WO2019058905A1

WO2019058905A1 - Parameter estimation method for hydraulic system

Info

Publication number: WO2019058905A1
Application number: PCT/JP2018/031865
Authority: WO
Inventors: 山田　崇; 西田　吉晴
Original assignee: 株式会社神戸製鋼所
Priority date: 2017-09-22
Filing date: 2018-08-29
Publication date: 2019-03-28
Also published as: JP6815299B2; JP2019057198A

Abstract

Provided is a parameter estimation method by which a physical quantity affecting the dynamic characteristics of a hydraulic system is estimated as a parameter, and which can be widely applied. This method is provided with: a step for selecting, from a state vector including a state quantity of a hydraulic system and a parameter of an estimation target, a corresponding state quantity and a corresponding estimation target parameter, thereby setting a corresponding state vector; a step for using the set state vector to set a state equation of the hydraulic system; and a step for applying a state estimation method based on Bayes estimation to the state equation, thereby estimating the value of the estimation target parameter included in the state vector.

Description

Parameter estimation method of hydraulic system

The present invention relates to a parameter estimation method of a hydraulic system in which a physical quantity affecting dynamic characteristics of the hydraulic system is estimated as a parameter.

In hydraulic system control, it is important to accurately model the dynamics of the hydraulic system. The dynamic characteristics of a hydraulic system largely depend on various physical quantities such as bulk modulus, viscosity and Reynolds number of hydraulic fluid. And some of these physical quantities depend on parameters that dynamically change during operation of the hydraulic system. For example, the bulk modulus of the hydraulic oil depends on the bubble mixing ratio to the hydraulic oil, the temperature and pressure of the hydraulic oil, and the like. Therefore, it is desirable to acquire the value of the physical quantity that affects the dynamic characteristics of the hydraulic system in real time.

For example, as a method of acquiring the bulk modulus of the hydraulic oil in real time, measuring the volume change of the hydraulic oil of the hydraulic system and the generated pressure to it, and calculating the ratio (that is, the definition itself of the bulk modulus) Conceivable. However, in a general hydraulic system, in order to accurately measure the volume change of the hydraulic fluid, a special circuit is provided to measure the interruption of the normal operation and the volume change of the hydraulic fluid and the pressure generated thereto. I need to These things cause the fall of the operation efficiency of a hydraulic system, and increase of operation cost.

As another method for acquiring the bulk elastic modulus of hydraulic oil in real time, it is conceivable to model the bulk elastic modulus with a mathematical function and measure and substitute physical parameters which are variables of the function with a sensor. However, it is difficult to directly measure the bubbling rate into the hydraulic oil by which the bulk modulus of the hydraulic oil is dependent by a sensor. Therefore, it is difficult to construct a mathematical model that guarantees sufficient accuracy for all states.

Therefore, application of system identification theory can be considered as a method for acquiring the bulk modulus of hydraulic oil in real time. As a parameter identification method using system identification theory, there is, for example, a least squares method.

Patent Document 1 below discloses a parameter identification method based on the least squares method. The parameter identification method described in Patent Document 1 defines a state space equation representing a nonlinear model of a vertical articulated hydraulic manipulator, and applies a new sequential identification method in which the conventional sequential identification method is modified to the state space equation. And to do. In this sequential identification method, in each step, using measured parameters and known parameters, a linear equation is established for unknown parameters including bulk modulus and flow coefficient, based on the state space equation. Identification calculation using is not performed. At the end of each step, two normal equations are derived by strictly integrating the linear equations for the unknown parameters into two linear equations across all the steps and combining them over time. Then, by solving these two normal equations, unknown parameters including the bulk modulus and the flow coefficient are identified.

However, the parameter identification method described in Patent Document 1 can be applied only when all of the states are observable and the state equation can be linearly deformed with respect to the identification parameters. In addition, as the number of identification parameters increases, the computational cost increases exponentially, making real-time estimation difficult. Therefore, the scope of application of the parameter identification method is extremely limited.

JP, 2015-77643, A

An object of the present invention is to provide a method of estimating a physical quantity that affects the dynamic characteristics of a hydraulic system as a parameter, and a method with a wide range of application.

The inventor of the present application has conceived of setting a state vector that includes a physical quantity to be estimated as a parameter to be estimated, in order to achieve the above object. Then, by applying the state estimation method based on Bayesian estimation or the sequential estimation method to the equation using the state vector, new findings have been obtained that the application range of the parameter estimation method can be expanded. . The present invention has been completed based on such findings.

What is provided is a parameter estimation method of a hydraulic system in which a physical quantity that affects the dynamic characteristics of the hydraulic system is selected as the estimation target parameter, and the value of the estimation target parameter is estimated.

The parameter estimation method for a hydraulic system according to the first aspect sets the state vector by selecting the state quantity of the state vector including the state quantity of the hydraulic system and the estimation target parameter and the estimation target parameter. The step of setting a state equation of the hydraulic system using the set state vector, and applying the state estimation method based on Bayesian estimation to the state equation, the estimation included in the state vector Estimating the value of the target parameter.

A parameter estimation method for a hydraulic system according to a second aspect includes the steps of: deriving a first equation indicating the dynamic characteristic of the hydraulic system; and second equation using a state vector including the estimation target parameter as the first equation And estimating the value of the estimation target parameter included in the state vector by applying a sequential estimation method to the second equation.

