JP6502063B2 - Electrohydrostatic actuator and parameter estimation method for electrohydrostatic actuator - Google Patents

Description

The present invention relates to an electro-hydrostatic actuator (EHA).

In a robot using a motor, force control is based on controlling the current flowing to the motor. For example, most of conventional robot actuators use a gear reducer, and output torque is obtained by subtracting friction torque from motor torque multiplied by reduction ratio, so output torque control controls current input torque. I was going by. However, in actuality, it is difficult to control the force directly by controlling the motor due to factors such as friction in the transmission system from the motor to the link system and errors in electromagnetic parameters.

The most basic method of robot force control is to measure external force and provide feedback to the current of the motor. In the simple case, an error between the external force and the target value is directly fed back to the motor current, and admittance control or the like for realizing a certain physical phenomenon by control is performed. This has been an effective way to reproduce accurate forces in actuator systems with poor back drivability, such as gearings with high reduction ratios. The same idea has been reported to be effective not only in motor and gear drive systems but also in hydraulic systems using servo valves.

However, the above method is not suitable for a phenomenon including a very high frequency component such as a collision because the control system band determines the limit of the behavior. In order to solve this problem essentially, it is necessary to improve the back drivability.

The present inventors have shown that the electrohydrostatic actuator (EHA) enhances back drivability and enables force sensitive control (Non-patent Document 1). Furthermore, a method was proposed to control the force of the electrohydrostatic actuator (EHA) by controlling the current of the motor (Non-Patent Document 2). However, the controller is complicated and the usable motor drive is limited to one capable of command current input.

Also, an actuator using a spring has been proposed by Pratt et al. (Patent Document 1, Non-patent Document 4), but the delay is large because the output torque is controlled by position control, and the dimension of system dynamics is high and stable. There was a problem in sex.

U.S. Patent No. 5,650,704

Taku Kaminaga, Hirokazu Tanaka, Tomoya Amari, Yamato Niwa, Hidehiko Nakamura, "Development of Power Assist for Statically Active Knee with Assist Control by Increasing Degree Function," Journal of the Robotics Society of Japan, Vol. 29, No. 7, pp 47-56, 2011. Tanaka, H., Kaminaga, H., and Nakamura, Y., “Pressure feedback control based on singular perturbation method of an electro-hydrostatic actuator for an exoskeletal power-assist system,” J. of Robotics and Mechatronics, Vol. 24 , No. 2, pp. 354-362, 2012. Kaminaga, H., Ono, J., Nakashima, Y., and Nakamura, Y., “Development of Backdrivable Hydraulic Joint Mechanism for Knee Joint of Humanoid Robots,” In Proc. Of IEEE Int'l Conf. Robotics and Automations , pp. 1577-1582, 2009. Pratt, G. A. and Williamson, M. M., "Series Elastic Actuators," In Proc. Of IEEE / RSJ Int'l Conf. On Intelligent Robots and Systems, Vol. 1, pp. 399-406, 1995.

In order to improve robot reliability in collaborative work between robots and people and in extreme environments, it is essential to improve robot force controllability. However, in the conventional method, accurate control is difficult due to the method of generating torque and transmission principle, and high speed control is difficult.
The present invention aims to provide an actuator that solves these problems.

The technical means adopted by the present invention is
A hydrostatic transmission system for converting an input of a first speed of a first hydraulic device on an input side into an output of a second speed of a second hydraulic device on an output side;
Driving means capable of driving the first hydraulic device and controlling a first speed of the first hydraulic device;
Means for detecting a second speed of the second hydraulic device;
An output control unit,
Equipped with
The output control unit receives the second speed of the second hydraulic device as an input, and achieves the target value of the force output from the second hydraulic device. Control the first speed,
It is an electrostatic hydraulic actuator.

