KR20200007527A - Robust input shaping commands based on linear features for ramped actuator - Google Patents

Abstract

The present invention relates to a linear-based robust input molding machine for a lamp type actuator, which increases robustness by increasing the performance of an input molding machine. According to the present invention, an impulse time for reducing residual vibration during a movement of a flexible system is calculated to be used in an input command for the movement of the flexible system so as to reduce the residual vibration.

Description

Robust Input Molding Machine Based on Ramp-Type Driver {ROBUST INPUT SHAPING COMMANDS BASED ON LINEAR FEATURES FOR RAMPED ACTUATOR}

The present invention relates to a linear-based robust input molding machine for a ramp-type driver, and more particularly, when the linear-based input molding machine is applied to a ramp-type driver, the occurrence of residual displacement is minimized and the performance of the input molding machine is minimized. The present invention relates to a linear-based robust input molding machine for a ramp-type driver that increases the robustness by increasing.

Since flexible systems have various effects such as productivity and safety in industrial sites, control of movement and location of these flexible systems is very important to increase work efficiency in industrial sites.

The input molding machine using the input molding control method is an effective means to reduce the displacement of the object and the displacement after the movement is completed, thereby reducing the residual displacement generated in the flexible system. However, due to various external factors in the industrial field, there is a problem in that residual displacement reduction performance due to system modeling error is reduced. In addition, when acceleration exceeding the performance of the motor or the motor driver is applied, the motor cannot respond to the trajectory, and when used in such a state, the acceleration of the motor or the motor driver is poor, and thus the acceleration is often limited.

In the industrial field, studies have been conducted on robust input molding machines for system errors. Singer developed three impulse type Zero Vibration Derivate (ZVD) input molding machines by using the derivative of the natural frequency of Zero Vibration (ZV) input molding machine.

In addition, Singhose, Seering and Singer presented a robust Extra Insensitivity (EI) input molding machine that allows constant displacement in the form of humps using a vector diagram approach by representing the residual displacement equation as a residual displacement vector. In the case of the EI input molding machine, instead of allowing the desired residual displacement, the robustness is improved, which is more robust against the system modeling error than the conventional ZVD input molding machine.

However, the EI input molding machine and the ZVD input molding machine both show robustness against the system modeling error, but the acceleration limitation is not taken into account, so there is a problem in that residual displacement performance does not appear as expected when used in an industrial site.

Input molding machine and input molding method applicable to Korea Patent Publication No. 10-2011-0132640

The present invention has been made to solve the above problems, the residual displacement occurs when applying the linear system-based input molding machine to the lamp-type driver to generate a robust command for the lamp-type driver based on the linear system The linear-based robustness of the ramp-type actuators with improved residual efficiency is minimized by the ramp-step function and phasor vector diagram to approximate the dynamic response of the ramp-type actuators. The purpose is to provide an input molding machine.

,

,

를 구하고, 상기 세 벡터를 이용하여 상기 유연시스템의 운동 중의 잔류 진동 감소를 위한 임펄스의 시간 t₂와 t₃를 다음과 같은 수학식으로 계산하며,The linear-based robust input molding machine for the ramp-type actuator according to the present invention uses the equations modeling the load on the pendulum system in the motion of the flexible system for the residual displacement in the form of a phasor vector. Vector using displacement vector

,

,

Using the three vectors, calculate the time t ₂ and t ₃ of the impulse for reducing the residual vibration during the movement of the flexible system by the following equation,

In order to reduce the residual vibration after the movement of the flexible system as described above, t ₅ , t ₆ for the stop motion is obtained by the following equation,

[In the above equation,

: 펜듈럼 시스템의 고유진동수

: Natural frequency of the pendulum system

: 구동기의 최대 속도가 될 수 있는 원하는 속도

Is the desired speed that can be the maximum speed of the actuator

: 속도함수를 정의하는 가속도

Is the acceleration that defines the velocity function.

:

로 펄스 지속시간(pulse duration)을 의미하는 것으로 시작동작의 지속시간을 의미함]

:

This means the pulse duration, which means the duration of the start operation.]

The t _2, t _3, t ₅ , and t ₆ are used to reduce the residual vibration by using the input command for the movement of the flexible system with limited acceleration and transient displacement.