It is a flowchart which shows the parameter estimation method of the hydraulic system by the 1st Embodiment of this invention. FIG. 1 is a circuit diagram showing a hydraulic system to which a parameter estimation method of a hydraulic system according to a first embodiment of the present invention is applied. _F hin used in the first embodiment of the present invention _{_{_{(x v), f hout (}}} x v), is a graph showing the _f rin _{(x v)} and _f rout _{(x v).} FIG. 7 is a graph showing the time change of the spool position of the directional flow control valve as an input to the hydraulic system. It is a graph which shows the presumed result in the 1st embodiment of the present invention, and shows the time change of the estimated value of the said bulk modulus K after starting estimation of the value of the bulk modulus K of hydraulic fluid. It is a graph. A graph showing estimation results of the first embodiment of the present invention, is a graph showing temporal changes of the estimated value of the pressure P _p from the start of the estimation of the value of the pressure Pp. A graph showing estimation results of the first embodiment of the present invention, is a graph showing temporal changes of the estimated value of the pressure P _h from the start of the estimation of the value of the pressure Ph. A graph showing estimation results of the first embodiment of the present invention, is a graph showing temporal changes of the estimated value of the pressure P _r from the start of the estimation of the value of the pressure Pr. A graph showing estimation results of the first embodiment of the present invention, is a graph showing temporal changes of the estimated value of the spool position x _c from the start of the estimation of the value of the spool position Xc. A graph showing estimation results of the first embodiment of the present invention, the time estimate of the spool speed from the start of the estimation of the spool speed value which is the time rate of change of the spool position x _c It is a graph which shows change. It is a flowchart which shows the parameter estimation method of the hydraulic system by the 2nd Embodiment of this invention. It is a graph which shows the result of having estimated the value of bulk modulus K of hydraulic fluid by the successive least squares method. It is a graph which shows the result of having estimated the value of bulk modulus K of hydraulic fluid by the successive least squares method. It is a graph which shows the result of having estimated the value of contraction flow coefficient C by the successive least squares method. It is a graph which shows the result of having estimated the value of bulk modulus K of hydraulic fluid by a weighted successive least squares method. It is a graph which shows the result of having estimated the value of contraction coefficient C by the weighted successive least squares method. It is a graph which shows the result of having estimated the value of bulk modulus K of hydraulic fluid by a weighted successive least squares method. It is a graph which shows the result of having estimated the value of contraction coefficient C by the weighted successive least squares method. It is a graph which shows the result of having estimated the value of bulk modulus K of hydraulic fluid by the frequency filter and the successive least squares method. It is a graph which shows the result of having estimated the value of contraction flow coefficient C by the frequency filter and the successive least squares method. Is a graph showing an estimation result value bulk modulus K ₀ at atmospheric pressure. Is a graph showing estimation results of a value of the proportional coefficient K _p. Is a graph showing an estimation result value bulk modulus K ₀ at atmospheric pressure. It is a graph which shows the presumed result of the value of proportionality coefficient Kp.

Hereinafter, embodiments of the present invention will be described in detail with reference to the attached drawings.

A parameter estimation method of a hydraulic system according to a first embodiment of the present invention will be described with reference to FIG. FIG. 1 is a flowchart showing a method of estimating a parameter of a hydraulic system according to a first embodiment.

The parameter estimation method of the hydraulic system according to the first embodiment selects a physical quantity that affects the dynamic characteristics of the hydraulic system as the estimation target parameter, and estimates the value of the estimation target parameter. The parameter estimation method for a hydraulic system according to the first embodiment includes the step of setting an equation indicating the dynamic characteristic of the hydraulic system (step S10), and the state of the state vector including the state quantity of the hydraulic system and the estimation target parameter. A step of setting the state vector by selecting an amount and the estimation target parameter (step S11), and setting a state equation and an observation equation of the hydraulic system using the set state vector (step S12); Estimating the value of the estimation target parameter included in the state vector by applying a state estimation method based on Bayesian estimation to the state equation (step S13).

Such a parameter estimation method is executed by, for example, a control CPU or a simulator. The control CPU controls, for example, a real machine system.

The parameter estimation method of the hydraulic system according to the first embodiment, for example, selects the bulk modulus K of the hydraulic oil of the hydraulic system 10 shown in FIG. 2 as the estimation target parameter and estimates the value of the bulk modulus K Is applied to the hydraulic system 10 concerned. The hydraulic system to which the parameter estimation method of the hydraulic system according to the first embodiment is applied is not limited to the hydraulic system 10 shown in FIG. Further, the estimation target parameter estimated by the parameter estimation method of the hydraulic system according to the first embodiment is not limited to the bulk modulus K of the hydraulic oil of the hydraulic system 10.

The hydraulic system 10 to which the parameter estimation method of the hydraulic system according to the first embodiment is applied will be described with reference to FIG. FIG. 2 is a circuit diagram showing the hydraulic system 10.

The spool displacement Xv of the spool type directional flow control valve 14 is input to the hydraulic system 10 as a control input. The hydraulic system 10 controls the operation of the hydraulic cylinder 16 based on the control input. The hydraulic system 10 includes a hydraulic pump 12, a directional flow control valve 14, a hydraulic cylinder 16, a hydraulic oil tank 18, and a relief valve 20.

The hydraulic pump 12 discharges hydraulic oil. The directional flow control valve 14 opens and closes so as to change the direction and flow rate of the hydraulic oil supplied from the hydraulic pump 12 to the hydraulic cylinder 16. The hydraulic cylinder 16 has a head side chamber 161, which is a liquid chamber on the cylinder head side, and a rod side chamber 162, which is a liquid chamber on the rod side, and the hydraulic oil discharged by the hydraulic pump 12 is It is driven by being supplied to the head side chamber 161 or the rod side chamber 162. The hydraulic oil tank 18 stores hydraulic oil to be discharged from the hydraulic pump 12. The relief valve 20 performs an opening and closing operation so that the pressure of the hydraulic fluid discharged from the hydraulic pump 12 does not exceed a predetermined pressure. The hydraulic pump 12 and the directional flow control valve 14 are connected by a pipe 22. The directional flow control valve 14 and the head side chamber 161 of the hydraulic cylinder 16 are connected by a pipe 24. The rod side chamber 162 of the hydraulic cylinder 16 and the directional flow control valve 14 are connected by a pipe 26.

Each step of the method of estimating the parameters of the hydraulic system 10 according to the first embodiment will be described with reference to FIG. 1 again.

First, in step S10, an equation indicating the dynamic characteristic of the hydraulic system 10 is set. The dynamic characteristics of the hydraulic system 10 are represented by the following equation.