The hydrostatic transmission system is a device for converting an input of one degree of freedom into an output of any one degree of freedom, and a distance along the direction of the one degree of freedom is a position, and its time derivative is a speed.
The operation on the output side of the hydrostatic transmission system is typically a rotational movement or a linear movement, but may be another operation.
In one aspect, the first hydraulic device is a hydraulic pump. In this case, the input of the hydrostatic transmission system is rotation.
In one aspect, the second hydraulic device is a hydraulic cylinder. In this case, a thrust can be obtained as an output of the hydrostatic pressure transmission system.
In one aspect, the second hydraulic device is a hydraulic motor. In this case, an output torque can be obtained as an output of the hydrostatic pressure transmission system.
In one aspect, the drive means is an electric motor. The driving means includes an engine and other prime movers.

In one aspect, the output control unit
The electrohydrostatic actuator according to claim 1, wherein the output control is performed based on.
here,
Is the target value of the first speed of the first hydraulic system,
Is the second speed of the second hydraulic system,
Is the target value of the force output from the second hydraulic system,
Each of A and B is a known constant.

More specifically, the constant A = k ₂₂ / k ₂₁ and the constant B = 1 / k ₂₁ ,
K ₂₁ is a constant indicating the influence of the first speed of the first hydraulic system on the differential pressure of the second hydraulic system,
K ₂₂ is a constant indicating the influence of the second speed of the second hydraulic system on the differential pressure of the second hydraulic system,
It is.
For the constants A (k ₂₂ / k ₂₁ ) and B (1 / k ₂₁ ), design values or values obtained by performing identification experiments can be used.
As the identification experiment, the least squares method can be used as a representative example as described later, but the acquisition method is not limited, and estimation is performed by numerical calculation methods other than the least squares method, machine learning, a combination of these, etc. Can.

In one aspect, the speed control of the drive means controls the first speed of the first hydraulic device.
In one aspect, the drive means is an electric motor,
Speed control of the first speed of the first hydraulic device is performed by control of the rotational speed of the electric motor.
In one aspect, the output control unit controls the rotational speed of the electric motor by voltage control.
In one aspect, the output control unit controls the rotational speed of the electric motor by current control. Although current control does not directly control the speed, it is possible by feedback, and such speed control is also included in the scope of the present invention.
In one aspect, the apparatus includes means for detecting the rotational speed of the electric motor, and the detected rotational speed of the electric motor is fed back to the output control unit.

In one aspect, the target value of the force output from the second hydraulic device is a target value of a differential pressure of the second hydraulic device.
In one aspect, a means for detecting a differential pressure of the second hydraulic device is provided, and the detected differential pressure is fed back to the output control unit.
In one aspect, a means for detecting a force output from the second hydraulic device is provided, and the detected force is fed back to the output control unit.

In one aspect, a means for detecting the acceleration of the second hydraulic device is provided, and the detected acceleration is fed back to the output control unit. This acceleration is used to calculate the target value of the force output from the second hydraulic device (see FIG. 10).
In one aspect, the means for detecting the second speed of the second hydraulic device comprises means (encoder) for detecting the position information of the second hydraulic device, and the speed information (and acceleration information) by differentiating the position information. And means for obtaining (controller).

Another technical means adopted by the present invention is
An electrohydrostatic actuator comprising a hydrostatic transmission system for converting an input of a first speed of a first hydraulic device on an input side into an output of a second speed of a second hydraulic device on an output side,
The relationship between the first speed of the first hydraulic system, the second speed of the second hydraulic system, and the force output from the second hydraulic system is defined by the following equation:
The output shaft of the second hydraulic device is fixed, the first hydraulic device is driven, and when the second speed of the second hydraulic device = 0, the first speed of the first hydraulic device and the second hydraulic device are outputted from the second hydraulic device. Recording the force, the measured data recorded, and the following formula
A parameter estimation method for estimating a parameter k ₂₁ indicating the influence of the first speed of the first hydraulic system on the force output from the second hydraulic system, using
An electrohydrostatic actuator comprising a hydrostatic transmission system for converting an input of a first speed of a first hydraulic device on an input side into an output of a second speed of a second hydraulic device on an output side,
The relationship between the first speed of the first hydraulic system, the second speed of the second hydraulic system, and the force output from the second hydraulic system is defined by the following equation:
The output shaft of the first hydraulic device is fixed, the second hydraulic device is driven by an external force, and when the first velocity of the first hydraulic device = 0, the second velocity of the second hydraulic device and the output from the second hydraulic device Recording the measured force, the measured data recorded, and the following equation
The parameter estimation method estimates the parameter k ₂₂ indicating the influence of the second speed of the second hydraulic device on the force output from the second hydraulic device using.
In one aspect, the parameters are estimated by least squares.

