KR102551659B1 - Method for estimating parameter of mechanical model for servo motor and system for controlling motor with Kalman filter using the same - Google Patents

Abstract

A parameter estimation method for a mechanical model of a servo motor and a motor control system having a Kalman filter using the method are provided. A method for estimating parameters for a mechanical model of a servo motor according to an embodiment of the present invention is a method for estimating mechanical model parameters based on a mechanical equation for a motor and a mechanical part connected to the motor, wherein the motor is operated at a low speed at which acceleration converges to zero. A first calculation step of calculating a static friction coefficient (C) and a load torque (T _L ) among mechanical model parameters based on torque generated by the motor while driving the; And _the moment of inertia ( _J ) and the _coefficient of motion friction ( and a second calculation step of calculating B).

Description

Method for estimating parameter of mechanical model for servo motor and system for controlling motor with Kalman filter using the same}

The present invention relates to a method for estimating parameters for a mechanical model of a servo motor and a motor control system having a Kalman filter using the method, and in particular, used for precision driving of ultra-precision manufacturing equipment such as machine tools, robots, and various micro-optical equipment. It relates to a parameter estimation method for a mechanical model of a servo motor that can be used in a motor controller that controls a servo motor and a motor control system having a Kalman filter using the same.

Most industrial equipment uses motors and controllers to control movement. These motor controllers require high-speed, high-precision movement and rapid target position arrival in order to improve productivity and maintain uniform product quality.

The motor controller has a structure in which a position controller, a speed controller, and a current controller are connected in series. In order to improve the control performance of each controller, the model and parameters of the feed-forward controller must first be approximated, and the control gain of the feedback controller must be increased to increase the target tracking performance.

At this time, in order to increase the control gain, the control period should be shortened and a noise-free signal should be fed back. However, there is a limit to increasing the gain of the speed controller due to the quantization noise of the speed calculation by the motor encoder.

A feed forward controller is used for fast response, and a Kalman filter is used to reduce measurement noise of the feedback signal. To use these feed forward controllers and Kalman filters, the parameters of the mechanical model of the motor must be known as accurately as possible.

Therefore, there is a need for a method of accurately estimating the parameters of the mechanical model of the servo motor and reducing the noise of the measured speed through a Kalman filter using the parameter.

KR 10-2005-0012800 A

In order to solve the problems of the prior art as described above, an embodiment of the present invention is a mechanical model of a servo motor that can accurately estimate the parameters of the mechanical model using a mechanical formula for a motor and a mechanical part connected to the motor. It is intended to provide a parameter estimation method.

In addition, an embodiment of the present invention is to provide a motor control system capable of reducing noise of measured speed using a Kalman filter based on parameters of an estimated mechanical model of a servo motor.

According to one aspect of the present invention for solving the above problems, in the method of estimating a mechanical model parameter based on a motor and a mechanical formula for a mechanical part to which the motor is connected, the motor is driven at a low speed at which the acceleration converges to zero. a first calculation step of calculating a static friction coefficient (C) and a load torque (T _L ) of the mechanical model parameters based on torque generated by the motor while driving; And torque (T _e ), time (t _k ) and position (θ _k ) data applied to the motor while controlling the speed of the motor with a trapezoidal profile. Moment of inertia (J) and motion among the mechanical model parameters A parameter estimation method for a mechanical model of a servo motor including a second calculation step of calculating a friction coefficient (B) is provided.

In one embodiment, the mechanical expression may be:

는 모터의 회전 가속도.Here, T _e is the torque generated by the motor, J is the moment of inertia of the motor and mechanical parts, B is the coefficient of kinetic friction proportional to speed, C is the coefficient of static friction, T _L is the torque due to the load, and ω is the rotational speed of the motor ,

is the rotational acceleration of the motor.

In one embodiment, the first calculating step may include rotating the motor in a forward direction at a first speed ω ₁ ; Calculating a first torque (T _e1 ) generated in the motor from the current flowing in the motor; rotating the motor in a reverse direction at a second speed (ω ₁ ) equal to the first speed (ω ₁ ); Calculating a second torque (T _e2 ) generated in the motor from the current flowing through the motor; and calculating the static friction coefficient (C) and the load torque (T _L ) by substituting the first torque (T _e1 ) and the second torque (T _e2 ) into the mechanical equation.