Here, m is the mass of the hydraulic cylinder 16 and the load object, x _c is the cylinder position (the position of the cylinder head in the hydraulic cylinder 16), A _h is the cross-sectional area of the head side chamber 161, and A _r is The cross-sectional area of the rod side chamber 162, P _p is the pressure in the pipe 22 and is the pump pressure which is the discharge pressure of the hydraulic pump 12, and P _h is the pressure in the pipe 24 and the head pressure of the hydraulic cylinder 16. P _r is the pressure in the pipe 26 and the rod pressure of the hydraulic cylinder 16, P _t is the tank pressure which is the pressure in the hydraulic oil tank 18, K is the bulk modulus of the hydraulic oil, and V _p is the volume of the pipe 22 V _h is the volume of the pipe 24, V _r is the volume of the pipe 26, l is the total length of the hydraulic cylinder 16, Q _p is the flow rate of hydraulic fluid discharged from the hydraulic pump 12, and Q _hin passes the directional flow control valve 14 Work that flows into the head side chamber 161 Oil flow rate, Q _hout is operated to inlet flow of the hydraulic fluid passing through the directional flow control valve 14 is discharged from the head-side chamber 161 to the, Q _rin passes through the directional flow control valve 14 to the rod side chamber 162 The flow rate of oil, _Qrout, is the flow rate of the hydraulic fluid discharged from the rod side chamber 162 and passing through the directional flow control valve 14, and _QpR is the flow rate of the hydraulic fluid passing through the relief valve 20.

_{Each of} the flow rates Q _p , Q _hin , Q _hout , Q _rin , Q _rout , and Q _pR is expressed by the following equation.

Here, x _v is the spool position is the position of the spool in the directional flow control valve 14, C is contraction coefficient, [rho is the density of the hydraulic fluid, A _hin is a the flow path forming said directional flow control valve 14 Opening area of the _head side meter-in flow passage for allowing hydraulic oil to flow toward the head side chamber 161, where A _hout is a flow passage formed by the directional flow control valve 14, and the head side chamber The opening area of the head-side meter-out flow passage which allows the hydraulic fluid discharged from 161 to flow into the tank, and A _rin is the flow passage formed by the directional flow control valve 14 and the hydraulic fluid is in the rod side chamber An opening area of the rod-side meter-in flow passage which allows the flow toward 162, _Arout is a flow passage formed by the directional flow control valve 14 and hydraulic oil discharged from the head side chamber 161 flows into the tank of The opening area of the head-side meter-out flow passage, A _pR is the opening area of the relief valve 20, and f _hin (x _v ) is the opening area A _hin of the head-side meter-in flow passage and the spool position An arbitrary function showing a relation with x _v , f _hout (x _v ) is an arbitrary function showing a relation between an opening area A _{hout of the head} side meter-out flow path and the spool position x _v , f _rin ( x _v ) is an arbitrary function showing the relationship between the opening area A _rin of the rod side meter-in flow path and the spool position x _v, and _frout (x _v ) is the opening area _{Arout of the} rod side meter out flow path any function indicating the relationship between the spool position _{_{_{x v, f pR (P p}}} -P t) , the relief valve opening area _{a pR} and the differential pressure _(P p -P _t) that the tank pressure and the pump pressure Is an arbitrary function indicating the relationship between the difference.

After the equation indicating the dynamic characteristic of the hydraulic system 10 is set, the state quantities of the state vector including the plurality of state quantities of the hydraulic system 10 and the estimation target parameter and the estimation target parameter are selected in step S11. .

Wherein the plurality of state quantities of the hydraulic system 10, the pressure _{P p,} the pressure _{P h,} the pressure _{P r,} the spool speed _x ^{c (1} is the time differential value of the spool position _{x c} and the spool position _{x c} ⁾ is selected. For convenience, the rank of the time derivative is indicated by the number of dots placed above the letter in each equation, and the rank of the time derivative is indicated by the parenthesized numbers attached to the right shoulder of the letter throughout the specification. Further, as described above, the bulk elastic modulus K is selected as the estimation target parameter. The state vector x of the hydraulic system 10, which is set by selecting such state quantities and estimation target parameters, is expressed as follows.

Thus, after the state vector x of the hydraulic system 10 is set, in step S12, the state equation and the observation equation of the hydraulic system 10 are set using the state vector x.

The equation of state of the hydraulic system 10 is non-linear and is expressed as follows.

That is, the state equation of the hydraulic system 10 is expressed in the form of a first-order differential equation.

Note that vεR ^{6 × 1} in the above equation of state represents a white noise vector whose mean vector is 0εR ^{6 × 1} and whose variance-covariance matrix is QεR ^{6 × 6} . That is, the above equation of state includes a noise term.

Here, it is assumed that the pressure P _p , the pressure P _h , the pressure P _r and the spool position x _c among the state quantities of the hydraulic system 10 can be observed by a pressure sensor or a position sensor. At this time, the observation equation of the hydraulic system 10 is expressed as follows.

Note that w 方程式 R ^{4 × 4} in the above observation equation represents a white noise vector whose mean vector is 0∈R ^{4 × 4} and whose variance-covariance matrix is R∈R ^{4 × 4} .

After the state equation and the observation equation of the hydraulic system 10 are set, the unscented Kalman filter (that is, a nonlinear state estimation method) as a state estimation method based on Bayesian estimation is applied to the state equation in step S13. The value of each element constituting the state vector x is estimated. Thereby, the value of the bulk elastic modulus K of the hydraulic oil which is the estimation target parameter included in the state vector x is estimated.

[Conditions used for estimation in the first embodiment]
Hereinafter, conditions used for estimation in the present embodiment and results of estimation using the conditions will be described.

The following Table 1 shows physical constants used in the present embodiment.

FIG. 3 shows the relationship between the functions f _hin (x _v ), f _hout (x _v ), f _rin (x _v ) and f _rout (x _v ) used in the present embodiment and the spool position x _v . The functions f _hin (x _v ) and f _rout (x _v ) are respectively zero (ie, the opening area is zero) when the spool position xv is negative, as shown by the solid line in FIG. When x _v is positive, it increases as the spool position x _v increases (ie, the opening area increases). The functions f _rin (x _v ) and f _hout (x _v ), respectively, as shown by the broken line in FIG. 3, decrease as the absolute value of the spool position x _v decreases when the spool position x _v is negative. Smaller (i.e. smaller opening area) and zero (i.e. zero opening area) if the spool position xv is positive. The hydraulic system 10, as its input, the spool position x _v of directional flow control valve 14 is provided as shown in FIG.