The present invention performs force control by speed control by using the relationship between the pressure and the speed of EHA, and can control the force stably and reproducibly as compared with the conventional actuator. More specific effects of the present invention can be read from the description of the present specification and the drawings.

It is the schematic of EHA. It is a conceptual diagram of EHA concerning this embodiment (basic form). It is a conceptual diagram of EHA concerning this embodiment (real form). It is a conceptual diagram of EHA concerning this embodiment (an example which improves accuracy using feedback of pressure). It is a conceptual diagram of EHA concerning this embodiment (an example which improves accuracy using feedback of force). It is a figure which shows force control of conventional EHA (basic form). It is a figure which shows force control of conventional EHA (real form). It is a figure which shows force control of EHA which concerns on this embodiment (basic form). It is a figure which shows force control of EHA which concerns on this embodiment (real form). It is a figure which shows force control of EHA which concerns on this embodiment (more exact mounting form). It is a block diagram of a force control system of EHA. The linear EHA and sensor (The encoder of a motor, the encoder of a hydraulic cylinder, a pressure sensor) which concern on embodiment are shown. Is a diagram showing the estimation of the parameter k _21. Dots indicate measurements and dashes indicate estimates obtained by the least squares method. Is a diagram showing the estimation of the parameter k _22. Dots indicate measurements and dashes indicate estimates obtained by the least squares method. The result when control is not performed is shown, the upper figure shows cylinder pressure (solid line is measured value, dash line is reference value), middle figure shows cylinder position (solid line) and cylinder speed (speed), lower figure shows motor speed It is. The upper figure shows the cylinder pressure (solid line is the measured value, the dash line is the reference value), the middle figure shows the cylinder position (solid line) and the cylinder speed (speed), and the lower figure shows the motor speed (speed). The reference values are indicated by dashed lines, but substantially overlap the solid line measurements. The results in the case of following 0.6MPa are shown, the upper figure shows cylinder pressure (solid line is measured value, dash line is reference value), middle figure shows cylinder position (solid line) and cylinder speed (speed), lower figure shows motor speed (The reference values are shown in dashes but substantially overlap the solid line measurements).

[A] Basic configuration of electro-hydrostatic actuator The electro-hydrostatic actuator (EHA) is a closed circuit type hydraulic system that drives a hydraulic motor or a piston by driving a servomotor with a hydro-static transmission. In contrast to a resistance control type hydraulic system using a servo valve, EHA is called a volume control type hydraulic system and is characterized by high efficiency and back drivability.

A typical EHA configuration is shown in FIG. A hydraulic pump is provided on the input side of the hydro static transmission, and a hydraulic cylinder is provided on the output side. The hydraulic pump is driven by a servomotor, and the output of the hydraulic cylinder is transmitted to the link of the robot. The servomotor is provided with means (encoder) for detecting the rotational angle or speed of the motor, and the hydraulic cylinder is provided with means (encoder) for detecting the position or speed of the output shaft. The actual circuit is equipped with a charge pump that prevents the circuit from becoming a negative pressure and a relief valve that protects the hydraulic circuit from excessive pressure. Previous studies have reported that EHA can improve back drivability by performing appropriate design (Non-Patent Document 1).

In this embodiment, a linear actuator EHA that increases the strength and the output of the small actuator is dealt with, but the discussion is applicable to a rotary system without losing generality.

