CN103942394A - Amplitude limiting optimizing method based on magneto-rheological damper - Google Patents

Abstract

The invention discloses an amplitude limiting optimizing method based on a magneto-rheological damper. The amplitude limiting optimizing method based on the magneto-rheological damper comprises the following steps that a control law is modified into uc=U(f)*H{(fc-f)f} by combining characteristics of the magneto-rheological damper and particularities of an aqueduct structure; the force corresponding to a force and relative speed hysteretic loop upper portion intersection is adopted as characterization, voltages are progressively increased by 0.1v to conduct simulation, and the disperse relation between the force and the voltages is obtained. According to the amplitude limiting optimizing method based on the magneto-rheological damper, the control law is modified by orienting to the characteristics of the magneto-rheological damper and combining the particularities of the aqueduct structure, the force corresponding to the force and relative speed hysteretic loop upper portion intersection is adopted as the characterization, the voltages are progressively increased by 0.1v to conduct the simulation, the disperse relation between the force and the voltages is obtained, the method is simple, operation is convenient, changes are conducted on an original basis, and the problems that in an existing amplitude limiting optimizing method, when certain low-amplitude vibration is caused, large control voltages are still be loaded, the changing amplitude of control force can be large, and local earthquake responses are possibly enlarged are well solved.

Description

A kind of method based on MR damper amplitude limit optimum

Technical field

The invention belongs to MR damper technical field, relate in particular to a kind of method based on MR damper amplitude limit optimum.

Background technology

At present, South to Northern Water Diversion Project of China is the large hydraulic engineering that the present situation for alleviating China North China and Water Resource in Northwest shortage is built, analysis on aqueduct structure is as the important component part in south water to north water delivery engineering, on Route, to apply one of more main crossing, and the water delivery line of work centerline passes through China's Areas of High Earthquake Intensity region, the seismic fortification intensity of the many sections of circuit reaches 8 degree, 49 of the total aqueducts of whole engineering water delivery general main canal, cumulative length reaches 5520m, and flow reaches 500m ³/ s, once there is earthquake, water delivery completely will be interrupted, and it closes on important trunk railways such as capital is wide, capital nine, may cause serious secondary disaster, therefore the quake-resistant safety of water delivery engineering is extremely important.

The amplitude limit optimal algorithm that Dyke proposes for MR damper has at present obtained application comparatively widely, and its control law can be described as:

u _c＝u _maxH{(f _c-f)f}

In formula, H{} is Heaviside step function, and this formula meaning is, if the damping force f that MR produces _cequal active controlling force f, keep current voltage constant; If f _cbe less than f, be adjusted to by applying voltage the control coupling expectation value that maximal value provides to impel MR; In other situations, voltage is made as to zero.

But, in the time that maximum voltage is set, there is certain subjectivity in this algorithm, and in working control, only have two grades of voltages adjustable, be null value and maximal value, to cause like this some low amplitude vibration time, still have larger control voltage-drop loading, like this change amplitude of control can be larger, likely can strengthen local seismic response.

Summary of the invention

The object of the embodiment of the present invention is to provide a kind of method based on MR damper amplitude limit optimum, when being intended to solve existing amplitude limit optimal algorithm and causing the vibration of some low amplitude, still there is larger control voltage-drop loading, the change amplitude of control can be larger, likely can strengthen the problem of local seismic response.

The embodiment of the present invention is achieved in that a kind of method based on MR damper amplitude limit optimum, should the method based on MR damper amplitude limit optimum comprise the following steps:

In conjunction with the singularity of MR damper characteristic and analysis on aqueduct structure, control law is revised as:

u _c＝U(f)*H{(f _c-f)f}

The employing power masterpiece corresponding with relative velocity hysteretic loop top intersection point is to characterize, and simulates with 0.1v incremental voltage, obtains the discrete relationship of power and voltage.

Further, discrete point is carried out to matching, finally U (f) is expressed as:

U(f)＝(af+b)*H{af+b}

In formula, a, b is the Relation Parameters of power and voltage.