In one embodiment, the second calculating step may include controlling the speed of the motor with the trapezoidal speed profile; Collecting torque (T _e ), time (t _k ), and position (θ _k ) data applied to the motor at regular intervals from the start to the end of the speed profile; Calculating a determinant by substituting the torque (T _e ) and the position (θ _k ) into the mechanical equation; and calculating the moment of inertia (J) and the kinetic friction coefficient (B) by a least squares method for the determinant.

In one embodiment, the speed profile is a shape in which the speed increases section (T ₁ ) and the speed decreases section (T ₃ ) is 65 to 75% compared to the entire section (T ₁ +T ₂ +T ₃ ) can have

In one embodiment, the second calculation step may include calculating a quadratic regression equation for a position (θ _k ) based on three recent data at all times; And calculating the speed (ω _k ) for each position (θ _k ) by differentiating at the midpoint among the three data; further comprising, the calculated speed (ω _k ) for each position (θ _k ) can be substituted into the determinant.

In one embodiment, the step of calculating the determinant is the torque (T _e ), the position ( The determinant can be calculated by substituting θ _k ) and the velocity ω _k for each position θ _k .

In one embodiment, the determinant may be calculated as the following equation.

In one embodiment, the determinant may be operated as a Moore-Penrose pseudoinverse.

In one embodiment, the second calculating step may include calculating the moment of inertia (J) and the kinetic friction coefficient (B) n times; a first elimination step of averaging the calculated values and removing a value having the largest error; a second elimination step of averaging the remaining values after the first step and removing a value having the smallest error; repeating the first removing step and the second removing step m times; and calculating final values of the moment of inertia (J) and the coefficient of kinetic friction (B) by averaging the remaining values after the repeating step.

According to another aspect of the present invention, a control system having a Kalman filter using parameters of a mechanical model of a servo motor estimated by the method described above, wherein the Kalman filter estimates the speed of the motor, as a predictive model A motor control system having a Kalman filter for estimating the speed of the motor using the mechanical and mechanical model parameters is provided.

A method for estimating parameters for a mechanical model of a servo motor and a motor control system having a Kalman filter using the same according to an embodiment of the present invention accurately estimates parameters for a mechanical model, thereby increasing control responsiveness by a feed forward controller Velocity noise can be reduced by using a Kalman filter.

In addition, a parameter estimation method for a mechanical model of a servo motor and a motor control system having a Kalman filter using the same according to an embodiment of the present invention can secure fast target following performance in servo motor control, and Vibration and noise can be reduced.

1 is a block diagram showing a control system of a servo motor.
2 is a flowchart illustrating a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.
3 is a flowchart illustrating a procedure for calculating a static friction coefficient (C) and a load torque (T _L ) in a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.
4 is a flowchart illustrating a procedure for calculating a moment of inertia (J) and a coefficient of kinetic friction (B) in a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.
5 is a graph showing an example of a speed profile in a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.
6 is a diagram for explaining speed estimation in a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.
7 is a flowchart illustrating a procedure for calculating final values of a static moment of inertia (J) and a coefficient of motion friction (B) in a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.
8 is a block diagram illustrating a control system having a Kalman filter using mechanical model parameters estimated by a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.
9 is a diagram illustrating the operation of the Kalman filter of FIG. 8 .
10 is a graph showing an example of speed estimation performance of a control system having a Kalman filter according to an embodiment of the present invention and a conventional control system.
11 is a graph showing another example of speed estimation performance of a control system having a Kalman filter according to an embodiment of the present invention and a conventional control system.

Hereinafter, with reference to the accompanying drawings, an embodiment of the present invention will be described in detail so that those skilled in the art can easily practice it. This invention may be embodied in many different forms and is not limited to the embodiments set forth herein. In order to clearly describe the present invention in the drawings, parts irrelevant to the description are omitted, and the same reference numerals are assigned to the same or similar components throughout the specification.