The time change f _K of the bulk modulus K of the hydraulic fluid may be zero or may be a positive value (for example, 50). If the temporal change f _K of the bulk modulus K of the hydraulic fluid is zero, an estimation is performed on the assumption that the bulk modulus K of the hydraulic fluid is a constant. On the other hand, if the time variation f _K of the bulk modulus K of the hydraulic fluid is a positive value, bulk modulus K of the hydraulic oil becomes variable parameter, it is possible to simulate the modeling error. In the present embodiment, the time change f _K of the bulk elastic modulus K of the hydraulic oil is 50.

Under such conditions, the value of the bulk modulus K of the hydraulic oil was estimated, and the results shown in FIGS. 5 to 10 were obtained.

As shown in FIG. 5, the estimated value of the volume elastic modulus K of the hydraulic oil changes from the initial value (500 MPa) to near the true value (1500 MPa) within 0.1 second after the estimation is started. This indicates that these values can be estimated even though the bulk modulus K of the hydraulic fluid and the cylinder speed are not directly measured.

Moreover, FIG. 5 also shows that the estimated value can follow the time change of the true value shown by the thick solid line, which is not considered in the estimated model. This indicates that a practical estimation can be realized by appropriately setting the variance-covariance matrix Q of the noise vector v even if the state equation contains a modeling error.

Further, in the present embodiment, the reliability of the estimation can be evaluated by using the standard deviation of the estimated value as an index. The standard deviations of the estimated values shown in FIG. 5 change from moment to moment according to the state of the oil flow, and can be used as a quantitative index when designing a controller taking into account the estimation error.

Further, as shown in FIG. 6 to FIG. 10, by setting the variance-covariance matrix R of the noise vector w appropriately, not only estimation of the value of the bulk elastic modulus K of the hydraulic oil but also the measurement value containing noise It is possible to estimate the true value of the state vector x from.

[Application Example of First Embodiment]
In the first embodiment, an Unscented Kalman filter is used as a state estimation method based on Bayesian estimation. However, for example, a linear Kalman filter, an extended Kalman filter, a particle filter, an ensemble Kalman filter, or the like may be used. In the case of using a linear Kalman filter, the state equation must be linear. For example, in the case of a hydraulic system having a limited operating range, a nonlinear state equation is approximated to a linear state equation within that range. Thus, a linear Kalman filter can be applied. In addition, under a limited assumption, for example, assuming that the flow of hydraulic oil is laminar flow, or assuming that a hydraulic motor is used instead of a hydraulic cylinder, it is possible to linearly represent a state equation of a hydraulic system it can.

When the estimation target parameter dynamically changes, known characteristics of the estimation target parameter may be reflected in the state equation. For example, the bulk modulus K of hydraulic fluid is proportional to the pressure under isothermal conditions, so this may be reflected in the equation of state.

The equation of state may be derived not by first principle modeling but by black box modeling, and the coefficients thereof may be estimated.

The estimated value obtained by the parameter estimation method of the hydraulic system according to the first embodiment may be used for control of the hydraulic system, or may be used to control the hydraulic system by presenting it to the operator of the hydraulic system. It may be provided for support and / or guidance.

A parameter estimation method of a hydraulic system according to a second embodiment of the present invention will be described with reference to FIG. FIG. 11 is a flowchart showing a method of estimating a parameter of a hydraulic system according to the second embodiment.

The parameter estimation method of the hydraulic system according to the second embodiment uses the successive estimation method instead of the state estimation method based on Bayesian estimation used in the parameter estimation method of the hydraulic system according to the first embodiment. It differs from the method according to the first embodiment in that the point and the state vector may include only the estimation target parameter.

The parameter estimation method for a hydraulic system according to the second embodiment comprises the steps of setting a first equation indicating the dynamic characteristic of the hydraulic system (step S20), and a second equation using a state vector including a parameter to be estimated. The step of deriving from one equation (step S21) and the sequential estimation method are applied to the second equation to estimate the values of the respective elements constituting the state vector, and thereby the values contained in the state vector And S (step S22) of estimating the value of the estimation target parameter.

Here, since the process of step S20 is the same as the process of step S10 in the first embodiment, the detailed description thereof is omitted. Details of steps S21 and S22 will be described later.

The parameter estimation method of the hydraulic system according to the second embodiment is similar to the parameter estimation method of the hydraulic system according to the first embodiment, for example, in the volume modulus K of the hydraulic oil of the hydraulic system 10 shown in FIG. It is applied to the hydraulic system 10 in order to estimate the value. The hydraulic system to which the parameter estimation method of the hydraulic system according to the second embodiment is applied is not limited to the hydraulic system 10 shown in FIG. Moreover, the estimation object parameter estimated by the parameter estimation method of the hydraulic system according to the second embodiment is not limited to the bulk modulus K of the hydraulic oil of the hydraulic system 10.

The successive estimation method is not particularly limited as long as the estimated value at each time step can be derived as a function of the estimated value at the previous time step. The successive estimation method includes a successive least squares method and a Kalman filter. The computational cost can be reduced by applying the successive estimation method.

Table 2 shows a combination of the sequential estimation method adopted in the present embodiment and the estimation target parameter. For example, the aspect which concerns on the combination of (1) shows the case where the value of the volume modulus K of hydraulic fluid is estimated by the successive least squares method.

Hereinafter, an aspect according to the combination of (1) to (8) shown in Table 2 will be described. In addition, since the blank in Table 2 can be implemented by applying the sequential estimation method demonstrated in the aspect which concerns on the other combination, it has only shown that the detailed description is abbreviate | omitted, and implementation It does not mean that it is impossible. For example, even if applying the successive least squares method with a frequency filter described in the aspect according to the combination of (5), it is possible to estimate the value of the bulk modulus K of the hydraulic oil.

In addition, in the following, estimation results of aspects according to the combination of (1) to (8) shown in Table 2 will be described. The conditions used for estimation are the same as the conditions in the first embodiment, that is, those shown in Table 1 and FIGS. 3 and 4, and thus detailed description thereof will be omitted.