[B] Overview of the Invention FIGS. 2 to 5 are conceptual diagrams of the present embodiment. As shown in FIG. 2, the electrohydrostatic actuator according to the present embodiment includes a backdatable hydro static transmission (HST) 1, and the hydro static transmission 1 serves as a first hydraulic device on the input side. And a hydraulic cylinder 3 (which may be a hydraulic motor) as a second hydraulic device on the output side. The electrohydrostatic actuator further includes a pump drive motor 4 for driving the hydraulic motor 2, a sensor (encoder) 5 for detecting the position or speed of the transmission output shaft (the output shaft 30 of the hydraulic cylinder), and a speed signal of the output shaft 30 And a controller (output control unit) 6 for controlling an applied voltage to the pump drive motor 4 so that a controlled force is transmitted to the link. In other words, the electrohydrostatic actuator shown in FIG. 2 converts the input of the first speed of the hydraulic pump 2 on the input side into the output of the second speed of the hydraulic cylinder 3 on the output side, and the hydraulic pump The output control unit 6 is provided with a pump drive motor 4 that can drive 2 and can control the first speed of the hydraulic pump 2, a sensor 5 that detects the second speed of the hydraulic cylinder 3, and an output control unit 6. The first speed of the hydraulic pump 2 is controlled via the pump drive motor 4 so that the target value of the force output from the hydraulic cylinder 3 is achieved with the second speed of the hydraulic cylinder 3 as an input. That is, the output control unit receives the speed of the second hydraulic device as an input, and achieves the target value of the force (output torque or thrust) output from the second hydraulic device via the drive means (pump drive motor). Control the speed of the first hydraulic system.

In the embodiment shown in FIG. 3, the electrohydrostatic actuator further includes a sensor (encoder) 7 for detecting the angle or speed of the pump drive motor 4, and the speed information of the pump drive motor 4 is input to the controller 6. Feedback control is performed.

In the embodiment shown in FIG. 4, the electrohydrostatic actuator further includes means (pressure sensor) 8 for detecting a differential pressure applied to the output shaft 30 of the transmission, and the differential pressure is input to the controller 6 and the pressure Use the feedback of to improve accuracy.

In the embodiment shown in FIG. 5, the electrohydrostatic actuator further comprises means (load cell) 9 for detecting the force acting on the output shaft 30 of the transmission, the force being input to the controller 6 and using force feedback Improve the accuracy.

The back drivable hydro static transmission according to the present embodiment transmits a force proportional to the speed difference between the hydraulic pump and the hydraulic cylinder (or hydraulic motor). By using this, it is possible to derive the pump rotational speed corresponding to the force to be output, and by controlling the speed of the pump, it is possible to control the thrust of the cylinder (the output torque of the hydraulic motor). Furthermore, closed loop control can be performed by using a sensor that measures the thrust of the cylinder (output torque of the hydraulic motor) or a sensor that measures the pressure of the cylinder (output torque of the hydraulic motor).

[C] Description of Symbols The symbols used in the description of the specification to FIGS. 6 to 11 are as follows.

[D] EHA dynamics The hydraulic circuit always has an internal leak from the high pressure side to the low pressure side. EHA allowed this internal leak is expressed by an equation of motion given by the following equation, using viscosity as a coupling term (see Non-Patent Document 3).
Where θ _i is position, J _i is mass, τ _i is an external force, k _ij is a constant, subscript i = 1 is a pump, and i = 2 is a hydraulic actuator unit. Also, I will consider the friction term omitted here.

There is the following relationship between the speed and pressure of the pump and cylinder.

[E] Force control of conventional EHA (Non-patent document 2)
The control of force at EHA is to control τ ₁ to bring τ ₂ to the desired value. Now,
Consider the case of
To become
Relationship is established. When the resistance of the pipeline connecting the pump and the cylinder can be ignored, p ₁ = p ₂ , so k ₂₃ / k ₁₃ is an amount corresponding to the reduction ratio. Furthermore, since τ _i = ki ₃ p _i in this case, the first term of (7) is zero. By using the relationship of (7), τ ₂ can be manipulated by control of τ ₁ . In practice, τ ₁ is realized by current control of the motor.