Hereinafter, a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention will be described in detail with reference to the drawings.

A parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention separates the d-axis and the q-axis for a Permanent Magnet Synchronous Motor (PMSM) such as a servo motor, and separates the torque and magnetic flux, respectively. It relates to parameter estimation for the mechanical model of servo motors in the field-oriented control (FOC) system that controls them.

1 is a block diagram showing a control system of a servo motor.

Referring to FIG. 1, the servo motor control system has a cascade structure in which a position controller 20, a speed controller 40, and a current controller 50 are connected in series.

Here, the d-axis current is controlled to be maintained at 0, and the q-axis current is controlled to generate torque in the motor. At the innermost part of the control loop, there are d-axis and q-axis current controllers 50, speed controller 40 includes current controller 50, and position controller 20 includes speed controller 40 and differentiator 60 ) is a structure containing

At this time, for model-based control, parameters related to the mechanical model of the motor must be known in advance. In addition, these mechanical parameters are necessary to determine the gain of the PI (Proportional, Integral) speed controller 40 and also to design a Kalman filter that reduces quantization noise of the speed fed back to the speed controller 40.

In addition, the gain of the PI speed controller 40 can be increased only when the noise of the speed signal is removed, and when configuring the feed-forward controller 30, the model and parameters must be accurate to ensure performance.

On the other hand, since mechanical model parameters such as moment of inertia, friction coefficient, and load torque vary depending on the mechanical part connected to the motor 1, they must always be newly found in the equipment in which the motor 1 is used.

At this time, the mechanical formula including the motor and equipment is displayed as follows.

는 모터의 회전 가속도이다. Here, T _e is the torque generated by the motor, J is the moment of inertia of the motor and mechanical parts, B is the coefficient of kinetic friction proportional to speed, C is the coefficient of static friction, T _L is the torque due to the load, and ω is the rotational speed of the motor ,

is the rotational acceleration of the motor.

Hereinafter, a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention will be described with reference to FIGS. 2 to 7 .

2 is a flowchart illustrating a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.

Parameter estimation method 100 for a mechanical model of a servo motor includes calculating a static friction coefficient (C) and a load torque (T _L ) (S110) and calculating a moment of inertia (J) and a kinetic friction coefficient (B). Step S120 is included.

More specifically, as shown in FIG. 2, first, the parameter estimation method 100 for the mechanical model of the servo motor drives the motor 1 at a low speed and stops based on the torque generated by the motor 1. The friction coefficient (C) and the load torque (T _L ) are calculated (step S110). At this time, the motor 1 may be slowly driven at a low speed. Here, the low speed may be a low speed at which the acceleration of the motor 1 converges to zero. Mechanical model parameters of the static friction coefficient (C) and the load torque (T _L ) may be calculated by Equation 1 based on the torque generated under such driving conditions.

Next, the parameter estimation method 100 for the mechanical model of the servo motor controls the speed of the motor 1 by a predetermined speed profile, and the moment of inertia (J ) and the kinetic friction coefficient (B) are calculated (step S120). Here, the velocity profile may have a trapezoidal shape in which an acceleration section, a constant speed section, and a deceleration section are successively configured. Based on the torque generated under such driving conditions, mechanical model parameters of the moment of inertia (J) and the coefficient of kinetic friction (B) may be calculated by Equation 1.

3 is a flowchart illustrating a procedure for calculating a static friction coefficient (C) and a load torque (T _L ) in a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.

The procedure 110 for calculating the static friction coefficient (C) and the load torque (T _L ) in the parameter estimation method for the mechanical model of the servo motor 110 calculates the motor-generated torque (T _e1 ) while rotating the motor 1 in the forward direction. Steps S111 and S112, calculating the motor-generated torque T _e2 while rotating the motor 1 in the reverse direction (S113 and S114) and calculating the static friction coefficient C and the load torque T _L include

)가 0이 되는 아주 느린 속도이다. 일례로, 제1속도(ω₁)는 0.0001 ~ 5 rad/s 일 수 있다. More specifically, as shown in FIG. 3 , first, the motor 1 is rotated in the forward direction at a first speed ω ₁ (step S111). Here, the first speed ω ₁ is the rotational speed of the motor 1 and means an angular speed. At this time, the first velocity (ω ₁ ) is the acceleration (

) becomes zero at a very slow rate. For example, the first speed (ω ₁ ) may be 0.0001 to 5 rad/s.