Further, the method for this method amplitude limit optimum control based on MR damper amplitude limit optimum is:

In the structure of n degree of freedom, add r controller, the structure half active control system equation of motion under the consistent input of earthquake motion is:

$M\stackrel{\·\·}{X}\left(t\right)+C\stackrel{\·}{X}\left(t\right)+\mathrm{KX}\left(t\right)=B_{s}U\left(t\right)+{\mathrm{MH}}_0{\stackrel{\·\·}{X}}_g\left(t\right)$

X(t ₀)＝X ₀

$\stackrel{\·}{X}\left(t_0\right)={\stackrel{\·}{X}}_0$

In formula, M, C and K are respectively quality, damping and the stiffness matrix of structure n × n dimension; X (t), with respectively displacement, speed and the vector acceleration of structure n dimension; it is earthquake ground motion acceleration time-histories; U (t) is r × 1 dimension control vector; H ₀it is n × 1 dimension earthquake ground motion acceleration location matrix; B _sthat n × r ties up half ACTIVE CONTROL damper position matrix;

Introduce state vector $Z=\left[\begin{array}{c}X\\ \stackrel{\·}{X}\end{array}\right],$ The equation of motion of structure is expressed as state equation:

$\stackrel{\·}{Z}\left(t\right)=\mathrm{AZ}\left(t\right)=\mathrm{BU}\left(t\right)+H{\stackrel{\·\·}{X}}_g\left(t\right)$

Z(t ₀)＝Z ₀

$Y=C\{\stackrel{\·}{Z}\left(t\right)-H{\stackrel{\·\·}{X}}_g\left(t\right)\}+v\left(t\right)$

Wherein, $A=\left[\begin{array}{cc}0& I\\ -M^{-1}K& -M^{-1}C\end{array}\right],B=\left[\begin{array}{c}0\\ M^{-1}{B}_s\end{array}\right],H=\left[\begin{array}{c}0\\ H_0\end{array}\right],$ C=[0 I], Y is observation output, for absolute acceleration is using as feedback, v (t) is for measuring noise;

The performance objective function of define system is:

$J=\underset{0}{\overset{\∞}{\∫}}[Z^T\mathrm{QZ}+U^T\mathrm{RU}]\mathrm{dt}$

Wherein, Q and R are weight matrix, make performance objective function get minimum value, can be in the hope of feedback gain G=R ^-1b ^tp is r × 2n dimension feedback of status gain matrix; P is that 2n × 2n ties up matrix, can be by Riccati matrix algebra equation solution;

Owing to being fed back to absolute acceleration, so need to introduce state estimation vector replace state vector Z, make keep optimum for output feedback problem, state estimation vector produced by Kalman wave filter:

$\stackrel{\·}{\tilde{Z}}\left(t\right)=A\tilde{Z}\left(t\right)+\mathrm{BU}\left(t\right)+L[Y\left(t\right)-\tilde{Y}\left(t\right)]$

Formula median filter gain L can be expressed as:

L＝P ₁C ^TV ^-1

V=E[v (t) v ^t(t)] for measuring noise covariance matrix, E[] expression mathematical expectation, P ₁solution for following formula:

AP ₁+P ₁A ^T+N-P ₁C ^TV ^-1CP ₁＝0

In formula, N=E[w (t) w ^t(t)] be input noise covariance matrix, Kalman wave filter makes the progressive covariance of state estimation error reach minimum.

Method based on MR damper amplitude limit optimum provided by the invention, by for MR damper characteristic, in conjunction with the singularity of analysis on aqueduct structure, control law is made to improvement, the employing power masterpiece corresponding with relative velocity hysteretic loop top intersection point is sign, simulate with 0.1v incremental voltage, obtain the discrete relationship of power and voltage, method is simple, easy to operate, make a change on the original basis, when preferably resolving existing amplitude limit optimal algorithm and causing the vibration of some low amplitude, still there is larger control voltage-drop loading, the change amplitude of control can be larger, likely can strengthen the problem of local seismic response.

