JP7138936B2 - A method for creating a model-based lookup table for estimating the control flow rate of a hydraulic system, a model-based lookup table for estimating the control flow rate, and a method for estimating pressure - Google Patents

Description

Article 30, Paragraph 2 of the Patent Act applies Publisher name: The Society of Instrument and Control Engineers, Control Division Publication name: The 5th Society of Instrument and Control Engineers, Control Division Multi-Symposium Catalog No. 18SY0003 Publication date: March 2018 8 days

The present invention relates to a hydraulic system used for agricultural machinery and the like. More specifically, in a hydraulic device having a spool-type hydraulic control valve that controls the supply of hydraulic pressure to a double-acting piston type hydraulic cylinder, the cap of the hydraulic cylinder is obtained from the spool displacement of the hydraulic control valve and the pressure on the cap side of the hydraulic cylinder. The present invention relates to a method for estimating the control flow rate of hydraulic oil flowing into the side and the rod side, and a method for estimating the cap side pressure and the rod side pressure.

Hydraulic devices used for drive control of agricultural machinery, BigDog (Non-Patent Document 1), unmanned construction machinery, vibrating devices, etc., have not only a higher output-to-load ratio than electric devices, but also vertical movement without consuming energy. It is possible to maintain a stationary posture. For this reason, hydraulic systems are widely used as working machines in fields such as construction, rescue, landmine removal, and agriculture, and further advanced automation is strongly desired. However, hydraulic systems are complex nonlinear systems governed not only by equations of motion, but also by continuity equations. In particular, the flow element is known as a multi-input nonlinear system and is more difficult to model than the electric arm.

Conventional modeling of hydraulic systems is basically based on Bernoulli's equation. That is, in hydraulic systems, many flow elements are modeled as square functions of pressure and linear functions of spool displacement using the usual Bernoulli equation (2, 3, 4). Bernoulli's equation assumes a steady flow, and is based on the premise that the supply and discharge of hydraulic fluid in the hydraulic system is a steady flow, and cannot model the unsteady flow elements that actually exist in the hydraulic system.

For example, in the hydraulic system shown in FIG. 1, which is the object of the present invention, the cap-side pressure p ₊ for the sinusoidal input (spool displacement u) as shown in FIGS. When measured by a sensor (curves shown as "Sensor" in FIGS. 12(e) and (f)) and when the cap-side pressure is calculated from the cap-side flow rate by Bernoulli's equation (FIGS. 12(e) and (f) As can be seen from the comparison with the curve shown as "Bernoulli" in (1), there is an operating region that greatly deviates from the actual pressure fluctuation. Therefore, in the control system of the hydraulic system, it is necessary to perform pressure control with high precision using the measured value of the pressure sensor. .

Therefore, unsteady flow elements are often expressed using a lookup table defined only from input/output measurement values (including flow rate sensor values) without using a physical model (including continuity equations). On-line estimation of hydraulic cylinder pressure because the lookup table does not require a steady flow assumption and is implemented as an array instead of a function (with if statements, switch statements) in multidimensional piecewise affine systems etc. Therefore, the computer load is relatively low. However, there is a strong trade-off between the measurement accuracy and measurement range of the flow rate, which is the output of the unsteady flow element, and it becomes a serious problem when it is difficult to define the lookup table with a single flowmeter. Inadequate is a serious problem. Furthermore, at present, the optimal method for reducing the dimensionality of the lookup table for reducing the load on the computer is also unknown.

Prior art documents referred to in this specification are listed below.

Marc Raibert, Kevin Blankespoor, Gabriel Nelson, Rob Playter and the BigDog Team: BigDog, the Rough-Terrain Quadruped Robot, Proc. IFAC World Congress, pp.10822-10825 (2008) H. Merrit: Hydraulic control systems, Jhon Willey & Sons (1967) Yuzo Maeshima, Satoru Sakai, Minoru Nakanishi, Koichi Osuga: Basic Parameter Identification Method and Model Verification of Hydraulic Arm, Transactions of the Japan Fluid Power System Society, Vol.43, No.1, pp.16-21 (2012) Yuzo Maeshima, Satoru Sakai: Parameter Identification and Model Verification of a Vertical Articulated Hydraulic Manipulator, Transactions of the Society of Instrument and Control Engineers, Vol.50, No.1, pp.91-100 (2014) D. Luenberger: Optimization by vector space method, Wiley interscience (1968) A. Kugi and W. kemmetmuller. Newenergy-based nonlinear controller for hydraulic piston actuators. European Journal of Control, 10(2), pages 163-173, 2004. J. L. Walsh: A closed set of normal orthogonal functions. American Journal of Mathmatics, 45(1), pages 5-524, 1923. Yusuke Fujimoto, Ichiro Maruta, Toshiharu Sugie, Simplification of Nonparametric Piecewise Affine Models Based on l1 Optimization, Transactions of the Institute of Systems, Control and Information Engineers, 27(4), pages 141-149, 2014. Ichiro Maruta, Henrik: Compression Based Identification of PWA Systems, Proc. of IFAC 2014, pages 4985-4992, 2014. Satoru Sakai, Yusuke Nabana: Optimal Non-Bernoulli modeling method for experimental hydraulic robots, In Proc. of IROS 2016, pages 2954-2959, 2016. Lars E. Bengtsson: Lookup Table Optimization for Sensor Linearization in Small Embedded System, Journal of Sensor Technology, 2, pages 177-184, 2012. S. Sakai and S. Stramigioli: Passivity force control of hydraulic robots. In Proc. of IFAC symposium on Robot Control, pages 20-25, 2009. Takao Nishiumi: Basics of Painting ``Hydraulics'', Nikkan Kogyo Shimbun, 2012. L. Ljung, System Identification: Theory for the User. Prentice-Hall, second edition, 1999.