와 같이 요약되는 ZVD(Zero Vibration Derivate) 입력성형기를 기반으로 한 것으로, 상기 수학식에서 T는 유연시스템의 주기,

이고, ζ=0인 경우에 대하여 설계한 것이 바람직하다.The input molding machine of the present invention

It is based on ZVD (Zero Vibration Derivate) input molding machine, which is summarized as follows.

It is preferable to design for the case of? = 0.

,

,

를 구하고,The linear-based robust input molding machine for the ramp-type actuator according to the present invention is a residual represented in the form of a phasor vector using an equation modeling the load on the pendulum system in the motion of the flexible system. Vector using displacement vector for displacement

,

,

Obtaining

Using the three vectors, the time t ₂ and t ₃ of the impulse for the starting motion for reducing the residual vibration during the movement of the flexible system are calculated by the following equation,

,

,

In order to reduce the residual vibration after the movement of the flexible system as described above, t ₅ , t ₆ for the stop motion is obtained by the following equation,

[In the above equation,

: 펜듈럼 시스템의 고유진동수

: Natural frequency of the pendulum system

: 구동기의 최대 속도가 될 수 있는 원하는 속도

Is the desired speed that can be the maximum speed of the actuator

: 속도함수를 정의하는 가속도

Is the acceleration that defines the velocity function.

:

로 펄스 지속시간(pulse duration)을 의미하는 것으로 시작동작의 지속시간을 의미함]

:

This means the pulse duration, which means the duration of the start operation.]

The t _2, t _3, t ₅ , and t ₆ are used to reduce the residual vibration by using the input command for the movement of the flexible system with limited acceleration and transient displacement.

와 같이 요약되는 The input molding machine

As summarized

는 입력성형방법이 적용되지 않은 unshaped에서 잔류변위 크기의 퍼센트(%)이며, ζ=0인 경우에 대하여 설계한 것이 바람직하다.Based on EI (Extra Insensitivity) input molding machine, T is the period of the flexible system,

Is the percentage (%) of residual displacement in the unshaped where the input molding method is not applied, and it is preferable to design for the case of ζ = 0.

The linear-based robust input molding machine for the lamp-type driver of the present invention increases the work efficiency in the industrial field by minimizing the occurrence of residual displacement through the application of a simple equation when the linear-based input molding machine is applied to the lamp-type driver. There is an advantage to implement a flexible system that increases the control performance for movement and position.

와

에 대하여 제1 입력성형기와 ZVD 입력성형기의 잔류변위 저감 성능을 비교한 그림,
도 11은

와

에 대하여 제1 입력성형기와 ZVD 입력성형기의 잔류변위 저감 성능을 비교한 그림,
도 12는 가속도

와 줄 길이 L 에 대하여 제1 입력성형기와 ZVD 입력성형기의 강건성을 비교한 그림,
도 13은 펄스 지속시간에 따른 EI 입력성형기와 제2 입력성형기의 명령 완성도를 표시한 그래프,
도 14는 줄 길이에 따른 제2 입력성형기와 EI 입력성형기의 간섭 커맨드와 긴 커맨드에서 잔류변위를 표시한 그래프,
도 15는

와

에 따른 제2 입력성형기와 EI 입력성형기의 잔류변위의 차이를 표시한 그래프,
도 16은

와

에 따른 제2 입력성형기와 EI 입력성형기의 잔류변위의 차이를 표시한 그래프,
도 17은 제2 입력성형기의 줄길이와 가속도에 대한 강건성을 표시한 그림,
도 18은 실험 검증을 위한 시뮬레이션에 적용된 미니 브리지 크레인의 일 실시예의 사시도,
도 19는 도 18의 미니 브리지 크레인의 하드웨어의 구성을 개념적으로 표시한 구성도,
도 20은 입력한 명령과 미니 브리지 크레인에서 실행하는 명령의 오차를 표시한 그래프,
도 21은 ZVD 입력성형기와 제1 입력성형기, EI 입력성형기와 제2 입력성형기의 페이로드 편향응답을 표시한 그래프,
도 22는 줄 길이(L)에 대한 시스템 모델링 오차에 대한 강건도 곡선을 표시한 그림,
도 23은 가속도에 따른 시스템 모델링 오차에 대한 강건성을 표시한 그림이다.1 is a graph showing the performance comparison when a ZVD input molding machine is applied to an ideal driver and a driver with limited acceleration and deceleration.
2 is a conceptual diagram illustrating a simplified command procedure by converting the original command procedure and an input command in a ramp form;
3 is a diagram showing the concept of a pendulum system,
4 is a view showing a range of a start command and a segmented profile;
5 is a graph showing the effect of the impulse size on the residual displacement of the ZVD input molding machine and the EI input molding machine,
6 is a diagram showing a vector diagram of a first input molding machine;
7 is a diagram showing a vector diagram of a second input molding machine,
8 is a graph showing the command completion of the ZVD input molding machine and the first input molding machine according to the pulse duration;
9 is a graph showing residual displacements in long commands of a first input molding machine and a ZVD input molding machine according to a row length;
10 is