Force control by current control of a conventional motor is shown in FIG. 6 (basic type) and FIG. 7 (real type). As shown in FIGS. 6 and 7, the desired force · torque −τ ₂ ^d is defined, and is approximated using τ ₁ ^d in a modified approximate expression obtained by modifying (7). difficult). Formula for conversion to motor voltage (known relationship), motor drive circuit (a known relationship, a device capable of approximately adjusting the voltage applied to the motor by adjusting the duty ratio by PWM), EHA The generated force · torque −τ ₂ is obtained using the dynamics (which is a known relationship and represented by equations (1) and (2)).

[F] is the force control described above the force control of EHA with speed control, in addition to requiring a current control of the motor, in fact the tau ₂ due to factors such as changes in viscosity of the error and the oil in the torque constants (7 ) It is difficult to control only. In the present embodiment, it is considered that force control is performed using the relationship of (2) explicitly.

Now, since there is a relationship of τ ₂ = k ₂₃ p ₂ between τ ₂ and p ₂ , p ₂ is controlled.
Now there is a speed
To achieve the desired pressure p ^d ₂ when the output shaft is moving at
Is
Given by

In this section, considering the pressure deviation from the target value, the speed to realize the pressure
The control rule of is defined by the following equation.
Here, C (s) is an operator representing a feedback gain, and if C (s) = _Kp, it is proportional control, and if C (s) = K _p + K _i 1 / s, it is PI control.

The target value of the speed obtained in (9) is calculated by the appropriate speed controller.
Shall be followed. A block diagram of the control system is shown in FIG. In FIG. 11, ^* is an estimated value of the parameter.

Force control according to the present embodiment is shown in FIG. 8 (basic form), FIG. 9 (real form), and FIG. 10 (more strict mounting form). As shown in FIGS. 8 and 9, the desired force / torque −τ ₂ ^d is defined and approximated by an approximation using the desired pressure p ₂ ^d , k ₂₃ . This approximate expression uses a known relationship, and can be approximated more exactly by compensating for the acceleration of the second hydraulic system as shown in FIG. Then, as described above, (8) is set, a conversion formula (known relation) to motor voltage, a motor drive circuit (known relation), and approximating a voltage applied to the motor by adjusting the duty ratio by PWM. adjusting a device capable of) the manner (a relationship known, (1) the dynamics of EHA, obtained by the force-torque-tau ₂ for generating with (2) shown in the expression).

The advantage of the proposed method is that there is less uncertainty between input and output compared to the case of taking τ ₁ as an input, and the controller can be designed separately, which makes it difficult to carry out current control. Force control can also be realized in the system.

[G] The compact linear EHA was used as the target of experimental force control. The specifications of the small linear motion EHA handled in the present embodiment are shown below.
This EHA has a shape shown in FIG. 12, and is provided with a pressure sensor of a cylinder, a motor encoder, a motor current sensor, and a cylinder position sensor as sensors.

First, preliminary experiments were conducted to determine the parameters. Since the relational expression used this time is (4), necessary parameters can be calculated by acquiring the following data.

1. Fix the output shaft and rotate the motor. And
At the time of
And it records the p _2.

2. Fix the pump shaft and drive the cylinder by external force. And
At the time of
And record p ₂ ,
Extract the part of

p ₁ is not used in the proposed method. The above 1 and 2 are respectively
Because of the form, it is possible to obtain k _2i by using the least squares method.

The estimation experimental results of k ₂₁ and k ₂₂ are shown in FIGS. 13 and 14, respectively. Also, derived parameters are shown below.