About the aspect which concerns on the combination of (1) First, the case where the value of the volume elastic modulus K of hydraulic fluid is estimated by a successive least squares method is demonstrated.

In this case, of the equations representing the dynamic characteristics of the hydraulic system 10 in step S21, the equations for the derivatives of the pressures P _p , P _h and P _r are compared to the bulk modulus K of the hydraulic oil as the estimation target parameter Discretize in a linear fashion.

First, the right side of the equation for the derivative of P _p , P _h and P _r is explicitly expressed as the product of K and the other terms a _p , a _h and a _r as follows.

When the left side of these expressions, that is, the derivatives of P _p , P _h and P _r are subjected to difference approximation with time division Δt, the following is obtained.

Here, k represents a time step discretized by the time interval Δt. Parameters other than K are assumed to be observable.

The sum of squared errors on both sides of the above equation at each time step n is as follows.

K (n) which minimizes such a sum of squared errors is derived by successive least squares method. Thereby, step S22 is performed. In the above equation, the calculation start time step a is a parameter adjusted in accordance with the characteristics of the hydraulic system 10.

FIG. 12 is a graph showing the estimation result of the value of bulk modulus K of hydraulic fluid. FIG. 12 shows that, as time passes, the estimated value of the bulk modulus K approaches the true value, and the accuracy of the estimation is improved. The reason why the estimated value does not coincide with the true value is due to an approximation error caused by differential approximation of the derivatives of Pp, Ph and Pr by the first-order Euler method.

About the aspect which concerns on the combination of (2) Then, the case where the value of the volume modulus K and hydraulic contraction coefficient C of hydraulic fluid is estimated by a successive least squares method is demonstrated.

In this case, in the step S21, among the equations representing the dynamic characteristics of the hydraulic system 10, the equations for the derivatives of P _p , P _h and P _r are linear with respect to K and K C as estimation target parameters It is discretized.

First, among the right sides of the equation for P _p , P _h and P _r differentiated, the terms K and KC are expressed explicitly as follows.

Here, k represents a time step discretized by the time interval Δt.

Assuming that the vector on the left side is y _LS (k), the vector on the right side is x _LS , and the matrix is A (k), the above equation is as follows.

Here, it is assumed that parameters other than x _LS are observable.

An x _LS (n) that minimizes such a sum of squared errors is derived by successive least squares method. Then, the value of contraction coefficient C is estimated by dividing KC by K. Thereby, step S22 is performed. In the above equation, the calculation start time step a is a parameter adjusted in accordance with the characteristics of the hydraulic system 10.

FIG. 13 is a graph showing the estimation result of the value of bulk modulus K of hydraulic fluid. FIG. 14 is a graph showing the estimation result of the value of the contraction coefficient C. In FIG 13 and FIG 14, the measured value _P _p, P h, not only the estimation result if there is no noise _{P r,} measured value _P _p, P h, even estimation results when there is noise _{P r} It shows. Noise is added to the measured values P _p , P _h and P _r with white noise having a mean of zero and a standard deviation of 0.04 [MPa], and a standard of zero with respect to the measured value x _c and a standard White noise with a deviation of 10 mm is added.

In FIG. 13, as the estimated value of the bulk elastic modulus K of the hydraulic oil approaches the true value shown by the thick broken line as time passes similarly to the case of (1), the accuracy of the estimation is improved Is shown. FIG. 14 shows that the value of the contraction coefficient C is also correctly estimated.

On the other hand, when there is noise in the measurement value, the accuracy of the estimation results of K and C is lowered as shown by the thin broken line. This is because noise contained in the measured values P _p , P _h and P _r passes through a non-linear function (square root) in the equation for the flow rate Q _p , Q _hin , Q _hout , Q _rin , Q _rout and Q _pR The main cause is to create a deviation in the average value of the flow rate. The decrease in the estimation accuracy becomes remarkable as the nonlinearity of the equation indicating the dynamic characteristic of the hydraulic system 10 increases and the magnitude of the noise with respect to the true value of the measurement data increases. This teaches that simply applying the successive least squares method is not preferable for hydraulic systems where the measurements have noise.

About the aspect which concerns on the combination of (3) Then, in order to reduce the fall of the estimation precision by the noise contained in measurement value, the value of the volume modulus K and contraction flow coefficient C of hydraulic fluid by a weighted successive least squares method The case of estimating. In this aspect, the process of step S21 is the same as the aspect according to the combination of (2).

In this aspect, x _LS (n) is derived that minimizes the weighted sum of the squared errors shown in Equation 13 below. Then, the value of contraction coefficient C is estimated by dividing KC by K. Thereby, step S22 is performed.

Here, W (k) is a weighting matrix at time step k, and is set according to known properties such as the reliability of the measurement value. As the magnitude of the noise with respect to the true value of the measurement value increases, the estimation accuracy decreases significantly. Therefore, as the absolute value of the measurement value increases, the weight is increased to increase the reliability of the measurement value. An estimate is made. W (k) is set, for example, as follows.

Here, α _p , α _h and α _r are tuning parameters for adjusting the size of the weight. Note that the setting of W (k) is not limited to this.

FIG. 15 is a graph showing the estimation result of the value of the bulk modulus K of hydraulic fluid. FIG. 16 is a graph showing an estimation result of the value of the contraction coefficient C. FIGS. 15 and 16 show that the estimation accuracy is improved in spite of the fact that the measurement value includes noise, as compared with the cases shown in FIGS. 13 and 14.

About the aspect which concerns on the combination of (4) Then, in order to reduce the fall of the estimation precision by the noise contained in measurement value, the value of the volume elastic modulus K of hydraulic fluid and the contraction flow coefficient C by a weighted successive least squares method The case of estimating. In the aspect which concerns on the combination of (4), weighting matrix W (k) is different compared with the aspect which concerns on the combination of (3). The weight matrix W (k) is set such that the weight decreases as the change in pressure in one time step increases. That is, when the change in pressure is larger than the value assumed for the operation of the hydraulic system 10, the measured value is regarded as noise, and the contribution to the estimation is reduced. The weight matrix W (k) is set, for example, as follows.