Next, the first torque T _e1 generated in the motor 1 is calculated from the current flowing through the motor 1 (step S112).

Next, the motor 1 is rotated in the reverse direction at the second speed ω ₂ (step S113). Here, since the second speed (ω ₂ ) is the same as the first speed (ω ₁ ) and the rotation direction is opposite, it can be expressed as -ω ₁ .

Next, the second torque T _e2 generated in the motor 1 is calculated from the current flowing through the motor 1 (step S114).

Next, after the motor 1 is stopped, the first torque (T _e1 ) and the second torque (T _e2 ) calculated as above are substituted into Equation 1 to obtain a static friction coefficient (C) and a load torque (T _L ) is calculated (step S115).

₁,

₂)는 0이 되며, 속도(ω₁, ω₂)도 0에 근사하게 된다. 따라서 수학식 1에서 운동 마찰계수(B) 및 관성 모멘트(J)를 무시할 수 있다. 즉, 수학식 1은 하기의 수학식 2 및 수학식 3과 같이 정리될 수 있다. Here, when the motor 1 is driven at a low speed constant speed, the acceleration (

₁ ,

₂ ) becomes 0, and the velocity (ω ₁ , ω ₂ ) also becomes close to 0. Therefore, in Equation 1, the kinetic friction coefficient (B) and the moment of inertia (J) can be ignored. That is, Equation 1 can be arranged as Equation 2 and Equation 3 below.

In this way, as shown in Equation 4 below, from the first torque T _e1 applied when the motor 1 rotates in the forward direction and the second torque T _e2 applied when the motor 1 rotates in the reverse direction Static friction coefficient (C) and load torque (T _L ) can be calculated.

Meanwhile, in order to calculate the moment of inertia (J) and the coefficient of kinetic friction (B), Equation 1 is converted as shown in Equation 5 below. At this time, as described above, since the static friction coefficient (C) and the load torque (T _L ) are calculated, the terms related to the moment of inertia (J) and the kinetic friction coefficient (B) to be obtained are placed on the right side, and the known We can transform the expression so that the constant term is placed on the left hand side.

)를 구하는 경우, 위치에 대하여 두 번의 미분을 수행해야 한다. 이 경우, 양자화 오차가 너무 크게 작용한다. 이를 방지하기 위해서 수학식 5에서 좌우변을 적분하여 하기의 수학식 6과 같이 정리한다.Using Equation 5, the acceleration (

), two derivatives must be performed with respect to the position. In this case, the quantization error acts too large. In order to prevent this, the left and right sides are integrated in Equation 5 and arranged as in Equation 6 below.

In Equation 6, the terms related to the moment of inertia (J) and the coefficient of kinetic friction (B) are transformed into functions of the speed (ω) and the position (θ) that can be directly calculated by driving the motor 1.

Therefore, while driving the motor 1 using an acceleration/deceleration profile, data on the velocity ω and position θ may be collected, and the moment of inertia J and the coefficient of motion friction B may be calculated based on the collected data.

4 is a flowchart illustrating a procedure for calculating a moment of inertia (J) and a coefficient of kinetic friction (B) in a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention, and FIG. A graph showing an example of a velocity profile in a parameter estimation method for a mechanical model of a servo motor according to an embodiment, and FIG. It is a drawing for explanation.

The procedure 120 for calculating the moment of inertia (J) and the coefficient of motion friction (B) in the parameter estimation method for the mechanical model of the servo motor is the step of controlling the speed of the motor 1 with a speed profile (S121), the motor 1 ) Collecting torque, time, and position data applied to (S122), calculating speed (ω _k ) with a quadratic regression equation (steps S123 and S124), calculating a mechanical determinant (S125), and Calculating the moment of inertia (J) and the coefficient of kinetic friction (B).