There is a high demand for low cost working machines used in fields such as construction and agriculture. For this purpose, it is necessary to realize the drive control system of the hydraulic system of the work machine by using as few sensors as possible, and also to construct a control system that can be implemented easily with less load on the CPU of the computer from a practical point of view. desired.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method for estimating the control flow rate of a hydraulic system, which can accurately estimate the control flow rate supplied to the hydraulic cylinder from the hydraulic control valve in the hydraulic system, and which can be easily installed in an actual machine. to propose a lookup table for

Another object of the present invention is to propose a pressure estimation method for a hydraulic system capable of accurately estimating the pressure acting on the hydraulic cylinder of the hydraulic system using this new lookup table for estimating the control flow rate.

The method of creating a lookup table for estimating the control flow rate of the present invention includes:
In a hydraulic system having a spool-type hydraulic control valve for controlling the supply of hydraulic pressure to a double-acting piston-type hydraulic cylinder, the cap of the hydraulic cylinder is determined from the displacement of the spool of the hydraulic control valve and the cap-side pressure and rod-side pressure of the hydraulic cylinder. Used to estimate the cap-side flow rate and rod-side flow rate of hydraulic oil flowing into the side hydraulic chamber and the rod-side hydraulic chamber, respectively,
In step 1, a nonlinear nominal model that defines the hydraulic system is set, and the measured values of the input and output of the hydraulic system that do not include the flow rate are processed offline to estimate the cap side flow rate based on the estimated value by the nonlinear nominal model. Obtain the rod side flow rate matrix for estimating the cap side flow rate matrix and the rod side flow rate for
In step 2, each of the cap-side flow rate matrix and the rod-side flow rate matrix obtained in step 1 is reduced in dimension based on Hilbert's projection theorem, and the cap-side optimum flow rate matrix used as a model-based lookup table for estimating the control flow rate. and the optimum flow rate matrix on the rod side.

Thus, the lookup table created by the method of the present invention is characterized in that it is model-based, unlike a normal lookup table. That is, if the conventional modeling and identification by Bernoulli's equation and continuity equation is white-box modeling, and the conventional look-up table is black-box modeling, the method of the present invention is gray-box modeling using continuity equation and look-up table. can be expressed as From this point of view, the lookup table created by the method of the present invention is hereinafter referred to as a model-based lookup table for estimating the control flow rate.

According to the verification experiments by the present inventors including comparison with the conventional method using Bernoulli's equation, the unsteady flow rate element (cap side control flow rate, rod side control flow rate) was confirmed.

Further, the method for estimating the pressure of the hydraulic system of the present invention uses the model-based lookup table for estimating the control flow rate provided with the above-mentioned cap-side optimum flow rate matrix and rod-side optimum flow rate matrix to obtain the cap-side pressure of the hydraulic cylinder and The rod side pressure is estimated,
a flow rate estimation step of searching and outputting a cap side flow rate and a rod side flow rate from a model-based lookup table for control flow rate estimation using the spool displacement of the hydraulic control valve and the cap side pressure and rod side pressure of the hydraulic cylinder; ,
Cap-side pressure a pressure change rate calculation step of calculating and outputting the change rate and the rod side pressure change rate;
an estimated pressure calculation step of integrating the calculated cap-side pressure change rate and rod-side pressure change rate, respectively, to calculate and output an estimated cap-side pressure and an estimated rod-side pressure,
In the above flow rate estimation step, the value measured by the position sensor is used as the spool displacement value, and the cap side pressure and rod side pressure values used for the search output of the initial cap side flow rate and rod side flow rate are determined in advance. Using an arbitrary initial value, the previous estimated cap side pressure obtained in the estimated pressure calculation step and the estimated Rod side pressure is used.

According to the verification experiment by the present inventors through online estimation using a model-based lookup table for estimating the control flow rate, based on the spool displacement, which is the input value of the hydraulic system, the cap side pressure and rod side pressure It was confirmed that it is possible to construct a control mechanism capable of estimating the pressure and accurately driving and controlling the hydraulic system without using a pressure sensor.

If there is no problem with the computer load, instead of using the cap-side optimum flow rate matrix and the rod-side optimum flow rate matrix as the model-based lookup table for estimating the control flow rate, the stage before reducing these It is also possible to use the cap-side flow rate matrix and the rod-side flow rate matrix obtained in .