Brief description of the drawings

Fig. 1 is the method flow diagram based on MR damper amplitude limit optimum that the embodiment of the present invention provides;

Fig. 2 is the control that provides of the embodiment of the present invention and the discrete relationship schematic diagram of voltage.

It is lower across span centre and the right time-histories across span centre response schematic diagram in the input of ElcentroNS seismic event that Fig. 3, Fig. 4 are respectively analysis on aqueduct structure.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.

Below in conjunction with drawings and the specific embodiments, application principle of the present invention is further described.

As shown in Figure 1, the method based on MR damper amplitude limit optimum of the embodiment of the present invention comprises the following steps:

S101: in conjunction with the singularity of MR damper characteristic and analysis on aqueduct structure, change control rule;

S102: the employing power masterpiece corresponding with relative velocity hysteretic loop top intersection point is to characterize, and simulates with 0.1v incremental voltage, obtains the discrete relationship of power and voltage.

Concrete steps of the present invention are:

The first step, in conjunction with the singularity of MR damper characteristic and analysis on aqueduct structure, changes control law into:

u _c＝U(f)*H{(f _c-f)f}

Wherein, U (f) is for characterizing the continuous function of voltage and power; H{} is Heaviside step function.

Second step, the employing power masterpiece corresponding with relative velocity hysteretic loop top intersection point is to characterize, and simulates with 0.1v incremental voltage, obtains the discrete relationship of power and voltage, as shown in Figure 2.

Active controlling force, by semi-active control law u=k (f _c, calculating f), draws the result of semi-active control law, result outputs to MR damper, finally exports half active controlling force.

As can be seen from Figure 2, linear relationship is comparatively obvious, and discrete point is carried out to matching, finally U (f) is expressed as:

U(f)＝(af+b)*H{af+b}

In formula, a, b is the Relation Parameters of power and voltage.

The method of amplitude limit optimum control of the present invention is:

In the structure of n degree of freedom, add r controller, the structure half active control system equation of motion under the consistent input of earthquake motion is:

$M\stackrel{\·\·}{X}\left(t\right)+C\stackrel{\·}{X}\left(t\right)+\mathrm{KX}\left(t\right)=B_{s}U\left(t\right)+{\mathrm{MH}}_0{\stackrel{\·\·}{X}}_g\left(t\right)$

X(t ₀)＝X ₀

$\stackrel{\·}{X}\left(t_0\right)={\stackrel{\·}{X}}_0$

\*MERGEFORMAT (1)

In formula, M, C and K are respectively quality, damping and the stiffness matrix of structure n × n dimension; X (t), with respectively displacement, speed and the vector acceleration of structure n dimension; it is earthquake ground motion acceleration time-histories; U (t) is r × 1 dimension control vector; H ₀it is n × 1 dimension earthquake ground motion acceleration location matrix; B _sthat n × r ties up half ACTIVE CONTROL damper position matrix.

Introduce state vector $Z=\left[\begin{array}{c}X\\ \stackrel{\·}{X}\end{array}\right],$ The equation of motion of structure can be expressed as state equation:

$\stackrel{\·}{Z}\left(t\right)=\mathrm{AZ}\left(t\right)=\mathrm{BU}\left(t\right)+H{\stackrel{\·\·}{X}}_g\left(t\right)$

Z(t ₀)＝Z ₀ \*MERGEFORMAT (2)

$Y=C\{\stackrel{\·}{Z}\left(t\right)-H{\stackrel{\·\·}{X}}_g\left(t\right)\}+v\left(t\right)$

Wherein, $A=\left[\begin{array}{cc}0& I\\ -M^{-1}K& -M^{-1}C\end{array}\right],B=\left[\begin{array}{c}0\\ M^{-1}{B}_s\end{array}\right],H=\left[\begin{array}{c}0\\ H_0\end{array}\right],$ C=[0 I], Y is observation output, be absolute acceleration using as feedback herein, v (t) is measurement noise.