Next, the behavior of pressure in the case where the proposed control was performed for different target pressures p ₂ ^d (0 MPa and 0.6 MPa) and in the case where the control was not performed was compared. In any case, disturbance was applied to the output shaft to evaluate the pressure following at that time. Pressure tracking was performed by PI control.

The result in the case where the control is not performed is shown in FIG. 15, the result in the case of following 0 MPa is shown in FIG. 16, and the result in the case of following 0.6 MPa is shown in FIG. Here, it should be noted that the scale of the vertical axis of the graph is different only in FIG. 15 with respect to pressure. The results of control evaluation are summarized below.

From the results, it was found that by performing control, the pressure is suppressed to 7.5% in the non-controlled state at the time of 0 MPa following. When the pressure was controlled to be constant at 0.6 MPa, when the velocity disturbance to the cylinder was 0.009919 m / s in RMS, the control error of the pressure remained at 0.05192 MPa in RMS. For reference, the background noise of the pressure sensor is 0.003726 MPa in RMS. In addition to the estimation error of k _2i , the error tends to be large at high motor speeds, and it is considered that the nonlinearity of the model appears and it can be suppressed by a disturbance observer etc. .

It is as follows when the result of this experiment example is put together, and the effectiveness of the proposed control system has been confirmed.
(A) In order to realize stable force control on the simple control side without considering the complex behavior of the electrohydrostatic actuator, we propose a control law that realizes the force control of the electrohydrostatic actuator by speed control of the motor did. In this experiment, we implemented pressure control that is the basis of force control.
(A) A method for estimating the parameters of the electrohydrostatic actuator was proposed, and the k ₂₁ and k ₂₂ parameters were estimated by the least squares method. In the small-sized direct acting electrostatic hydraulic actuator used, k ₁₂ = 442.2 Pa · s / rad and k ₂₂ = 64. 39 × 106 Pa · s / m.
(C) By performing PI control that follows 0 MPa, the pressure fluctuation improved to 7.5% compared to the non-control time. At this time, compared with the velocity disturbance applied to the output shaft being 0.007495 m / s at the non-control time, it can be understood that the pressure following capability is high even considering that it is 0.012485 m / s at the control time.
(D) By control to follow a constant value of 0.6 MPa, when the speed disturbance was 0.009919 m / s, the follow-up error was 0.051916 MPa.

As described above, in the present embodiment, it is proposed to perform force control by motor speed control by explicitly using the relationship between the pressure and the speed of EHA. In this method, it is not always necessary to control the current of the motor, the gain of the control system can be increased by using a sensor with a very high signal-to-noise ratio as an encoder, and the control system is simplified. There is an advantage. In addition, the dimension of the input is velocity, and control can be performed faster than displacement for force control of an actuator using elasticity. In this embodiment, the result of having implemented and evaluated force control as pressure control which is a substantially equivalent control amount was reported. Further, this control is widely applicable to a hydrostatic drive system combining general hydraulic equipment.

1 Hydro-static transmission 2 Hydraulic motor (1st hydraulic system)
3 Hydraulic cylinder (2nd hydraulic system)
30 Output shaft 4 Pump drive motor (drive means)
5 Position / speed detection sensor (encoder)
6 Controller (output control unit)
7 Position / speed detection sensor (encoder)
8 Pressure sensor 9 Force sensor (load cell)

Claims (16)

