction of speed feedback and jerk feedback has no influence on the hydraulic resonance frequency;
ii when
When n is more than n0The hydraulic resonance frequency is improved;
iii when
When n is less than n0The hydraulic resonance frequency is reduced.
For systems in which the servo valve 90 ° phase shift frequency is relatively close to the system hydraulic resonance frequency, the hydraulic resonance frequency of the system can be reduced by introducing jerk feedback, thereby reducing the effect of the servo valve characteristics on system performance. The control effect graph is shown in fig. 5.
(6) When gainC is 0, T is determined in step 2fWhen the value is equal to 0, namely no displacement integral signal, filtering is not considered, and under the action of an acceleration feedforward signal and three-parameter feedback control, the transfer function of a driving signal synthesized by the multi-parameter generator is as follows:
wherein,
from the above analysis, it can be seen that:
the above formula is converted into a first order link and a second order link:
wherein,
utilizing the following relationships
The resultant control signal can be expressed as:
the system transfer function of the three-parameter feedback control is as follows:
order:
then there are:
the transfer function of the driving signal synthesized by the multi-parameter device with the participation of the acceleration feedforward is introduced into the transfer function of the three-parameter feedback control system to obtain:
under the acceleration control mode and the multi-parameter control method with the participation of jerk feedforward, the transfer function of the system is as follows:
due to the multi-parameter control with the participation of jerk feedforward, G is introduced into the transfer function of the systemboGcoCan be paired with GbGcThe characteristics are compensated, thereby realizing the purpose of expanding the used frequency band and controllingThe effect is shown in fig. 6.
(7) In the step 1, a static error exists in the electro-hydraulic servo system, and the reasons of the static error are mainly null shift, dead zones, static friction caused by internal interference and the like of the system. The simplified transfer function of the static error of the system caused by the zero drift and the dead zone of the system is as follows:
in the formula phief1Transfer function of static error of system caused by system null drift and dead zone; x is the number off1The displacement of a hydraulic cylinder of the system caused by the zero drift and the dead zone of the system; Δ udAnd Δ uDRespectively representing the voltage values of zero drift and dead zone converted from the servo amplifier and the servo valve to the input end of the servo valve.
The steady state error of the system caused by the null shift and the dead zone is:
the steady state error caused by the interference inside the system is:
in the formula, ef1For systematic steady-state errors due to zero drift, dead zone, ef2For steady state errors caused by systematic internal dare to escape, FfStatic friction caused by interference inside the system. Ignoring the static error caused by internal interference, under three-parameter control, the influence of the static error caused by the zero drift and dead zone of the system on the displacement signal is shown in fig. 7.
When A'a＝Av'＝A'j0, and said step 2 is aa＝Av＝AjIn the case of 0, in the case of the vibration table system under the displacement closed loop and displacement error integral control, the error transfer function of the system is:
due to the existence of the integral link, the static error of the system can be eliminated, meanwhile, in order to avoid the influence of integral saturation on the control performance of the system, the displacement error integral link is realized by adopting an integral separation multi-parameter control algorithm, the flow chart is shown in figure 8, the displacement error integral link is introduced into a vibration table multi-parameter control system, and the control effect chart is shown in figure 9.