The performance objective function of define system is

$J=\underset{0}{\overset{\∞}{\∫}}[Z^T\mathrm{QZ}+U^T\mathrm{RU}]\mathrm{dt},\backslash *\mathrm{MERGEFORMAT}---\left(3\right)$

Wherein, Q and R are weight matrix.Make performance objective function get minimum value, can be in the hope of feedback gain G=R ^-1b ^tp is r × 2n dimension feedback of status gain matrix; P is that 2n × 2n ties up matrix, can be by Riccati matrix algebra equation solution.

Owing to being fed back to absolute acceleration, so need to introduce state estimation vector replace state vector Z, make keep optimum for output feedback problem, state estimation vector produced by Kalman wave filter:

$\stackrel{\·}{\tilde{Z}}\left(t\right)=A\tilde{Z}\left(t\right)+\mathrm{BU}\left(t\right)+L[Y\left(t\right)-\tilde{Y}\left(t\right)]$

\*MERGEFORMAT (4)

Formula median filter gain L can be expressed as

L＝P ₁C ^TV ^-1 \*MERGEFORMAT (5)

V=E[v (t) v ^t(t)] for measuring noise covariance matrix, E[] expression mathematical expectation, P ₁for the solution of following formula

AP ₁+P ₁A ^T+N-P ₁C ^TV ^-1CP ₁＝0 \*MERGEFORMAT (6)

In formula, N=E[w (t) w ^t(t)] be input noise covariance matrix.Kalman wave filter makes the progressive covariance of state estimation error reach minimum.

As shown in Figure 3 and Figure 4, be the damping effect schematic diagram of the embodiment of the present invention, can find out by Fig. 3 and Fig. 4, the present invention has good damping performance.

It is lower across span centre and the response of the right time-histories across span centre in the input of ElcentroNS seismic event that Fig. 3 and Fig. 4 are respectively analysis on aqueduct structure, in figure, directions X coordinate time is time shaft, unit is second, Y-direction coordinate axis Displacement is displacement response, unit is rice, Z direction coordinate Velocity is speed responsive, unit is meter per second, in figure, the representative of the dotted portion of curve is the time-histories response of aqueduct in the time not adding control device, in figure, the representative of the solid line part of curve is the time-histories response of analysis on aqueduct structure under this control program, from solid line and dotted line to recently, there is following characteristics:

1, within the scope of seismic event input maximum value (two time periods of 5-10s and 15-20s), solid line (control program) numerical value will significantly be less than dotted line (without control) numerical value, illustrates that control program has good control effect to the peak value of seismic response.

2, in the less scope of seismic event input value, the value envelope of solid line, within dotted line numerical value, illustrates that control program also has certain effect, controls effect steady, does not occur enlarge-effect.

It is lower across span centre and the response of the right time-histories across span centre in the input of ElcentroNS seismic event that Fig. 3 and Fig. 4 are respectively analysis on aqueduct structure, in figure, directions X coordinate time is time shaft, unit is second, Y-direction coordinate axis Displacement is displacement response, unit is rice, Z direction coordinate Velocity is speed responsive, unit is meter per second, in figure, the representative of the dotted portion of curve is the time-histories response of aqueduct in the time not adding control device, in figure, the representative of the solid line part of curve is the time-histories response of analysis on aqueduct structure under this control program, from solid line and dotted line to recently, there is following characteristics:

1. within the scope of seismic event input maximum value (two time periods of 5-10s and 15-20s), solid line (control program) numerical value will significantly be less than dotted line (without control) numerical value, illustrates that control program has good control effect to the peak value of seismic response.

In the less scope of seismic event input value, the value envelope of solid line, within dotted line numerical value, illustrates that control program also has certain effect, controls effect steady, does not occur enlarge-effect.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any amendments of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.

Claims (3)

1. the method based on MR damper amplitude limit optimum, is characterized in that, should the method based on MR damper amplitude limit optimum comprise the following steps:

In conjunction with the singularity of MR damper characteristic and analysis on aqueduct structure, control law is revised as:

u _c＝U(f)*H{(f _c-f)f}

The employing power masterpiece corresponding with relative velocity hysteretic loop top intersection point is to characterize, and simulates with 0.1v incremental voltage, obtains the discrete relationship of power and voltage.