1 is a configuration diagram showing a one-degree-of-freedom hydraulic system to which the present invention is applied, and a schematic block diagram showing a pressure estimation observer function; FIG. It is explanatory drawing which shows STEP1 of the optimal flow matrix identification method. It is explanatory drawing which shows STEP2 of the optimal flow matrix identification method. It is explanatory drawing which shows the experimental machine used for the identification experiment of the optimal flow matrix. It is a block diagram which shows the flow of the signal of an experimental machine. It is a graph which shows an example of the experimental result of CaseA. It is explanatory drawing which shows an example of the unsteady flow rate element of the identified cap side flow rate matrix. It is explanatory drawing which shows an example of the unsteady flow element of the identified rod side flow matrix. FIG. 10 is an explanatory diagram showing unsteady flow rate elements of a cap-side flow rate matrix calculated from a conventional method using Bernoulli's equation; FIG. 5 is an explanatory diagram showing unsteady flow rate elements of a rod-side flow rate matrix calculated from a conventional method using Bernoulli's equation; Fig. 10 is a graph showing cap side pressure and rod side pressure at input Aon = 2.0 V, f = {0.5, 5.0} Hz; 5 is a graph showing estimated values of flow rate by the proposed method and the conventional method, respectively; FIG. 10 is a graph showing verification results of a low frequency of 0.5 Hz used for identification; FIG. FIG. 5 is a graph showing verification results for a high frequency of 5.0 Hz that was not used for identification; FIG.

A method of creating a model-based lookup table for estimating the control flow rate of a hydraulic system to which the present invention is applied and a method of estimating pressure will be described below with reference to the drawings.

<Configuration example of hydraulic system>
FIG. 1(a) is a configuration diagram showing a one-degree-of-freedom hydraulic system according to an embodiment, and FIG. 1(b) is a schematic block diagram showing its pressure estimation observer function. The hydraulic device 1 includes a double-acting piston type hydraulic cylinder 2, a spool type hydraulic control valve 3 for driving the hydraulic cylinder 2, and a control device 4 mainly composed of a computer. The position (spool position u) of the spool 5 of the hydraulic control valve 3 is controlled (the valve opening degree is controlled) based on command input by hydraulic pressure supplied from a hydraulic source (not shown) or driving force by an electromagnetic solenoid. , the cap-side hydraulic chamber 6 and the rod-side hydraulic chamber 7 of the hydraulic cylinder 2 are controlled to move the piston 8 connected to the load side. The spool displacement u is provided as an input for control and the piston displacement is detected by a position sensor 9 attached to the piston.

A control device 4 to which the present invention is applied has a pressure estimation observer function 10 in which a model-based lookup table LUT for control flow rate estimation is implemented. The pressure estimation observer function 10 is based on the estimated control flow rate (cap side flow rate, rod side flow rate) retrieved and output from the model-based lookup table LUT for control flow rate estimation and the piston displacement measured by the position sensor 9. The cap-side pressure and rod-side pressure of the hydraulic control valve 3 are estimated. The control device 4 controls the spool displacement (valve opening) of the hydraulic control valve 3 based on the estimated cap-side pressure and rod-side pressure, thereby controlling the drive of the hydraulic cylinder 2 .

In FIG. 1, the subscripts + and - denote the cap side and the rod side, respectively. The origin of the piston displacement s is the midpoint of the stroke, the origin of the spool displacement u is the normal position, and the pressure p _± and the supply pressure P are origins of the atmospheric pressure. The symbols and subscripts used in this specification are shown below.

<Non-linear nominal model of hydraulic system>
A non-linear nominal model of the hydraulic mechanism composed of the hydraulic cylinders 2 and the hydraulic control valves 3 of the hydraulic system 1 is represented by the following (Equation 1) (see Non-Patent Documents 9 and 10).

The cap-side cylinder volume and the rod-side cylinder volume are defined by the following equations.

Conventionally, the cap-side flow rate Q ₊ (p ₊ , u) and the rod-side flow rate Q ₋ (p ₋ , u), which are the input flow rates, are the flow rates that pass through the spool opening, and Bernoulli's equation is used. is approximated by the following equation.

<Optimal matrix identification method: creation of model-based lookup table for control flow rate estimation>
A model-based lookup table LUT for estimating the control flow rate mounted in the control device 4 is defined by an optimum matrix in which the unsteady flow rate element (cap-side flow rate, rod-side flow rate) is one point on the matrix space. The optimal identification method for finding the optimal matrix according to the present invention consists of two steps (STEP1 and STEP2).

2A and 2B are conceptual diagrams showing the processing contents in STEP1 and STEP2. In step 1 (STEP1), the hydraulic system 1 is driven, the input and output that do not include the control flow rate (cap side flow rate, rod side flow rate) are measured, and the obtained measured values are processed offline to obtain a nonlinear nominal model Identify the flow rate matrix (cap side flow rate matrix, rod side flow rate matrix) from the estimated value by In step 2 (STEP 2), Hilbert's projection theorem (see Non-Patent Literature 9) is applied to optimally reduce the dimension of a rational flow matrix that does not require trial and error to obtain an optimal flow matrix. A model-based lookup table LUT for control flow rate estimation is defined by the calculated optimum flow rate matrix (cap-side optimum flow rate matrix, rod-side optimum flow rate matrix).