Claims (8)
1. A control method of an earthquake simulation vibration table is characterized by comprising the following steps: the method comprises an acceleration feedback link, a displacement feedback link and a speed synthesis link, and comprises a control parameter synthesis link for generating a speed signal and a displacement signal through an acceleration command signal, and is characterized in that a differential signal of the acceleration command signal is obtained through differentiation and is also called as a jerk feedforward signal and a differential signal of the acceleration feedback signal and is also called as a jerk feedback signal, a displacement error integral signal is obtained by integrating a difference value of displacement feedforward and feedback, and the acceleration command differential signal, the acceleration feedback differential signal and the displacement error integral signal are summed with the existing three parameter command signals, so that a composite multi-parameter control signal is obtained;
the control gains of the acceleration instruction differential signal, the acceleration feedback differential signal and the displacement error integral signal are obtained by considering the frequency domain analysis of a hydraulic system model with the high-order characteristics of a servo valve and a sensor link;
the hydraulic system model frequency domain analysis comprises the following steps:
step 1, obtaining an open-loop transfer function of a vibration table system according to a hydraulic system three-continuous equation; introducing displacement feedback, speed feedback, acceleration feedback, jerk feedback and displacement integral feedback into the system open loop transfer function to obtain the vibration table system transfer function with multi-parameter feedback;
step 2, obtaining a transfer function of the multi-parameter generator under acceleration control according to the maximum function curve of the vibration table;
step 3, substituting the transfer function of the multi-parameter generator obtained in the step 2 into the transfer function of the vibration table system with multi-parameter feedback obtained in the step 1 to obtain the whole transfer function of the vibration table control system;
the step 1 specifically comprises the following steps: the three continuous equations of the hydraulic system are transformed by Laplace:
wherein M is the load mass; x is the piston displacement; a. thepIs the effective bearing area of the piston; p is a radical ofLIs the load drop; qLLoad flow, control cavity volume, β oil elastic modulus, CcIs the leakage coefficient; k is a radical ofqIs the flow gain of the spool valve near the steady state operating point; kcIs the flow pressure coefficient of the slide valve near the steady-state action point; s is a Laplace change factor; e is the spool displacement of the spool valve;
the system open loop transfer function is simplified by three continuous equations as follows:
in the formula, n0The oil column resonance frequency, commonly referred to as the moving cylinder; d0Is the damping ratio;
introducing displacement feedback, speed feedback, acceleration feedback, jerk feedback and displacement integral feedback on the basis of a system open-loop transfer function, wherein the spool displacement E of the spool valve is as follows:
substituting the formula into a system open-loop transfer function to obtain a system transfer function of the vibration table with multi-parameter feedback, wherein the system transfer function is as follows:
setting:
u＝Adu0
Ka＝A′aKa0
Kv＝A′vKv0
Kd＝A′dKd0
KI＝A′IKI0
Kj＝A′jKj0
in the formula u0Is a control command signal; u is a control signal; a. thedInputting a gain for the displacement; a'dIs the displacement feedback gain; a'vA velocity feedback gain; a'aIs the acceleration feedback gain; a'IIntegrating the feedback gain for the displacement; a'jA gain is added to the acceleration feedback; kdIs a displacement feedback coefficient; kd0The sensitivity is normalized for displacement feedback; kvIs a velocity feedback coefficient; kv0Normalizing the sensitivity for velocity feedback; kaIs an acceleration feedback coefficient; ka0Normalizing the sensitivity for acceleration feedback; kIIs a displacement integral feedback coefficient; kI0Feeding back the normalized sensitivity for displacement integration; kjIs a jerk feedback coefficient; kj0Feeding back the normalized sensitivity for the jerk;
the system transfer function is simplified as follows:
2. the method of claim 1, wherein the method comprises the steps of: integrating the acceleration signal to generate a speed signal, integrating the speed signal to obtain a displacement signal, integrating the displacement signal to obtain a displacement integral signal, and incompletely differentiating the acceleration signal to obtain an acceleration differential signal; and eliminating integral saturation phenomenon by an integral separation method in a displacement error integral link.
3. The method of claim 1, wherein the method comprises the steps of: the step 2 specifically comprises the following steps: generating a speed signal by primary integration of an input acceleration signal, integrating the obtained speed signal to obtain a displacement signal, integrating the obtained displacement signal to obtain a displacement integral signal, and carrying out incomplete differentiation on the acceleration signal to obtain an acceleration signal, wherein the acceleration, speed, displacement integral and acceleration signal of the acceleration sensor have the following corresponding equations:
wherein,
in the formula, gainA, gainB and gainC are integral gains; gjIs a transfer function corresponding to an acceleration differentiator, TDIs a differential time constant; gfTransfer function, T, for low-pass filter of acceleration signalfIs the filter coefficient; e.g. of the typeaIs an acceleration control signal; e.g. of the typevIs a speed control signal; e.g. of the typedIs a displacement control signal; e.g. of the typeIIntegrating the control signal for the displacement; e.g. of the typejIs a jerk control signal; k is a radical ofaAn acceleration gain in the multi-parameter generator; k is a radical ofdFeedback coefficients for the displacements in the multi-parameter generator; k is a radical ofvFeedback coefficients for the velocity in the multi-parameter generator; k is a radical ofIIntegrating feedback coefficients for the displacements in the multi-parameter generator;
then:
synthesizing five signals output by the multi-parameter generator into a control signal, wherein the formula is as follows:
u＝Aaea+Avev+Aded+AIeI+Ajej。
4. the method of claim 1, wherein the method comprises the steps of: the step 3 specifically comprises the following steps: substituting the synthesized control signal under the acceleration control mode into a system transfer function with multi-parameter feedback control, and simultaneously considering the second-order characteristics of a servo valve and a sensor to obtain the system transfer function under the multi-parameter control;
consider a servo valve as a second order system:
Ksv＝Gqkq
wherein,
in the formula, KsvIs the transfer function of the electro-hydraulic servo valve; gqIs kq1 is the transfer function of the servo valve; n isqIs the natural frequency of the second-order system of the servo valve; dqThe inherent damping ratio of a second-order system of the servo valve;
considering the sensor as a second order system, the transfer function of the feedback signal is
Wherein,
in the formula, GaIs the transfer function of the sensor; n isaIs a second order system of the sensorA system natural frequency; daIs the inherent damping ratio of the second-order system of the sensor.