Wow

Figure 1 compares the residual displacement reduction performance of the first input molding machine and the ZVD input molding machine.
11 is

Wow

Figure 1 compares the residual displacement reduction performance of the first input molding machine and the ZVD input molding machine.
12 is the acceleration

Figure 1 compares the robustness of the first input molding machine and ZVD input molding machine for
FIG. 13 is a graph showing the command completion of the EI input molding machine and the second input molding machine according to the pulse duration;
14 is a graph showing residual displacements in the long command and the interference command of the second input molding machine and the EI input molding machine according to the line length;
15 is

Wow

Graph showing the difference between the residual displacement of the second input molding machine and the EI input molding machine according to
16 is

Wow

Graph showing the difference between the residual displacement of the second input molding machine and the EI input molding machine according to
17 is a diagram showing the robustness to the string length and acceleration of the second input molding machine,
18 is a perspective view of one embodiment of a mini bridge crane applied to a simulation for experimental verification;
19 is a configuration diagram conceptually showing a configuration of hardware of the mini bridge crane of FIG. 18;
20 is a graph showing the error between the input command and the command executed in the mini bridge crane,
21 is a graph showing payload deflection responses of a ZVD input molding machine, a first input molding machine, an EI input molding machine, and a second input molding machine;
FIG. 22 is a plot showing the robustness curve for system modeling error for line length (L),
23 is a diagram showing the robustness to the system modeling error according to the acceleration.

Hereinafter, a linear-based robust input molding machine for a ramp-type driver according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings. As the inventive concept allows for various changes and numerous embodiments, particular embodiments will be illustrated in the drawings and described in detail in the text. However, this is not intended to limit the present invention to a specific disclosure form, it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention. In describing the drawings, similar reference numerals are used for similar elements. In the accompanying drawings, the dimensions of the structures are shown in an enlarged scale than actual for clarity of the invention.

Terms such as first and second may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as the second component, and similarly, the second component may also be referred to as the first component.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, the terms "comprise" or "have" are intended to indicate that there is a feature, number, step, action, component, part, or combination thereof described on the specification, and one or more other features. It is to be understood that the present invention does not exclude the possibility of the presence or the addition of numbers, steps, operations, components, parts, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art, and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

The linear-based robust input molding machine for the lamp-type driver of the present invention can be divided into a first embodiment based on a ZVD input molding machine and a second embodiment based on an EI input molding machine.

Hereinafter, the linear-based robust input molding machine for the ramp-type driver of the first embodiment based on the ZVD input molding machine and the linear-based robust input molding machine for the ramp-type driver of the second embodiment based on the EI input molding machine will be described. This is referred to as an input molding machine.

As described above, the first input molding machine is developed based on the ZVD input molding machine, and the ZVD input molding machine is briefly summarized as follows.

이다. 이때, ζ=0인 경우에 대하여 제1 입력성형기를 설계하였다. ZVD 입력성형기는 계단 입력과 임펄스 시퀀스의 합성을 통해 세 개의 계단 입력 명령 프로파일로 나타나며, 도 1의 이상적인 구동기(Ideal Actuator)를 갖춘 유연 시스템에 적용되는 경우 잔류변위의 크기를 0으로 만든다. Where T is the cycle of the flexible system,

to be. At this time, the first input molding machine was designed for the case of ζ = 0. The ZVD input molding machine is represented by three step input command profiles through the combination of step input and impulse sequences, and the residual displacement is zero when applied to the flexible system with the ideal actuator of FIG.

In this case, when the input command of the ZVD input molding machine is applied to a flexible system having an acceleration limit / acceleration limited ramp type actuator (Acceleration Limit Actuator), as shown in FIG. 1, the input molding control performance is degraded due to the distorted command. Therefore, a robust input profile command is needed, considering that the acceleration and deceleration of the ramp type driver are not the same.