(STEP1)
The second equation (1-1) and the third equation (1-2) of (Equation 1), which are the nonlinear nominal models of the hydraulic mechanisms (2, 3), are replaced with the flow rate elements Q ₊ (p ₊ , u), Q ₋ Arranging (p ₋ , u) yields the following (formula 2-1) and (formula 2-2).

Using the right sides of (Equation 2-1) and (Equation 2-2), the flow rate on the left side can be calculated from the time derivative of the cap pressure, the time derivative of the rod pressure, and the piston velocity. (Equation 2-1) and (Equation 2-2) are continuous equations and do not assume a steady flow unlike Bernoulli's equation. Based on (Equation 2-1) and (Equation 2-2), the flow rate matrix is defined by the following (Equation 3-1) and (Equation 3-2) from the estimated value by the nonlinear nominal model.

The time derivative of the cap-side pressure p ₊ and the rod-side pressure p ₋ and the piston speed cannot be measured, but can be sufficiently estimated by off-line processing. Also, the bulk elastic modulus b ₊ and b ₋ including the effect of pipe elasticity, which is generally unknown, can be identified by the parameter identification method proposed in Non-Patent Document 2, for example. Based on this, the measured values of the input and output were processed offline to estimate the time derivative of the cap side pressure p ₊ , the time derivative of the rod side pressure p ₋ , and the piston speed. Also, the bulk modulus was identified by a known parameter identification method. Then, from the nonlinear nominal model, the m×n flow rate matrix defined by the above (Equation 3-1) and (Equation 3-2) was obtained. A flow matrix can be imaged as a pattern of pixels (nonlinear flow elements) with different hues, brightnesses, and saturations. Note that FIGS. 2A and 2B show a 4 (=m)×4 (=n) flow rate matrix. Also, in FIGS. 2A, 2B and FIGS. 6 to 9 described later, color pixels representing each nonlinear flow element are displayed in gray scale for convenience.

(STEP2)
In STEP 2, the calculated m×n flow rate matrix was optimally reduced in dimension to obtain an optimum flow rate matrix of a practical size suitable for mounting on an actual machine. The low-order matrix of the flow rate matrix is represented by the following (formula 4-1) and (formula 4-2) from Hilbert's projection theorem, and uniquely exists.

Here, Walsh bases rearranged in ascending order of spatial resolution (see Non-Patent Document 11) are used as orthonormal bases. The order reduction matrix of the flow rate matrix is an optimal matrix that minimizes the order reduction error, which is the distance on the matrix space. The order reduction error is expressed by the following equation.

Finally, the unsteady flow rate elements of the optimum flow rate matrix are defined by the following (Formula 5-1) and (Formula 5-2). where [x] is the floor function of x.

<Identification experiment>
An identification experiment for the optimum flow rate matrix (model-based lookup table for estimating control flow rate) created as described above was performed as follows.

(1) Experimental method Fig. 3 shows the appearance of the experimental machine, and Fig. 4 shows the signal flow of the experimental machine. The experimental machine consists of the following components.
Hydraulic unit: Daikin Industries, NDR-81-071H-30,
Discharge flow rate 0.195×10 ⁻³ m ³ /s
Pump supply pressure P=7.0×10 ⁶ (Pa)
Hydraulic piping: Yokohama Rubber, NWP70-6, 1/4 inch inner diameter
Base plate: Yuken Kogyo, MMC-03-T-2-21
Manifold: Yuken Kogyo, DSGM-03-4009
Control valve: Yuken Kogyo, LSVG-01EH-20-WC-A1-10, zero wrap type,
Rated flow rate 1/3×10 ⁻³ m ³ /s,
Maximum stroke 1.0×10 ^-3 (m)
Flowmeter: Nippon Flow Control, VS01GPO,
Measurement range 1/6×10 ^-6 -1/6×10 ^-3 m ³ /s)
Hydraulic cylinder: JPN, KW-1CA30×75,
Maximum stroke L = 7.5 x 10 ^-3 (m)
Hydraulic oil: ISO VG32, density 860 (kg/m ³ ) (15°C)
Oil filter: Taisei Kogyo, UM-03-20U-1V

In order to obtain a sufficient estimated value, identification was made under two conditions with different rod piping volumes, namely, the condition where the rod flowmeter was attached (Case A below) and the condition where the rod flowmeter was removed (Case B below). The input is a command voltage, from a computer (EPSON, LX7700, online Linux (registered trademark), 2.53 GHz, measurement cycle 1 ms, physical memory 240 MB), via a DA converter (Interface, PCI-3325, 12 bits) applied to the control valve.

Input for Case A and input for Case B were as follows.

Output u is the differential transformer inside the control valve (0.5×10 ⁻³ m/10V), output p _± is the pressure sensor (Keyence, AP-15S), output s is the potentiometer (Midori Instruments, LP-100F- C) and stored in a computer via an AD converter (Interface, PCI-3155, 16bit).

Also, the time-differentiated values of the piston velocity and pressure, which are not directly measured, are estimated off-line from the piston displacement pressure through a five-point approximation formula and a 51st-order central moving average filter, respectively. Oil temperature (30±2° C.) is measured by a thermocouple (Nihon Densoku, TN1-3.2-10-EXA4M).