Here, α is a tuning parameter for adjusting the assumed change amount. Note that the setting of W (k) is not limited to this.

FIG. 17 is a graph showing the estimation result of the value of bulk modulus K of hydraulic fluid. FIG. 18 is a graph showing an estimation result of the value of the contraction coefficient C. It can be seen that the estimation accuracy is improved compared to FIGS. 13 and 14 despite the fact that the measurement value includes noise.

About the aspect which concerns on the combination of (5) Then, in order to reduce the fall of the estimation precision by the noise contained in measurement value, it is a frequency filter and successive least squares method by the volume elastic modulus K and contraction flow coefficient C of hydraulic fluid. The case of estimating the value will be described.

In this case, among the frequency components of the pressure measurement value, components other than the frequency component assumed as the operation of the hydraulic system 10 are regarded as noise and removed by the filter, and the least squares method is sequentially applied to the measurement value after the filter processing. Applied. The frequency filter used is a moving average filter as follows.

Here, P _filtered is a pressure value after application of a filter, and P is a pressure measurement value (P _p , P _h , P _{r in} this embodiment).

In addition, the frequency filter to be used is not limited to a moving average filter, For example, a linear filter, a Butterworth filter, a Chebyshev filter etc. may be sufficient.

FIG. 19 is a graph showing the estimation result of the value of bulk modulus K of hydraulic fluid. FIG. 20 is a graph showing the estimation result of the value of the contraction coefficient C. 19 and 20 show estimation results using the moving average filter with N = 21 in the above equation. The estimation result indicates that the estimation accuracy is improved as compared to FIGS. 13 and 14 despite the fact that the measurement value includes noise.

About the aspect which concerns on the combination of (6) Then, the aspect which concerns on the combination of (6) is demonstrated. This aspect is a case where the value of the bulk elastic modulus K of the hydraulic fluid is estimated by the Unscented Kalman filter in order to reduce the decrease in estimation accuracy due to the noise contained in the measurement value. The method of estimating the value of the bulk elastic modulus K of the hydraulic oil by this Unscented Kalman filter is the same as that described in the first embodiment, and thus the detailed description thereof is omitted.

According to this method, it is possible to simultaneously estimate the state quantity of the hydraulic system 10 and the value of the estimation target parameter (volume elastic modulus K of the hydraulic fluid), so that it is not necessary to measure all the state quantities of the hydraulic system 10 . In addition, since estimation is performed in consideration of known characteristics such as the magnitude of noise, the estimation accuracy is excellent.

About the aspect which concerns on the combination of (7) Then, the aspect which concerns on the combination of (7) is demonstrated. This aspect estimates the pressure dependency of the bulk modulus K of hydraulic oil based on the successive least squares method.

It is known that the bulk modulus K of hydraulic fluid changes in accordance with the pressure of the hydraulic fluid. For example, in the isothermal and low pressure region, the bulk modulus K of hydraulic fluid can be approximated as a function proportional to pressure as follows.

Here, K ₀ is a bulk modulus at atmospheric pressure, K _p is a proportional coefficient, and P is a gauge pressure (pressure measurement value). K ₀ and K p depend on dynamically changing parameters such as temperature of hydraulic fluid and bubble content of hydraulic fluid. Therefore, it is estimated by the successive estimation method.

In step S21, among the equations representing the dynamic characteristics of the hydraulic system 10, the equations for derivatives of the pressures P _p , P _h and P _r are discretely linear with respect to K ₀ and K _p as estimation target parameters Be

First, among the equations representing the dynamic characteristics of the hydraulic system 10, the above equations are substituted for the equations for the derivatives of P _p , P _h and P _r , and the terms of K ₀ and K _p are If it shows, it becomes as follows.

The left side, that is, the differentials of the pressures P _p , P _h and P _r are subjected to time difference Δt and the difference approximation is as follows.

Here, k represents a time step discretized by the time interval Δt.

Here, it is assumed that parameters other than x _LS are observable.

An x _LS (n) that minimizes such a sum of squared errors is derived by successive least squares method. Thereby, step S22 is performed. In the above equation, the calculation start time step a is a parameter adjusted in accordance with the characteristics of the hydraulic system 10.

FIG. 21 is a graph showing the estimation result of the value of bulk modulus K ₀ at atmospheric pressure. FIG. 22 is a graph showing the estimation result of the value of the proportional coefficient Kp. In FIGS. 21 and 22, the pressure measurement _P _p, P h, not only the estimation result if there is no noise _{P r,} the pressure measurement _P _p, P h, even estimation results when there is noise _{P r} It shows. In the latter case, the pressure measurements _P _p, P h, added white noise average relative _{P r} is the standard deviation at zero is 0.02 [MPa], and that the average relative measurements _{x c} This is the case where white noise with a standard deviation of 10 mm is added at zero.

In FIGS. 21 and 22, while sufficient estimation accuracy is ensured when there is no noise, the accuracy of the estimation results of the values of K ₀ and K _p is reduced when there is noise in the measurement value It is shown that. This teaches that simply applying the successive least squares method in the latter case is not preferred.

About the aspect which concerns on the combination of (8) Then, the aspect which concerns on the combination of (8) is demonstrated. This aspect, like (7), estimates the pressure dependence of the bulk modulus K of hydraulic oil, but an unscented Kalman filter is applied instead of the successive least squares method.

First, in step S21, a state equation and an observation equation of the hydraulic system 10 are set. Specifically, it is as follows.

A hydraulic system 10 is obtained by adding estimated parameters K ₀ and K _p to the state quantities (pressure P _p , pressure P _h , pressure P _r , cylinder position x _c , cylinder speed x _c ⁽¹⁾⁾ of the hydraulic system 10 The ten state vectors x are set as follows.

At this time, the state equation of the hydraulic system 10 is expressed as follows.

In the above equation of state, v における R ^{7 × 1} has an average vector of 0∈R ^{7 × 1} ,
Represents a white noise vector whose variance covariance matrix is QεR ^{7 × 7} .

The time variation _{f Kp} time variation _{f K0} and _{K p} of _{K 0} will be zero.