The instruction design procedure can be simplified by converting it into an input instruction in the form of a ramp as shown in FIG. The formula of the input molding machine that limits the acceleration can be used while satisfying the condition of the following equation (2).

와

는 임펄스의 크기와 임펄스 시간,

는 원하는 속도

는 가속도,

는 감가속도이다. here

Wow

Impulse size and impulse time,

Want speed

Is the acceleration,

Is deceleration.

When the condition of Equation (2) is satisfied in consideration of the ideal ZVD input molding machine and the cycle of the system, a phaser vector diagram of a pendulum system, which is a typical flexible system, is maintained while maintaining the generality of the input molding technology shown in FIG. A phasor vector diagram can be used to present an analytical approach.

The equation modeling the load on a pendulum system is shown in equation (3).

로 속도입력 명령이고, L은 시스템 줄 길이, 그리고 g는 중력가속도를 말한다. 이 때

를 미소 각도로 가정하면, 식 (3)은 라플라스 변환하여 다음과 같이 표현할 수 있다.here

Is the speed input command, L is the system string length, and g is the acceleration of gravity. At this time

Assuming a small angle, Equation (3) can be expressed as Laplace transform as follows.

은 펜듈럼 시스템의 고유진동수이고,

는

를 라플라스 변환한 것이다. here

Is the natural frequency of the pendulum system,

Is

Is a Laplace transform.

는 페이저(phasor) 형태로 나타내기 위해 시스템 입력

와 사인 입력(sine input)형태로 나타내면 다음과 같다.Output of the system

Inputs the system to represent a phasor

And in the form of sine input:

The key to the input molding method in residual vibration is to express the steady-state response from Eq. (5) as

의 크기는 0이어야 한다. 따라서

은 도 4의 (b)와 같이 입력 성형기의 임펄스 시간에 대한 분할된 명령에 의해 결정될 수 있다. 전체속도 프로파일은 다음과 같이 표현된다.If there is no residual vibration, in (6)

The size of must be zero. therefore

Can be determined by the divided command for the impulse time of the input molding machine as shown in FIG. The overall velocity profile is expressed as

는 도 4의 각 영역의 함수이며, 구동기의 불균등 가속 및 감가속을 다음과 같이 처리하는 램프 형태의 함수로 근사화된다.here

Is a function of each region of FIG. 4 and is approximated as a ramp-shaped function that processes the unequal acceleration and deceleration of the driver as follows.

는 가속도 또는 감가속도에 따라 결정되고

는 구동기의 최대 속도가 될 수 있는 원하는 속도이다.Speed technology

Depends on acceleration or deceleration

Is the desired speed which can be the maximum speed of the driver.

The Laplace transform of Equation (8) is expressed as the magnitude and phase angle of the vector as follows.

Using the steady-state response of Equation (6) and the magnitude and phase angle of the vector of the input command in ramp form, each region intensity vector in FIG. 4 is obtained as follows.

에 대하여 미분하였을 때, 음형태(implicit form)로 나타나 적절한 해결책(exact solution)을 구할 수 없다.In designing the first input molding machine

When differentiated for, it appears in implicit form and no appropriate solution can be found.

5 shows the effect of the impulse size on the residual displacement of the ZVD input molding machine and the EI input molding machine, which is a robust input molding controller.

In the absence of a system modeling error, residual displacement is allowed for an EI input molding machine but zero residual displacement for a ZVD input molding machine.

Since the residual displacement of the first input molding machine of this embodiment should be 0, A ₁ , A ₂ , and A ₃ are assumed to be the size of the existing ZVD input molding machine.

Normalizing each instruction vector with respect to equation (11), the phasor vector is expressed as follows.

here

The normalized pager vector expression above can be used in a vector diagram.

벡터와 점선

벡터의 사잇각을 α,

벡터와 점선

벡터의 사잇각을 β라고 할 때 코사인 법칙(cosine law)을 활용하여 결정된 α,β는 다음과 같다.The magnitude of the residual displacement of the first input molding machine for the ramp type driver is determined by the sum of the three vectors in FIG. In Figure 6

Vector and dotted line

The angle of the vector is α,

Vector and dotted line

When the vector angle of the vector is β, α, β determined by using the cosine law is as follows.

,

로 나타낼 수 있으며, 이를 이용한 임펄스 시간

와

는 다음과 같이 결정된다.The phase angle of the vector using FIG. 6 and equations 15 and 16dmf is

,

Impulse time

Wow

Is determined as follows.