Table 1 shows the parameters used in STEP1. However, the bulk elastic modulus is identified by the parameter identification method described in Non-Patent Documents 2 and 3. The order of the flow rate matrix is n×m=128×128=16384. The truncation number of the orthonormal basis in STEP 2 was l=64×64=4096.

(Table 1)

(2) Results and Consideration FIG. 5 shows the experimental results of Case A at Aon=2.0V, f=0.5+(4.0−0.5)/35·tHz as an example. Distortion of pressure waveform and asymmetry of piston displacement were observed. It is confirmed that the hydraulic arm is a complex nonlinear system governed not only by the equation of motion but also by the continuity equation.

Table 2 shows the minimum values and ranges of the cap pressure, rod pressure, and spool displacement calculated from the experimental results (obtained by off-line processing). Both the pressure waveform and the piston displacement do not reach the upper and lower limits, and it is considered that the saturation factor can be ignored.

(Table 2)

6 and 7 show unsteady flow rate elements of the cap-side flow rate matrix and the rod-side flow rate matrix identified as described above. For comparison, FIGS. 8 and 9 show unsteady flow rate elements of the cap-side flow rate matrix and the rod-side flow rate matrix calculated by the conventional method using Bernoulli's equation. When the flow rate gains C ₊ and C ₋ in Bernoulli's equation (Non-Patent Document 3) identified by the parameter identification method of Non-Patent Document 2 are converted into dimensionless flow coefficients α ₊ and α ₋ respectively,
α ₊ =0.62
α ₋ =0.58
, and the difference from the normal flow coefficient of 0.6 to 0.8 (Non-Patent Document 2) was sufficiently small.

From the comparison of FIGS. 6 and 8 and the comparison of FIGS. 7 and 9, the unsteady flow rate element identified by the proposed method according to the present invention is non-linear There was good agreement between the steady-state flow factor and the macroscopic trend (maximum difference between the two is 1.4×10 ⁻⁵ m ³ /s, average difference is 1.5×10 ⁻⁶ m ³ /s). 6 and 7 are considered to be the results of identification experiments based on sufficient estimated values.

FIG. 11 shows estimated values of the flow rate by the proposed method and the conventional method, respectively. In each graph of FIG. 11, the curve indicated as "Proposed" is the estimated value by the proposed method, and the curve indicated as "Bernoulli" is the estimated value by the conventional method. At a high frequency of 3.0 Hz, an outlier was confirmed in the output of the proposed method at 0.4 s. The outliers are around (p ₊ , u)=(3.0×10 ⁶ , 0.075×10 ⁻³ ) in FIG. 10 or (p ₋ , u)=(3.3×10 ⁶ , 0.075×10 ⁻³ ), which is near the zero flow region in FIG. Outliers are thought to have occurred because they reached a difficult-to-measure region (a region with a low frequency of use in the first place).

As mentioned above, unlike the conventional Bernoulli's equation, we proposed a method of identifying the flow rate element and the matrix space to reproduce the unsteady flow. The proposed model according to the present invention was compared with a conventional model using Bernoulli and a flow meter, and the effectiveness of the proposed model and the feasibility of online implementation were verified by online model verification. The feature of the proposed model is that the lookup table is treated as an element of the matrix space and treated as a matrix to provide a functionally unique low-dimensional model. The output of the proposed model is considered to be able to express the flow rate in the transient state, unlike the conventional expression based on Bernoulli. In addition, from the point that nonlinear pressure can be reproduced, it can be applied to nonlinear pressure estimation described below.

<Online Estimation: Construction of Observer for Pressure Estimation>
Next, by comparing the estimated pressure and the measured pressure of the unsteady flow elements identified by the proposed method, online estimation of the cap-side pressure and rod-side pressure using the unsteady flow elements identified above is examined. do.

In general, there is a trade-off between resolution and range in metrology tools. In particular, the trade-off of flowmeters for hydraulic systems is strong, and a single flowmeter rarely satisfies both resolution and range. In fact, part of the popularity of Bernoulli's equation is thought to be the ability to use a pressure gauge instead of a flow meter.

_{Therefore , the pressure} Verify p ₊ , p ₋ . At the same time, these second formula (1-1) and third formula (1-2) are implemented in a computer to evaluate whether online estimation is possible. Unlike Bernoulli's equation, which requires discretization, the proposed model does not require discretization and is directly implemented as an array without using functions such as if statements and switch statements.

(1) Experiment method The experimental machine is the same as Case A. For the unsteady flow element identified by the proposed method shown in FIG. Calculate an estimate of the flow rate by entering the spool displacement u and the pressure p _± at {0.5, 5.0} Hz. Further, the estimated value of the flow rate, the piston displacement s, and the piston speed are substituted into the second equation (1-1) and the third equation (1-2) to estimate the pressures p ₊ and p ₋ online.

Here, the piston velocity is estimated on-line from the piston displacement s through the first-order difference of retraction and a low-pass filter (first-order, 10 Hz). The second equation (1-1) and the third equation (1-2) of (Equation 1) are implemented by bilinear transformation. The pressures p ₊ , p ₋ input to the unsteady flow elements are on-line estimates, and pressure measurements are not used in principle except for initial values.