Further, it is assumed that among the state quantities of the hydraulic system 10, the pressure P _p , the pressure P _h , the pressure P _r and the spool position x _c can be observed by the pressure sensor or the position sensor. At this time, the observation equation of the hydraulic system 10 is expressed as follows.

After the state equation and the observation equation of the hydraulic system 10 are set, in step S22, by applying an Unscented Kalman filter to the state equation, the state quantity of the estimated hydraulic system 10 and the estimation target parameters included in the state vector x The value is estimated.

FIG. 23 is a graph showing the estimation result of the value of bulk modulus K ₀ at atmospheric pressure. Figure 24 is a graph showing estimation results of the value of the proportionality factor K _p. FIGS. 23 and 24 show not only the estimation result when there is no noise in the pressure measurement values P _p , P _h and P _r but also the estimation result when there is noise in the measurement values P _p , P _h and P _r ing. In the latter case, white noise with an average of zero and a standard deviation of 0.02 [MPa] is added to the measured values P _p , P _h and P _r , and the average is zero with respect to the measured value x _c The standard deviation is 10 [mm] when white noise is added.

23 and 24, as compared with the case shown in FIGS. 21 and 22, despite the estimation target parameter K _0, K _p and cylinder speed x _c is not measured directly, and improves estimation accuracy Show that.

The second embodiment can be modified as follows.

In the second embodiment, although the calculation start step a is used as a parameter for adjusting the dependency on the past measurement value, the weight of the past measurement value may be reduced exponentially using a forgetting factor. It may be done.

The second embodiment includes setting a weight according to the absolute value of the measurement value, but instead, excludes the measurement value having an absolute value smaller than a predetermined threshold value from the measurement values used for estimation. May be included.

Although the second embodiment includes approximating the bulk modulus of hydraulic oil as a linear function with respect to pressure, the bulk modulus may be approximated as a non-linear function with respect to pressure.

The second embodiment includes modeling the bulk modulus of hydraulic fluid as a function of pressure, but modeling the bulk modulus as a function of an arbitrary parameter and determining its coefficient is performed. May be For example, the bulk modulus of hydraulic fluid may be modeled as a function of temperature or as a function of temperature and pressure.

For example, a linear Kalman filter, an extended Kalman filter, a particle filter or the like may be used instead of the Unscented Kalman filter used in the second embodiment. When using a linear Kalman filter, the state equation must be linear, but for example, in a hydraulic system with a limited operating range, by approximating a nonlinear state equation within that range to a linear state equation , Linear Kalman filter can be applied. In addition, under a limited assumption, for example, assuming that the flow of hydraulic fluid is laminar flow, or assuming that a hydraulic motor is used instead of a hydraulic cylinder, it is possible to linearly represent the state equation of the hydraulic system it can.

The equation of state may be derived not by first principle modeling but by black box modeling, and its coefficients may be estimated.

The estimated value obtained by the parameter estimation method of the hydraulic system according to the second embodiment can also be used for control of the hydraulic system, or can be presented to the operator of the hydraulic system to operate the hydraulic system by the operator. It can also be provided for support and / or guidance.

As mentioned above, although the embodiment of the present invention has been described in detail, these are merely examples, and the present invention is not construed as being limited in any way by the description of the embodiment described above.

As described above, a method of estimating a physical quantity that affects the dynamic characteristics of a hydraulic system as a parameter is provided, and a method with a wide range of application is provided.

Since the parameter estimation method of the hydraulic system according to the first aspect applies the state estimation method based on Bayesian estimation, even if all the state quantities of the hydraulic system included in the state vector are not observable, the state vector is included in the state vector It is possible to estimate the value of the estimated parameter to be estimated. This makes it possible to extend the application range of the parameter estimation method.

In the parameter estimation method of the hydraulic system according to the first aspect, preferably, the estimation target parameter is a bulk modulus of hydraulic oil in the hydraulic system. This method makes it possible to obtain the bulk modulus of the hydraulic fluid without stopping the operation of the hydraulic system.

In the parameter estimation method for a hydraulic system according to the first aspect, the state equation may be non-linear. In this case, in the step of estimating the estimation target parameter, preferably, the value of the estimation target parameter included in the state vector is estimated by applying a non-linear state estimation method to the state equation. In this aspect, since the value of the estimation target parameter can be estimated even if the state equation is non-linear, the application range of the parameter estimation method can be expanded.

In the parameter estimation method for a hydraulic system according to the first aspect, preferably, the state equation includes a noise term, and in the step of estimating the value of the estimation target parameter, the Kalman filter is applied to the state equation. The value of the estimation target parameter is estimated. This makes it possible to estimate the value of the estimation target parameter in consideration of the influence of noise and the like that the hydraulic system has.

The parameter estimation method of the hydraulic system according to the second aspect makes it possible to suppress an increase in calculation cost when estimating the value of the estimation target parameter by applying the successive estimation method. Thereby, the application range of the parameter estimation method can be expanded.

In the parameter estimation method for a hydraulic system according to the second aspect, preferably, in the step of estimating the value of the estimation target parameter, the state vector is included by applying the least squares method to the second equation one by one. The value of the estimation target parameter is estimated. In this aspect, the estimated value of the estimation target parameter at a certain time step can be derived sequentially (with less computational cost) as a function of the estimation value of the estimation target parameter at the previous time step.

The parameter estimation method for a hydraulic system according to the second aspect preferably further comprises the step of measuring the state quantity of the hydraulic system, and in the step of estimating the value of the estimation target parameter, the measured value of the state quantity In order to reduce an estimation error of the estimation target parameter caused by the included noise, the measurement value of the state quantity is corrected when the successive least squares method is applied to the second equation. As described above, the estimation accuracy of the estimation target parameter can be improved by estimating the value of the estimation target parameter using the corrected measurement value of the state quantity.

In the parameter estimation method for a hydraulic system according to the second aspect, in the step of estimating the value of the estimation target parameter, the weight of the state quantity is increased as the absolute value of the measurement value of the state quantity is larger. The measured values may be corrected. This correction makes it possible to adjust the influence of the measurement of the state quantity on the estimation error of the estimation target parameter according to the magnitude of the absolute value of the measurement of the state quantity, whereby the value of the estimation target parameter is obtained. The estimation accuracy of can be improved.