는 실수가 되어야 하고, cos^-1 함수에 양수가 필요하다.Impulse time

Must be a real number and a positive number is required for the cos ^-1 function.

와

는 다음과 같이 표현된다.The switch time for the stop operation has the same procedure as the start operation, and the sign of the impulse magnitude is changed asymmetrically. For stop motion

Wow

Is expressed as

로 펄스 지속시간(pulse duration)을 의미하며, 시작 동작의 지속시간을 의미한다.here

This means the pulse duration and the duration of the start operation.

In this case, in order to verify the effect of the residual displacement performance of the first input molding machine, the constraint of Equation (24) must be satisfied.

If Eq. (24) is satisfied, the first input molding machine is capable of reducing residual displacement in a flexible system having a lamp-type driver.

Using equations (20) to (23), the first input molding machine for the start and stop commands of the flexible system is expressed as follows.

Equation (25) above is used to generate a ramp-shaped command using a driver with asymmetric acceleration and braking by convolution of a robust input command.

The analysis development procedure of the first input molding machine can be extended to generate various commands with the non-ideal driver.

The second input molding machine was developed based on the EI input molding machine to generate an input molding command with increased robustness instead of allowing residual displacement.

The EI input molding machine is as follows.

은 입력성형방법이 적용되지 않은 unshaped에서의 잔류변위 크기의 퍼센트(%)이다.Where T is the period of the flexible system,

Is the percentage of residual displacement in unshaped that the input molding method is not applied to.

(%) 만큼의 크기를 갖는다. 이때 ζ=0 인 경우에 대한 제2 입력성형기를 설계하였다.The EI input molding machine is represented by three step input command profiles through the convolution of the step input and the impulse sequence to suppress the residual vibration of the ideal flexible system.

It has size as much as (%). At this time, the second input molding machine for the case of ζ = 0.

In the case of the EI input molding machine based on the linear system, similar to the ZVD input molding machine described above, when applied to the ramp type driver, the control performance is degraded due to the distorted command. Therefore, a robust input shape command for the ramp type driver is required.

The command design procedure of the second input molding machine can be simplified by converting it into a ramp type input command similarly to the procedure of the first input molding machine described above.

The formula of the input molding machine that limits the acceleration can be used with satisfying the condition of Equation (2). In consideration of the ideal EI input molding machine and the cycle of the system, an analytic approach can be proposed by utilizing a phasor vector diagram of a pendulum system having a ramp-shaped profile.

Using the equation (6), which is the steady-state response to the pendulum system, and the equation (8), which approximates each area of the velocity profile according to the acceleration limitation as a ramp shape function, the command vector of each area of the second input molding machine is Is obtained together.

In designing the second input molding machine, when it is differentiated with respect to ω, it appears in an implicit form and an appropriate solution cannot be obtained. From Figure 5 it can be seen that the impact of the impulse size of the ZVD and EI input molding machine, a robust input molding controller on the residual displacement.

When there is no system modeling error, residual displacement is allowed for EI input molding machine but zero residual displacement for ZVD input molding machine. Accordingly, since the second input molding machine has a characteristic of allowing residual displacement, A ₁ , A ₂ , and A ₃ are assumed to be the size of the existing EI input molding machine.

Normalizing each instruction vector with respect to equation (27), the phasor vector is expressed as follows.

In the case of the second input molding machine, the input molding machine permits residual displacement and is designed by dividing into three areas in order to express the hump type sensitivity.

일 때, 두 번째는

일 때, 그리고 세 번째는

일 때이다. 첫 번째와 세 번째 영역에서의 잔류변위는 0%이고, 두 번째

영역에서는

%만큼의 잔류변위를 허용한다.at first

When is the second

And the third is

When The residual displacement in the first and third zones is 0%, the second

In the realm

Allow residual displacement by%.

를 가정한다. 위의 정규화된 페이저 벡터

의 크기와 위상각을 이용해 벡터 다이어그램(vector diagram)으로 나타내면 도 7로 나타난다. 여기서 빨간 점선은

, 파랑 점선은

, 그리고 검은색 실선은

을 나타낸다.For the symmetry of the sensitivity curve

Assume Normalized pager vector above

7 is shown as a vector diagram using the magnitude and phase angle of. Where the red dotted line

, Blue dotted line

And the solid black line

Indicates.