Similarly, calculate the flow rate estimate by inputting the same measured values of spool displacement u and pressure p _± . Furthermore, the estimated value of the flow rate, the piston displacement s, and the piston speed are substituted into the second equation (1-1) and the third equation (1-2) of (Equation 1) to estimate the pressures p ₊ and p ₋ online. do.

(2) Results and Consideration FIG. 12 shows the verification result of the low frequency of 0.5 Hz used for identification, and FIG. 13 shows the verification result of the high frequency of 5.0 Hz that was not used for identification. 12(a) and 13(a) are spool displacement, FIGS. 12(b) and 13(b) are piston displacement, FIGS. 12(c) and 13(c) are cap side flow rates, and FIG. 12(d) ), FIG. 13(d) shows the rod-side flow rate, FIGS. 12(e) and 13(e) show the cap-side pressure, and FIGS. 12(f) and 13(f) show the rod-side pressure, respectively. In these figures, the curve labeled "Proposed" is the estimated value by the proposed method, the curve labeled "Bernoulli" is the estimated value by the conventional method, and the curve labeled "Sensor" is the measured value. In these figures, by comparing the measured values of the cap side pressure p ₊ and rod side pressure p ₋ in FIG. 10 with the online estimated values of the cap side pressure p ₊ and rod side pressure p ₋ in FIGS. Online estimation was realized without delaying the period. The computer load due to the unsteady flow element by the proposed method is considered to be sufficiently small. Note that the Reynolds number in FIG. 11 was about 350 or less. In a laminar flow, the flow coefficient decreases sharply at a Reynolds number of 100 or less (see Non-Patent Document 2). Therefore, before and after the sign change of the flow rate, near the zero flow region, the Reynolds number of the unsteady flow element actually existing in the hydraulic arm is small, and the flow rate difference is considered to be large.

In FIGS. 12 and 13, before and after the sign change of the flow rate, the conventional method does not model the unsteady flow element that actually exists in the hydraulic system, so the flow rate difference is considered to be large. Before and after the flow rate amplitude peak, in the case of the low frequency of 0.5 Hz, the steady state characteristics of the flow rate became stronger, and it is considered that the difference in the flow rate became smaller from the assumption of the steady flow in the conventional method. Before and after the flow rate amplitude peak, in the case of a high frequency of 3.0 Hz, compared to the steady flow rate characteristic, the influence before and after the sign change of the flow rate does not disappear, so the flow rate difference is considered to be large.

In FIGS. 12 and 13, compared with the pressure estimates of the conventional method, the pressure estimates of the proposed method were sufficiently close to the pressure measurements in terms of amplitude and phase. Especially around 1.0 s, the pressure estimated value and the pressure measurement value of the conventional method were significantly different. Before and after the sign change of the flow rate, because of Bernoulli's equation that assumes a steady flow, the conventional method cannot model the unsteady flow element that actually exists in the hydraulic system, and it is difficult to estimate the pressure.

Table 3 shows the evaluation results of the Fit rate at each frequency.

(Table 3)

In Table 3, the Fit rate for the rod side pressure was higher than the Fit rate for the cap side pressure. This is probably because the amplitude of the rod-side flow rate is smaller than the amplitude of the cap-side flow rate, and the influence before and after the sign change of the flow rate tends to disappear. A high Fit rate was obtained by the proposed method even at high frequencies that were not used for identification, but the cap-side pressure resulted in a negative Fit rate in the conventional method. This is because Bernoulli's equation cannot model the unsteady flow in the conventional method. Also, the Fit rate of the rod side pressure was higher than the Fit rate of the cap side pressure. This is probably because the amplitude of the rod-side flow rate is smaller than the amplitude of the cap-side flow rate.

(Pressure estimation method)
From the above, it was confirmed that the proposed method can be implemented online and is effective as a result of model verification. Based on this result, a pressure estimation observer function (function for estimating cap-side pressure and rod-side pressure) implemented in the control mechanism of the hydraulic system can be constructed as follows.

Referring to FIG. 1, the pressure estimation observer function 10 implemented in the control device 4 composed of a computer estimates the cap-side pressure and the rod-side pressure online through the following steps.
Cap side flow rate Q _{+ (} p _{+ ,} u) and a flow rate estimation step for retrieving and outputting the rod side flow rate Q ₋ (p ₋ , u) From the retrieved cap side flow rate Q ₊ (p ₊ , u) and rod side flow rate Q ₋ (p ₋ , u), Using the piston displacement s of the hydraulic control valve 3 and the time derivative of the piston displacement s, and the previously identified cap-side bulk elastic modulus b ₊ and rod-side bulk elastic modulus b ₋ , the cap-side pressure change rate and the rod-side Pressure change rate calculation step for calculating and outputting pressure change rate Estimation for calculating and outputting estimated cap side pressure and rod side pressure by integrating the calculated cap side pressure change rate and rod side pressure change rate, respectively Pressure calculation step (Below, the formula for calculating the cap side pressure obtained from the second formula (1-1) of (Formula 1) is shown. The calculation of the rod side pressure is the same.)