More specifically, as shown in FIG. 4, first, the speed of the motor 1 is controlled with a trapezoidal speed profile (step S121). At this time, a trapezoidal velocity profile may be output as a velocity command through the velocity profile generating unit 10 .

As shown in FIG. 5 , the trapezoidal velocity profile may include a section in which the speed increases (T ₁ ), a section in which the speed is constant (T ₂ ), and a section in which the speed decreases (T ₃ ). At this time, since the moment of inertia (J) is a value proportional to the acceleration of the motor 1 and the kinetic friction coefficient (B) is a value proportional to the speed of the motor 1, the speed profile changes in speed while maintaining a constant acceleration. should be set so that it can occur sufficiently.

For example, the speed increasing section (T ₁ ) and the speed decreasing section (T ₃ ) may be set to 65 to 75% compared to the entire section (T ₁ +T ₂ +T ₃ ). Preferably, the section in which the speed increases (T ₁ ) and the section in which the speed decreases (T ₃ ) may be set to 70% of the entire section (T ₁ +T ₂ +T ₃ ). That is, the section in which the speed increases (T ₁ ) is 35% of the total, the section in which the speed is constant (T ₂ ) is 30% of the total, and the section in which the speed decreases (T ₃ ) can be set to 35% of the total. .

Next, torque (T _e ), time (t _k ), and position (θ _k ) data applied to the motor 1 are collected at regular intervals from the start to the end of the speed profile (step S122). At this time, torque (T _e ), time (t _k ), and position (θ _k ) data applied to the motor 1 may be collected in a 1 ms cycle. Data collected in this way may be recorded in a memory.

At this time, as shown in FIG. 6, the rotational position of the actual motor continuously changes. However, the encoder value of the motor 1 changes in the form of a discontinuous step. Therefore, if the speed is calculated by differentiating the encoder value as the position value, quantization noise is generated according to the encoder resolution. This is because the lower the resolution of the encoder, that is, the larger the step difference of the discontinuous step, the larger the quantization noise, and the measurement of such an erroneous speed value reduces the precision of the calculation. To prevent this, the speed of the motor 1 similar to the actual speed is measured in the following process.

First, for all times, a quadratic regression equation for the position (θ _k ) is calculated based on the last three data (step S123). At this time, the quadratic regression equation passing through the three points can be defined as in Equation 7 below.

By differentiating the quadratic regression equation for the position (θ _k ), the velocity (ω _k ) for the corresponding position (θ _k ) can be obtained. That is, if the coefficients (a, b, c) of the quadratic regression equation for the position (θ _k ) are obtained, the velocity (ω _k ) can be calculated therefrom. At this time, it is assumed that the speed is calculated by differentiating the point (t ₁ ) located in the middle among the three points. This method is possible because the rotational speed of the motor 1 does not change significantly in a very short time of hundreds of microseconds.

As _measured in the previous step, _three points (t ₀ , θ ₁ ), (t ₁ , θ ₁ ), ( t ₂ , θ ₂ ), the three points are converted as shown in Equation 8 below based on k=1.

In addition, when the coefficients a and b are calculated by substituting the three points into the quadratic regression equation of Equation 7, the following Equation 9 is obtained.

Next, the velocity (ω _k ) for each position (θ _k ) is calculated by differentiating at the midpoint among the three data (step S124). At this time, when the quadratic regression equation of Equation 7 is differentiated, the following Equation 10 is obtained.

Here, the speed (ω ₁ ) when k = 1 is as shown in Equation 11 below.

As described above, since the value of the coefficient b of the quadratic regression equation was calculated by Equation 9, the velocity ω ₁ with respect to the position θ ₁ can be calculated from Equation 11.

Next, a determinant is calculated by substituting the calculated torque (T _e ), position (θ _k ), and velocity (ω _k ) for each position (θ _k ) into a mechanical equation (step S125). At this time, the mechanical formula of Equation 1 is transformed into an equation for the moment of inertia (J) and the coefficient of kinetic friction (B), and then the previously calculated torque (T _e ), position (θ _k ) and angle By substituting the velocity (ω _k ) for the position (θ _k ), the determinant of Equation 12 below can be calculated.