일 때는 벡터의 합이 unshaped 잔류 변위의

크기를 가져야 하고,

일 때의 빨간 점선과

일 때의 파란 점선에서는 벡터의 합이 0의 잔류변위를 가져야 한다. The normalized pager vector expression can be used in a vector diagram. Solid black line in FIG.

When the sum of the vectors is the unshaped residual displacement

Should have a size,

When the red dotted line and

In the blue dotted line, the sum of the vectors must have a residual displacement of zero.

을 활용하여 빨간 점선과 파란 점선의 잔류변위를 0으로 만들면 식 (33)의 조건식과 같다. Cosine law and trigonometric formula

If the residual displacements of the red dotted line and the blue dotted line are made to 0 by using the same formula as in (33).

벡터와 이동한

벡터의 사잇각을 a,

벡터와 연장된

벡터의 사잇각을 b라고 할 대, 코사인 법칙을 활용하여 결정된 a, b는 다음과 같다. Similarly, make a triangle using the extension line of black line

Moved with vector

The angle of vector a,

Vector and extended

Assuming that the vector angle of the vector is b, a and b determined using the cosine law are

,

로 나타낼 수 있으며 이를 이용한 임펄스 시간

와

는 다음과 같이 결정된다.7 and phase angles using equations (31) and (32) fmf are

,

Impulse time

Wow

Is determined as follows.

대신 감가속도

를 사용하여 정지동작에 대한 임펄스 시간

와

는 다음과 같이 표현된다.The switch time for the stop operation has the same procedure as the start operation, and the sign of the impulse magnitude is changed asymmetrically. Acceleration in start motion in stop motion

Deceleration instead

Impulse time for stop motion using

Wow

Is expressed as

로 펄스 지속시간(pulse duration)을 의미하며, 시작 동작의 지속시간을 의미한다. 이 때 제2 입력성형기 또한 제1 입력성형기와 마찬가지로 램프 형태의 속도 프로파일의 경사 기울기로 인하여 식 (22)의 제약 조건에서 사용해야 한다. here

This means the pulse duration and the duration of the start operation. At this time, the second input molding machine, like the first input molding machine, should also be used under the constraint of Equation (22) due to the inclination of the ramp profile.

If Eq. (22) is satisfied, the second input molding machine exhibits performance in reducing residual displacement in a flexible system having a lamp-type driver.

Using equations (36) to (39), the second input molding machine for the start and stop commands of the flexible system is expressed as follows.

Equation (40) above is used to generate a ramp-shaped command using a driver with asymmetric acceleration and braking by convolution of a robust input command. The analysis development procedure of the second input molding machine can be extended to generate various commands with the non-ideal driver.

), 줄 길이(

)에 따른 입력성형 커맨드의 완성도와 system modeling error에 대한 강건성에 대하여 평가하였다. The residual displacement reduction performance of the first input molding machine and the second input molding machine described above is a

), Line length (

We evaluated the completion of input shaping command and robustness against system modeling error.

The control effect of the first input molding machine and the second input molding machine was compared with the conventional ZVD input molding machine and the EI input molding machine using the pendulum system of FIG. 3. Numerical simulation (MATLAB) was used as a numerical simulation for this, and the parameter values necessary for designing the rice cake mold were set as shown in Table 1.

The first input molding machine uses the parameters of Table 1 to evaluate the completeness of the instructions generated due to the ramp shape in FIGS. 8 and 9.

)에 따른 ZVD 입력성형기와 제1 입력성형기의 커맨드(command)의 완성도를 나타낸다 입력성형 제어 방법은 지속시간(

)에 따라 3개의 영역으로 나눠진다. 여기서 A 영역은 짧은 커맨드(short command)로 램프 형태의 명령이 완성되기 전에 지속시간(

)가 작용하여 약간의 잔류변위가 발생한다. B 영역은 간섭 커맨드(interference command)로 짧은 커맨드(short command)와 긴 커맨드(long command) 사이에서 지속시간(

)가 작용하여 잔류변위가 가장 크게 나타난다. C 영역은 긴 커맨드(long command)로 램프 형태의 명령이 완성되며 제1 입력성형기가 ZVD 입력성형기보다 우수한 성능을 보인다.8 shows the pulse duration (

The ZVD input molding machine and the command of the first input molding machine according to the command.

Are divided into three areas. In this case, the A area is a short command, and a duration of time before the ramp type command is completed.