Here, in the flow rate estimation step, the value measured by the position sensor 9 is used as the value of the spool displacement s. However, in the initial search output of cap side flow rate Q ₊ (p ₊ , u) and rod side flow rate Q ₋ (p ₋ , u), the values of cap side pressure p ₊ and rod side pressure p ₋ are unknown. . Therefore, predetermined arbitrary initial values are used as these values. The values of the cap-side pressure and rod-side pressure used for searching and outputting the cap-side flow rate and rod-side flow rate after the first time use the previous estimated cap-side pressure and estimated rod-side pressure calculated in the estimated pressure calculation step. . The experimental results (estimated pressure) of online estimation shown in FIGS. For example, it was confirmed that the estimated pressure converges toward the actual pressure in a short time even when an arbitrary value is given as the initial value.

In the above description, the model-based lookup table LUT for estimating the control flow rate includes both the cap-side optimum flow rate matrix and the rod-side optimum flow rate matrix. Moreover, in the online estimation method using the model-based lookup table LUT for estimating the control flow rate, both the cap-side pressure and the rod-side pressure are estimated. The present invention is not limited to both flow matrix estimations and both pressure estimations. A model-based lookup table LUT for estimating the control flow rate is provided with one of the optimum cap-side flow rate matrix and the rod-side optimum flow rate matrix, and by online estimation using this, the cap-side pressure and rod-side Of course, it is also possible to estimate one of the pressures, and such cases are also included in the scope of the present invention.

1 Hydraulic device 2 Hydraulic cylinder 3 Hydraulic control valve 4 Control device 5 Spool 6 Cap-side hydraulic chamber 7 Rod-side hydraulic chamber 8 Piston 9 Position sensor 10 Observer function LUT for pressure estimation Model-based lookup table for control flow rate estimation

Claims (5)

In a hydraulic device having a spool type hydraulic control valve for controlling the supply of hydraulic pressure to a double-acting piston type hydraulic cylinder, the hydraulic pressure is calculated from the spool displacement of the hydraulic control valve and the cap side pressure and rod side pressure of the hydraulic cylinder. A method for creating a model-based lookup table for estimating a control flow rate used for estimating a cap-side flow rate and a rod-side flow rate of hydraulic oil flowing into a cap-side hydraulic chamber and a rod-side hydraulic chamber of a cylinder, respectively, comprising:
In step 1, a nonlinear nominal model that defines the hydraulic system is set, and the cap-side flow rate is estimated from the nonlinear nominal model by offline processing the input/output measurement values that do not include the flow rate of the hydraulic system. Obtaining a rod side flow rate matrix for estimating the cap side flow rate matrix and the rod side flow rate for
In step 2, each of the cap-side flow rate matrix and the rod-side flow rate matrix obtained in step 1 is reduced in dimension, and the cap-side optimum flow rate matrix and rod-side used as a model-based lookup table for estimating the control flow rate Find the optimal flow matrix,
In step 1,
The nonlinear nominal model representing the hydraulic system is defined by an input state equation represented by the following (Equation 1),

By driving the hydraulic device, the piston displacement of the hydraulic cylinder with respect to the spool displacement of the hydraulic control valve, the cap-side pressure, and the rod-side pressure are measured at a constant sampling cycle, and the obtained measured values are using offline processing to calculate the time derivative of each of the piston displacement, the cap side pressure and the rod side pressure,
Based on the nonlinear nominal model, the cap side flow rate and the rod side flow rate are represented by flow matrices defined by the following (Equation 3-1) and (Equation 3-2),

Using each measured value obtained by the measurement, the time derivative calculated by the offline processing, and the cap-side bulk modulus and rod-side bulk modulus values identified in advance, the cap-side flow rate matrix and the Identify the rod-side flow matrix,
In step 2,
Based on Hilbert's projection theorem in matrix space, the cap-side optimum flow rate matrix and the rod-side optimum flow rate matrix obtained by reducing the order of the cap-side flow rate matrix and the rod-side flow rate matrix. Using the Walsh function, the following (Formula 4-1) and (Formula 4-2) are defined,

The cap-side flow rate and the rod-side flow rate of the non-linear flow elements in the cap-side optimum flow rate matrix and the rod-side optimum flow rate matrix, respectively, are expressed by the following (Equation 5-1) and (Equation 5-2)