Next, the moment of inertia (J) and the coefficient of kinetic friction (B) are calculated by the least square method for the calculated determinant (step S126). At this time, since A in the determinant is not a square matrix, the x value can be calculated with a Moore-Penrose pseudoinverse as shown in Equation 13 below.

On the other hand, although the moment of inertia (J) and the coefficient of kinetic friction (B) can be calculated by the method described above, it is difficult to guarantee that the mechanical model parameters of the system are properly calculated in one test. Therefore, if similar values are repeatedly obtained through repeated tests, the mechanical model parameters can be trusted.

At this time, the moment of inertia (J) is greatly affected by the accuracy of the speed. In particular, when the resolution of the encoder of the motor 1 is low, quantization noise greatly affects the speed value obtained by differentiating the position, so that the calculation result of the mechanical model parameters is inaccurate. In order to overcome this problem, the moment of inertia (J) and the coefficient of kinetic friction (B) are determined according to the following procedure.

7 is a flowchart illustrating a procedure for calculating final values of a static moment of inertia (J) and a coefficient of motion friction (B) in a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention.

In the parameter estimation method for the mechanical model of the servo motor, the procedure 130 for calculating the final values of the moment of inertia (J) and the coefficient of kinetic friction (B) calculates the moment of inertia (J) and the kinetic friction coefficient (B) n times. (S131), repeating the removal of the average and error values m times (steps S132 to S134), and calculating the final values of the moment of inertia (J) and the coefficient of kinetic friction (B) (S135). .

More specifically, as shown in FIG. 7, first, the moment of inertia (J) and the coefficient of kinetic friction (B) are calculated n times (step S131). At this time, the moment of inertia (J) and the coefficient of kinetic friction (B) may be calculated n times according to the procedure shown in FIG. 4 .

Next, the calculated values are averaged to remove the value having the largest error (step S132). That is, after calculating the average of the calculated values n times for each of the moment of inertia (J) and the kinetic friction coefficient (B), the value with the largest error from the average is removed.

Next, the remaining values after the previous step are averaged to remove the value with the smallest error (step S133). That is, after calculating the average for each of the n-1 moments of inertia (J) and the kinetic friction coefficient (B), a value having the smallest error with the average is removed.

Next, it is determined whether the removal of error values is repeated m times (step S134). As a result of the determination, if the number is less than m, the process proceeds to step S132 and steps S132 to S134 are repeatedly performed. That is, the process of removing error values in steps S132 and S133 is repeated m times.

Next, the final values of the moment of inertia (J) and the coefficient of kinetic friction (B) are calculated by averaging the remaining values after the repetition step (step S135). That is, an average value for each of n-(2*m) moments of inertia (J) and kinetic friction coefficient (B) may be determined as a final value.

Accordingly, the parameter estimation method for the mechanical model of the servo motor according to an embodiment of the present invention can accurately estimate the parameters for the mechanical model, thereby increasing control responsiveness by the feed forward controller and increasing the speed of the servo motor by using the Kalman filter. noise can be reduced.

8 is a block diagram showing a control system having a Kalman filter using a mechanical model parameter estimated by a parameter estimation method for a mechanical model of a servo motor according to an embodiment of the present invention, and FIG. This diagram shows the operation of the filter.

Referring to FIG. 8 , the servo motor control system according to an embodiment of the present invention is obtained by adding Kalman filters 70 and 80 to the current measurement unit and the speed measurement unit of the server motor control system of FIG. 1 .

More specifically, the current Kalman filter 70 contributes to increasing the control gain of the closed-loop current controller 50 by removing measurement noise from the current measured by the current sensor.

The speed Kalman filter 80 contributes to increasing the control gain of the closed loop speed controller 40 by removing quantization noise from the differential speed of the position measured by the encoder of the motor 1 . Here, the output of the velocity Kalman filter 80 is input to the current controller 50 after passing through the attenuator 90. In order to use such a Kalman filter, correct mechanical parameters of the motor 1 must be used. If the wrong machine parameter is used, an error occurs in the estimated value of the speed, which degrades the control performance.