A hydrostatic transmission system for converting an input of a first speed of a first hydraulic device on an input side into an output of a second speed of a second hydraulic device on an output side;
Driving means capable of driving the first hydraulic device and controlling a first speed of the first hydraulic device;
Means for detecting a second speed of the second hydraulic device;
An output control unit,
Equipped with
The output control unit receives the second speed of the second hydraulic device as an input, and achieves the target value of the force output from the second hydraulic device. a controls the first speed,
The output control unit calculates a target value of the first speed based on a second speed of the second hydraulic device and a target value of a force output from the second hydraulic device, and calculates the target of the first speed. Controlling a first speed of the first hydraulic device based on a value to control a force output from the second hydraulic device;
Electrostatic hydraulic actuator. The output control unit has the following formula
The electrohydrostatic actuator according to claim 1, wherein the output control is performed based on.
here,
Is the target value of the first speed of the first hydraulic system,
Is the second speed of the second hydraulic system,
Is the target value of the force output from the second hydraulic system,
Each of A and B is a known constant. The drive means is an electric motor,
Speed control of the first speed of the first hydraulic device is performed by control of the rotation speed of the electric motor.
The electrohydrostatic actuator according to any one of claims 1 and 2. The output control unit controls the rotational speed of the electric motor by voltage control.
An electrohydrostatic actuator according to claim 3. The output control unit controls the rotational speed of the electric motor by current control.
An electrohydrostatic actuator according to claim 3. Means for detecting the rotational speed of the electric motor;
The detected rotational speed of the electric motor is fed back to the output control unit.
The electrohydrostatic actuator according to any one of claims 3 to 5. The target value of the force output from the second hydraulic device is a target value of the differential pressure of the second hydraulic device,
The electrohydrostatic actuator according to any one of claims 1 to 6. A means for detecting a differential pressure of the second hydraulic device;
The detected differential pressure is fed back to the output control unit.
The electrohydrostatic actuator according to claim 7. Means for detecting a force output from the second hydraulic device;
The detected force is fed back to the output control unit.
The electrohydrostatic actuator according to any one of claims 1 to 8. Means for detecting an acceleration of the second hydraulic device;
The detected acceleration is fed back to the output control unit.
The electrohydrostatic actuator according to any one of claims 1 to 9. The first hydraulic device is a hydraulic pump,
The electrohydrostatic actuator according to any one of claims 1 to 10. The second hydraulic device is a hydraulic cylinder,
The electrohydrostatic actuator according to any one of claims 1 to 11. The second hydraulic device is a hydraulic motor.
The electrohydrostatic actuator according to any one of claims 1 to 11. An electrohydrostatic actuator comprising a hydrostatic transmission system for converting an input of a first speed of a first hydraulic device on an input side into an output of a second speed of a second hydraulic device on an output side,
First speed of first hydraulic system
And the second speed of the second hydraulic system
When the relationship between the forces p ₂ outputted from the second hydraulic system, the parameter k ₂₁ showing a first speed of impact of the first hydraulic system for power output from the second hydraulic device, is output from the second hydraulic system Defined by the following equation using a parameter k ₂₂ indicating the influence of the second speed of the second hydraulic system on the
The output shaft of the second hydraulic device is fixed, the first hydraulic device is driven, and when the second speed of the second hydraulic device = 0, the first speed of the first hydraulic device and the second hydraulic device are outputted from the second hydraulic device. Recording the force, the measured data recorded, and the following formula
A parameter k ₂₁ for estimating a parameter k ₂₁ indicating the influence of the first speed of the first hydraulic system on the force output from the second hydraulic system, using An electrohydrostatic actuator comprising a hydrostatic transmission system for converting an input of a first speed of a first hydraulic device on an input side into an output of a second speed of a second hydraulic device on an output side,
First speed of first hydraulic system
And the second speed of the second hydraulic system
When the relationship between the forces p ₂ outputted from the second hydraulic system, the parameter k ₂₁ showing a first speed of impact of the first hydraulic system for power output from the second hydraulic device, is output from the second hydraulic system Defined by the following equation using a parameter k ₂₂ indicating the influence of the second speed of the second hydraulic system on the
The output shaft of the first hydraulic device is fixed, the second hydraulic device is driven by an external force, and when the first velocity of the first hydraulic device = 0, the second velocity of the second hydraulic device and the output from the second hydraulic device Recording the measured force, the measured data recorded, and the following equation
A parameter k ₂₂ for estimating the influence of the second speed of the second hydraulic system on the force output from the second hydraulic system, using. The parameter estimation method according to any one of claims 14 and 15, wherein the parameter is estimated by a least squares method.