A method for creating a model-based lookup table for estimating the control flow rate of a hydraulic system, characterized by being defined by: In a hydraulic device having a spool type hydraulic control valve for controlling the supply of hydraulic pressure to a double-acting piston type hydraulic cylinder, the spool displacement of the hydraulic control valve and the cap side pressure or the rod side pressure of the hydraulic cylinder A model-based lookup table for control flow rate estimation used to estimate the control flow rate of hydraulic fluid flowing into the cap-side hydraulic chamber or the rod-side hydraulic chamber of the hydraulic cylinder on which the cylinder pressure acts from at least one of the cylinder pressures. and
Optimizing one of the cap-side optimum flow rate matrix for estimating the cap-side flow rate created by the method according to claim 1 and the rod-side optimum flow rate matrix for estimating the rod-side flow rate A model-based lookup table for control flow estimation of a hydraulic system, characterized in that it comprises a flow matrix or an optimum flow matrix of both. Hydraulic spool type for controlling the supply of hydraulic pressure to a double-acting piston type hydraulic cylinder using the model-based lookup table for estimating the control flow rate according to claim 2, which includes the optimum flow rate matrix for the cap side. A hydraulic system pressure estimation method for estimating the cap side pressure of the hydraulic cylinder in a hydraulic system having a control valve,
a flow rate estimation step of searching and outputting the cap-side flow rate from the model-based lookup table for estimating the control flow rate using the spool displacement of the hydraulic control valve and the cap-side pressure of the hydraulic cylinder;
From the retrieved and output cap-side flow rate, the cap-side pressure change rate is calculated and output using the piston displacement of the hydraulic cylinder, the time derivative of the piston displacement, and the cap-side bulk elastic modulus identified in advance. a rate of change calculation step;
and an estimated pressure calculation step of integrating each of the calculated cap-side pressure change rates to calculate and output an estimated cap-side pressure,
In the flow estimation step,
Using a value measured by a position sensor as the value of the spool displacement,
Using an arbitrary predetermined initial value as the value of the cap-side pressure used for initial search output of the cap-side flow rate and the rod-side flow rate,
A pressure estimating method for a hydraulic system, wherein the previous estimated cap-side pressure obtained in the estimated pressure calculating step is used as the value of the cap-side pressure used for retrieval output of the cap-side flow rate after the first time. As the model-based lookup table for estimating the control flow rate according to claim 2, using a table that includes both the cap-side optimum flow rate matrix and the rod-side optimum flow rate matrix,
A hydraulic system pressure estimation method for estimating the cap side pressure and the rod side pressure of a hydraulic cylinder in a hydraulic system having a spool-type hydraulic control valve for controlling the supply of hydraulic pressure to a double-acting piston hydraulic cylinder. hand,
Using the spool displacement of the hydraulic control valve and the cap-side pressure and the rod-side pressure of the hydraulic cylinder, search and output the cap-side flow rate and the rod-side flow rate from the model-based lookup table for estimating the control flow rate. a flow rate estimation step for
Using the piston displacement of the hydraulic cylinder, the time derivative of the piston displacement, and the previously identified cap-side bulk modulus and rod-side bulk modulus, a pressure change rate calculation step of calculating and outputting the cap side pressure change rate and the rod side pressure change rate;
an estimated pressure calculation step of integrating the calculated cap-side pressure change rate and rod-side pressure change rate, respectively, to calculate and output an estimated cap-side pressure and an estimated rod-side pressure,
In the flow estimation step,
Using a value measured by a position sensor as the value of the spool displacement,
Using an arbitrary predetermined initial value as the values of the cap side pressure and the rod side pressure used for the initial search output of the cap side flow rate and the rod side flow rate,
The previous estimated cap side pressure and the estimated A hydraulic system pressure estimation method using rod-side pressure. A hydraulic system pressure estimation method for estimating a cap side pressure and a rod side pressure of a hydraulic cylinder in a hydraulic system having a spool type hydraulic control valve for controlling supply of hydraulic pressure to a double-acting piston hydraulic cylinder, comprising: ,
Using the spool displacement of the hydraulic control valve and the cap-side pressure and rod-side pressure of the hydraulic cylinder, from a model-based lookup table for estimating the control flow rate created in advance, the cap-side hydraulic chamber of the hydraulic cylinder and the a flow rate estimation step of searching and outputting a cap-side flow rate and a rod-side flow rate of hydraulic oil flowing into the rod-side hydraulic chamber;
Using the piston displacement of the hydraulic cylinder, the time derivative of the piston displacement, and the previously identified cap-side bulk modulus and rod-side bulk modulus, a pressure change rate calculation step of calculating and outputting the cap side pressure change rate and the rod side pressure change rate;
an estimated pressure calculation step of integrating the calculated cap-side pressure change rate and rod-side pressure change rate, respectively, to calculate and output an estimated cap-side pressure and an estimated rod-side pressure,
A nonlinear nominal model representing the hydraulic system is defined by an input state equation represented by the following (Equation 1),

By driving the hydraulic device, the piston displacement of the hydraulic cylinder with respect to the spool displacement of the hydraulic control valve, the cap-side pressure, and the rod-side pressure are measured at a constant sampling cycle, and the obtained measured values are using offline processing to calculate the time derivative of each of the piston displacement, the cap side pressure and the rod side pressure,
Based on the nonlinear nominal model, the cap side flow rate and the rod side flow rate are represented by flow matrices defined by the following (Equation 3-1) and (Equation 3-2),

Using each measured value obtained by the measurement, the time derivative calculated by the offline processing, and the cap-side bulk modulus and rod-side bulk modulus values identified in advance, the cap-side flow rate matrix and the Identify the rod-side flow matrix,
A model-based lookup table for estimating the control flow rate is defined by the identified cap-side flow rate matrix and rod-side flow rate matrix,
In the flow estimation step,
Using a value measured by a position sensor as the value of the spool displacement,
Using an arbitrary predetermined initial value as the values of the cap side pressure and the rod side pressure used for the initial search output of the cap side flow rate and the rod side flow rate,
The previous estimated cap side pressure and the estimated A hydraulic system pressure estimation method using rod-side pressure.

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