5. The method of claim 1, wherein the method comprises the steps of: the multi-parameter control system transfer function considering the second-order characteristics of the servo valve and the sensor is as follows:
6. the method of claim 1, wherein the method comprises the steps of: in the step 1: in the case of separate introduction of jerk feedback on the basis of the system open loop transfer function, i.e. when A'a＝A′v＝A′d＝A′IWhen the content is equal to 0, the content,
wherein,
in the formula, njFor the hydraulic resonance frequency of the system under jerk feedback, DjThe damping ratio of the system under the condition of jerk feedback is adopted;
when jerk feedback is negative feedback: a'jKj0＞0，nj＜n0，Dj＜D0The hydraulic resonance frequency and the damping ratio of the system are reduced;
in the case of jerk feedback introduced on the basis of three-parameter feedback, i.e. when A'IWhen the content is equal to 0, the content,
the above formula is simplified as follows:
wherein,
in the formula, n is the hydraulic resonance frequency of the multi-parameter feedback system based on the jerk feedback, and D is the damping ratio of the multi-parameter feedback system based on the jerk feedback;
thus:
namely:
i. when in use
When n is equal to n0At the moment, the introduction of speed feedback and jerk feedback has no influence on the hydraulic resonance frequency;
ii when
When n is more than n0The hydraulic resonance frequency is improved;
iii when
When n is less than n0The hydraulic resonance frequency is reduced;
for systems in which the servo valve 90 ° phase shift frequency is relatively close to the system hydraulic resonance frequency, the hydraulic resonance frequency of the system can be reduced by introducing jerk feedback, thereby reducing the effect of the servo valve characteristics on system performance.
7. A method as claimed in claim 3, wherein the method comprises the steps of: in the step 2: when gainC is 0, TfWhen the driving signal transfer function is equal to 0, namely under the condition of no displacement integral signal and no consideration of filtering, under the action of the jerk feedforward signal and the three-parameter feedback control, the transfer function of the driving signal synthesized by the multi-parameter generator is as follows:
wherein,
from the above analysis, it can be seen that:
the above formula is converted into a first order link and a second order link:
wherein,
utilizing the following relationships
The resultant control signal can be expressed as:
the system transfer function controlled by three-parameter feedback is:
order:
then there are:
and substituting a drive signal transfer function synthesized by a multi-parameter device with the participation of jerk feedforward into the following steps:
in the acceleration control mode, under a multi-parameter control algorithm with jerk feedforward participating, the transfer function of the system is as follows:
due to the multi-parameter control with the participation of jerk feedforward, G is introduced into the transfer function of the systemboGcjCan be paired with GbGcThe characteristics are compensated, thereby achieving the purpose of expanding the used frequency band.
8. A method as claimed in claim 3, wherein the method comprises the steps of: in the step 1, static errors exist in the electro-hydraulic servo system, and displacement differences exist among all the stations of the array system, so that the displacement of the array system is asynchronous; when A'a＝A′v＝A′j0, and said step 2 is aa＝Av＝AjUnder the condition of 0, namely under the control of displacement closed loop and displacement error integral, the static error of the system can be eliminated due to the existence of the integral link; the error transfer function of the system is:
but the control performance of the system is reduced due to the phenomenon of possible integral saturation, and in order to avoid the influence of the integral saturation on the control performance, an integral separation multi-parameter control algorithm is introduced in a displacement error integral link.
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