In the parameter estimation method for a hydraulic system according to the second aspect, in the step of estimating the value of the estimation target parameter, the weight of the state quantity is decreased as the change amount of the measurement value of the state quantity increases. The measured values may be corrected. This correction makes it possible to adjust the influence of the measured value of the state quantity on the estimation error of the estimation target parameter according to the magnitude of the change amount of the measured value of the state quantity, thereby estimating the estimation target parameter Accuracy can be improved.

In the parameter estimation method of the hydraulic system according to the second aspect, in the step of estimating the value of the estimation target parameter, the measured value of the state quantity may be corrected by removing the noise with a filter. The filter removal of the noise contained in the measured value of the state quantity makes it possible to improve the estimation accuracy of the value of the estimation target parameter.

In the parameter estimation method for a hydraulic system according to the second aspect, preferably, the second equation includes a noise term, and in the step of estimating the value of the estimation target parameter, a Kalman filter is applied to the second equation. The value of the estimation target parameter included in the state vector is estimated. This makes it possible to estimate the value of the estimation target parameter in consideration of the influence of noise and the like that the hydraulic system has.

In the parameter estimation method of the hydraulic system according to the second aspect, preferably, the estimation target parameter is a bulk modulus of hydraulic oil in the hydraulic system. This method makes it possible to obtain the bulk modulus of the hydraulic fluid without stopping the operation of the hydraulic system.

In the parameter estimation method of the hydraulic system according to the second aspect, preferably, the estimation target parameter is a bulk modulus and a contraction flow coefficient of hydraulic oil in the hydraulic system. According to this method, it is possible to estimate not only the value of the bulk modulus of the hydraulic oil but also the value of the contraction coefficient.

In the parameter estimation method for a hydraulic system according to the second aspect, preferably, the estimation target parameter indicates the pressure dependency of the bulk modulus of the hydraulic oil in the hydraulic system. According to this method, it is possible to estimate the degree to which the bulk modulus of hydraulic fluid depends on the pressure of hydraulic fluid.

Claims

A parameter estimation method for a hydraulic system, which selects a physical quantity affecting dynamic characteristics of a hydraulic system as an estimation target parameter and estimates a value of the estimation target parameter,
Setting the state vector by selecting the state amount of the state vector including the state amount of the hydraulic system and the estimation target parameter, and the estimation target parameter;
Setting a state equation of the hydraulic system using the set state vector;
Estimating the value of the estimation target parameter included in the state vector by applying a state estimation method based on Bayesian estimation to the state equation.
The method of estimating a parameter of a hydraulic system according to claim 1, wherein the estimation target parameter is a bulk modulus of hydraulic oil in the hydraulic system.
The parameter estimation method for a hydraulic system according to claim 1 or 2, wherein the state equation is non-linear, and in the step of estimating the value of the estimation target parameter, a non-linear state estimation method is applied to the state equation. The parameter estimation method of a hydraulic system by which the value of the said estimation object parameter contained in the said state vector is estimated.
The method of estimating a parameter of a hydraulic system according to claim 1 or 2, wherein the state equation includes a noise term, and in the step of estimating the value of the estimation target parameter, a Kalman filter is applied to the state equation. A parameter estimation method of a hydraulic system, wherein a value of the estimation target parameter included in the state vector is estimated.
A parameter estimation method for a hydraulic system, which selects a physical quantity affecting dynamic characteristics of a hydraulic system as an estimation target parameter and estimates a value of the estimation target parameter,
Deriving a first equation indicative of the dynamic characteristics of the hydraulic system;
Deriving a second equation using a state vector including the estimation target parameter from the first equation;
Estimating a value of the estimation target parameter included in the state vector by applying a successive estimation method to the second equation.
The method of estimating a parameter of a hydraulic system according to claim 5, wherein in the step of estimating the value of the estimation target parameter, the value of the estimation target parameter is obtained by applying the least squares method to the second equation one by one. Method of estimating parameters of hydraulic system estimated.
The method of estimating a parameter of a hydraulic system according to claim 6, further comprising the step of measuring a state amount of the hydraulic system, wherein the step of estimating the value of the estimation target parameter includes the measured value of the state amount. A parameter estimation method of a hydraulic system, wherein the measured value of the state quantity is corrected when applying the successive least squares method to the state equation in order to reduce an estimation error of the estimation target parameter caused by noise.
The method of estimating a parameter of a hydraulic system according to claim 7, wherein in the step of estimating the value of the estimation target parameter, the state is such that the weight is increased as the absolute value of the measured value of the state quantity is larger. Method of estimating parameters of a hydraulic system, wherein the measurement of quantity is corrected.
The method of estimating a parameter of a hydraulic system according to claim 7, wherein in the step of estimating the value of the estimation target parameter, the state is such that the weight decreases as the amount of change of the measured value of the state amount increases. Method of estimating parameters of a hydraulic system, wherein the measurement of quantity is corrected.
The hydraulic system parameter estimation method according to claim 7, wherein in the step of estimating the value of the estimation target parameter, the measured value of the state quantity is corrected by removing the noise with a filter. Parameter estimation method of the system.
The method of estimating a parameter of a hydraulic system according to claim 5, wherein the second equation includes a noise term, and in the step of estimating the value of the estimation target parameter, a Kalman filter is applied to the second equation. A parameter estimation method of a hydraulic system, wherein a value of the estimation target parameter included in the state vector is estimated.
The method of estimating a parameter of a hydraulic system according to any one of claims 5 to 11, wherein the estimation target parameter is a bulk modulus of hydraulic oil in the hydraulic system.
The parameter estimation method of a hydraulic system according to any one of claims 5 to 11, wherein the estimation target parameter is a bulk modulus and a contraction coefficient of hydraulic oil in the hydraulic system. Estimation method.
The parameter estimation method for a hydraulic system according to any one of claims 5 to 11, wherein the estimation target parameter indicates the pressure dependency of the bulk modulus of hydraulic fluid in the hydraulic system. Parameter estimation method of the system.