In order to prevent such errors from occurring and deterioration of control performance, the speed Kalman filter 80 may use parameters of the mechanical model of the servo motor estimated by the method described above.

The operation of the velocity Kalman filter 80 is performed while repeating the process of predicting and updating as shown in FIG. 9 .

At this time, the velocity Kalman filter 80 repeatedly estimates a vector x consisting of two state variables as shown in Equation 14 below.

Here, P is the covariance matrix for the vector x, and the hat (^) symbol used for ω and T _L means the estimated value of the value calculated by the speed Kalman filter 80, and should be distinguished from the actual measured speed. .

The velocity Kalman filter 80 uses the mechanical and mechanical model parameters of Equation 1 as a predictive model. To this end, Equation 1 is converted into a state equation form as shown in Equation 15 below.

At this time, Equation 15 is changed to have the shape of the prediction equation of the velocity Kalman filter 80.

Then, the state vector x is calculated by Equation 16 below using the input value u.

The covariance matrix P is calculated by Equation 17 below.

Here, A, W, and Q are as shown in Equation 18 below.

The velocity Kalman filter 80, as an update model, uses the relationship between the state vector x and the input value z, which is shown in Equation 19 below.

Here, the Kalman gain K is calculated as in Equation 20 below.

At this time, the estimated value x is updated from the measured value z to Equation 21 below.

The covariance matrix P is updated to Equation 22 below.

When such a velocity Kalman filter 80 is used, velocity quantization noise can be reduced.

Accordingly, the method for estimating parameters for a mechanical model of a servo motor according to an embodiment of the present invention can ensure fast target following performance in servo motor control, and can reduce vibration and noise of the servo motor.

10 is a graph showing an example of speed estimation performance of a control system having a Kalman filter according to an embodiment of the present invention and a conventional control system. Here, (a) is a speed graph when the motor 1 is rotating at a constant speed, (b) is a speed graph when the motor 1 is accelerating, and (c) is a speed graph when the motor 1 is rotated at a low speed. This is the speed graph when rotating with . In the drawings, the green graph represents the speed calculated by differentiating the encoder value of the motor 1, and the blue graph represents the estimated speed passing through the speed Kalman filter 80.

Referring to FIG. 10 , when the motor 1 rotates at a constant speed (a), the green graph changes speed between 0 and 15 rpm, but the blue graph has a value between about 1 and 4 rpm. Looking at the variation width of the graph, it can be seen that the quantization noise for speed can be reduced to about 1/5 level. In addition, it can be seen that the quantization noise for the speed can be reduced to a certain level even when the motor 1 accelerates (b) and at a low speed (c).

In this way, if noise is reduced, speed tracking performance can be improved by setting a gain of a higher bandwidth to the speed controller 40.

11 is a graph showing another example of speed estimation performance of a control system having a Kalman filter according to an embodiment of the present invention and a conventional control system. Here, (a) is a case where the load torque is not compensated for when the motor shaft is shaken by hand while the motor 1 is stopped, and (b) is a case where the compensation is made. In the drawings, a red graph is a position error, and a green graph is an estimated load torque value.

Referring to FIG. 11, when the load torque is estimated by the speed Kalman filter 80 and the load torque is compensated through the feed-forward controller 20 (b), compared to the case where the load torque is not compensated (a) It can be seen that the position error is greatly reduced.

Although one embodiment of the present invention has been described above, the spirit of the present invention is not limited to the embodiments presented herein, and those skilled in the art who understand the spirit of the present invention may add elements within the scope of the same spirit. However, it will be possible to easily suggest other embodiments by means of changes, deletions, additions, etc., but this will also be said to fall within the scope of the present invention.