2. the method based on MR damper amplitude limit optimum as claimed in claim 1, is characterized in that, discrete point is carried out to matching, finally U (f) is expressed as:

U(f)＝(af+b)*H{af+b}

In formula, a, b is the Relation Parameters of power and voltage.

3. the method based on MR damper amplitude limit optimum as claimed in claim 1, is characterized in that, the method for being somebody's turn to do the method amplitude limit optimum control based on MR damper amplitude limit optimum is:

In the structure of n degree of freedom, add r controller, the structure half active control system equation of motion under the consistent input of earthquake motion is:

$M\stackrel{\·\·}{X}\left(t\right)+C\stackrel{\·}{X}\left(t\right)+\mathrm{KX}\left(t\right)=B_{s}U\left(t\right)+{\mathrm{MH}}_0{\stackrel{\·\·}{X}}_g\left(t\right)$

X(t ₀)＝X ₀

$\stackrel{\·}{X}\left(t_0\right)={\stackrel{\·}{X}}_0$

In formula, M, C and K are respectively quality, damping and the stiffness matrix of structure n × n dimension; X (t), with respectively displacement, speed and the vector acceleration of structure n dimension; it is earthquake ground motion acceleration time-histories; U (t) is r × 1 dimension control vector; H ₀it is n × 1 dimension earthquake ground motion acceleration location matrix; B _sthat n × r ties up half ACTIVE CONTROL damper position matrix;

Introduce state vector $Z=\left[\begin{array}{c}X\\ \stackrel{\·}{X}\end{array}\right],$ The equation of motion of structure is expressed as state equation:

$\stackrel{\·}{Z}\left(t\right)=\mathrm{AZ}\left(t\right)=\mathrm{BU}\left(t\right)+H{\stackrel{\·\·}{X}}_g\left(t\right)$

Z(t ₀)＝Z ₀

$Y=C\{\stackrel{\·}{Z}\left(t\right)-H{\stackrel{\·\·}{X}}_g\left(t\right)\}+v\left(t\right)$

Wherein, $A=\left[\begin{array}{cc}0& I\\ -M^{-1}K& -M^{-1}C\end{array}\right],B=\left[\begin{array}{c}0\\ M^{-1}{B}_s\end{array}\right],H=\left[\begin{array}{c}0\\ H_0\end{array}\right],$ C=[0 I], Y is observation output, for absolute acceleration is using as feedback, v (t) is for measuring noise;

The performance objective function of define system is:

$J=\underset{0}{\overset{\∞}{\∫}}[Z^T\mathrm{QZ}+U^T\mathrm{RU}]\mathrm{dt}$

Wherein, Q and R are weight matrix, make performance objective function get minimum value, can be in the hope of feedback gain G=R ^-1b ^tp is r × 2n dimension feedback of status gain matrix; P is that 2n × 2n ties up matrix, can be by Riccati matrix algebra equation solution;

Owing to being fed back to absolute acceleration, so need to introduce state estimation vector replace state vector Z, make keep optimum for output feedback problem, state estimation vector produced by Kalman wave filter:

$\stackrel{\·}{\tilde{Z}}\left(t\right)=A\tilde{Z}\left(t\right)+\mathrm{BU}\left(t\right)+L[Y\left(t\right)-\tilde{Y}\left(t\right)]$

Formula median filter gain L can be expressed as:

L＝P ₁C ^TV ^-1

V=E[v (t) v ^t(t)] for measuring noise covariance matrix, E[] expression mathematical expectation, P ₁solution for following formula:

AP ₁+P ₁A ^T+N-P ₁C ^TV ^-1CP ₁＝0

In formula, N=E[w (t) w ^t(t)] be input noise covariance matrix, Kalman wave filter makes the progressive covariance of state estimation error reach minimum.