1: motor 10: speed profile generating unit
20: position controller 30: feed-forward controller
40: speed controller 50: current controller
60: differentiator 70: current Kalman filter
80: speed Kalman filter 90: attenuator

Claims (11)

A method for estimating mechanical model parameters based on a mechanical equation for a motor and a mechanical part to which the motor is connected,
a first calculation step of calculating a static friction coefficient (C) and a load torque (T _L ) among the mechanical model parameters based on a torque generated by the motor while driving the motor at a low speed at which acceleration converges to 0; and
Moment of inertia (J) and kinetic friction among the mechanical model parameters based on data of torque (T _e ), time (t _k ) and position (θ _k ) applied to the motor while controlling the speed of the motor with a trapezoidal profile A second calculation step of calculating the coefficient B,
The mechanical formula is the following formula,

Here, T _e is the torque generated by the motor, J is the moment of inertia of the motor and mechanical parts, B is the coefficient of kinetic friction proportional to speed, C is the coefficient of static friction, T _L is the torque due to the load, and ω is the rotational speed of the motor ,

is the rotational acceleration of the motor,
In the first calculation step,
Rotating the motor in a forward direction at a first speed (ω ₁ );
Calculating a first torque (T _e1 ) generated in the motor from the current flowing in the motor;
rotating the motor in a reverse direction at a second speed (ω ₂ ) equal to the first speed (ω ₁ );
Calculating a second torque (T _e2 ) generated in the motor from the current flowing through the motor; and
calculating the static friction coefficient (C) and the load torque (T _L ) by substituting the first torque (T _e1 ) and the second torque (T _e2 ) into the mechanical formula;
Including,
The second speed (ω ₂ ) is -ω ₁ ,
In the second calculation step,
controlling the speed of the motor with the trapezoidal speed profile;
Collecting torque (T _e ), time (t _k ), and position (θ _k ) data applied to the motor at regular intervals from the start to the end of the speed profile;
Calculating a determinant by substituting the torque (T _e ) and the position (θ _k ) into the mechanical equation; and
Calculating the moment of inertia (J) and the kinetic friction coefficient (B) by a least square method for the matrix equation;
Including,
The mechanical equation is transformed into an equation for the moment of inertia (J) and the coefficient of kinetic friction (B), and then integrated, so that the term for the moment of inertia (J) and the kinetic friction coefficient (B) depends on the driving of the motor. A parameter estimation method for a mechanical model of a servo motor that is deformed as a function of directly calculated speed (ω) and position (θ). delete delete delete According to claim 1,
The speed profile is a parameter for a mechanical model of a servo motor having a shape in which the speed increasing section (T1) and the speed decreasing section (T3) are 65 to 75% of the entire section (T1+T2+T3). estimation method. According to claim 1,
In the second calculation step,
For all times, calculating a quadratic regression equation for the position (θ _k ) based on the last three data; and
Calculating the speed (ω _k ) for each position (θ _k ) by differentiating at the midpoint among the three data; further comprising,
A parameter estimation method for a mechanical model of a servo motor in which the calculated speed (ω _k ) for each position (θ _k ) is substituted into the determinant. According to claim 6,
Calculating the determinant may include transforming the mechanical equation into an equation for the moment of inertia (J) and the coefficient of kinetic friction (B), and then calculating the torque (T _e ), the position (θ _k ) and the angle A parameter estimation method for a mechanical model of a servo motor in which the determinant is calculated by substituting the velocity (ω _k ) for the position (θ _k ). According to claim 7,
The method of estimating parameters for a mechanical model of a servo motor in which the matrix equation is calculated by the following equation.

According to claim 8,
The method of estimating parameters for a mechanical model of a servo motor in which the determinant is calculated as a Moore-Penrose pseudoinverse. According to claim 6,
In the second calculation step,
Calculating the moment of inertia (J) and the kinetic friction coefficient (B) n times;
a first elimination step of averaging the calculated values n times and removing a value having the largest error;
a second elimination step of averaging remaining values after the first elimination step and removing a value having the smallest error;
repeating the first removing step and the second removing step m times; and
Calculating final values of the moment of inertia (J) and the coefficient of kinetic friction (B) by averaging the remaining values after the repeating step;
Parameter estimation method for the mechanical model of the servo motor further comprising. A control system having a Kalman filter using parameters for a mechanical model of a servo motor estimated by the method according to any one of claims 1 and 5 to 10,
The Kalman filter estimates the speed of the motor, but a motor control system having a Kalman filter for estimating the speed of the motor using the mechanical and mechanical model parameters as a predictive model.

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