), Some residual displacement occurs. The area B is an interference command, and the duration (between short and long commands)

) Has the largest residual displacement. In the C region, a ramp-shaped command is completed by a long command, and the first input molding machine performs better than the ZVD input molding machine.

에 따른 제1 입력성형기와 ZVD 입력성형기의 긴 커맨드(long command)에서 잔류변위를 나타낸다. 전반적으로 램프형 구동기에 대한 제1 입력성형기의 경우 0의 잔류변위를 나타내며, 긴 커맨드의 경우 가속도가 제한된 램프 형태의 명령이 완성되는 영역으로 이상적인 ZVD 입력성형기의 경우 불규칙적으로 0.1cm ~ 0.4cm의 잔류변위가 나타난다. 9 is the row length

Residual displacement in the long command of the first input molding machine and ZVD input molding machine according to In general, the first input molding machine for the ramp-type driver shows a residual displacement of 0. In the case of a long command, a ramp-type command with limited acceleration is completed. Residual displacement appears.

와

에 대하여 제1 입력성형기와 ZVD 입력성형기의 잔류변위 저감 성능을 비교한 것이다.

와

의 범위를 0.3~5m/sec² 영역에서 진행하였다. 10 is

Wow

The residual displacement reduction performance of the first input molding machine and the ZVD input molding machine is compared.

Wow

The range of was advanced in the 0.3 ~ 5m / sec ² area.

와

가 같을 경우 ZVD 입력성형기와 제1 입력성형기의 임펄스의 시간이 동일한 값을 갖게 되어 잔류변위가 발생하지 않는다.In the case of the first input molding machine, the residual displacement in the entire area is 0, but in the case of the ZVD input molding machine, the displacement is 0 to 0.73 cm on the graph.

Wow

If is equal to, the impulse time of the ZVD input molding machine and the first input molding machine has the same value, so that no residual displacement occurs.

와

에 대하여 제1 입력성형기와 ZVD 입력성형기의 잔류변위 저감 성능을 비교한 것이다.

의 범위를 0.3~5m/sec²,

의 범위를 2~5(sec)로 설정하여 진행하였다.11 is

Wow

The residual displacement reduction performance of the first input molding machine and the ZVD input molding machine is compared.

The range of 0.3 ~ 5m / sec ² ,

The range was set to 2 to 5 (sec) to proceed.

In the case of the first input molding machine, the residual displacement in the entire area is 0, but in the case of the ZVD input molding machine, the displacement is about 0.2 to 1 cm on the graph.

값에따라 잔류변위의 크기가 주기적인 특성을 보이는 반면 제1 입력성형기는 긴 커맨드(long command)로 설계되어 잔류변위가 0으로 나타난다.ZVD input molding machine

While the magnitude of the residual displacement shows periodic characteristics according to the value, the first input molding machine is designed as a long command so that the residual displacement is zero.

와 줄길이 L에 대하여 제1 입력성형기와 ZVD 입력성형기의 강건성을 나타낸다. 변수 설정은 표 1과 동일하며,

을 1, L을 0.8로 설정하고 진행하였다. 제1 입력성형기의 경우 전체적인 영역에서의 잔류 변위가 ZVD 입력성형기보다 낮게 나타나고 있다. 또한

과,

의 값이 1일때, 잔류변위의 크기가 0으로 낮게 나타나고 system modeling error에 대한 강건함이 나타난다.12 is the acceleration

The robustness of the first input molding machine and the ZVD input molding machine is shown with respect to and the length L. Variable settings are the same as in Table 1.

Proceeded with 1, L set to 0.8. In the case of the first input molding machine, the residual displacement in the whole area is lower than that of the ZVD input molding machine. Also

and,

When the value of 1 is 1, the residual displacement size is low as 0 and robust to the system modeling error.

)에 따른 EI 입력성형기와 제2 입력성형기의 커맨드의 완성도를 나타낸다. 여기서 A 영역은 짧은 커맨드, B 영역은 간섭 커맨드(interference command)로 잔류변위가 가장 크게 나타난다. C 영역은 긴 커맨드로 제2 입력성형기가 EI 입력성형기보다 우수한 성능을 보여준다. 허용한 잔류 오차 범위는 5%이며, 검은색 점선으로 표시되었다. The second input molding machine uses the parameters of Table 1 to evaluate the completeness of the instructions generated due to the ramp shapes of FIGS. 13 and 14. 13 is the pulse duration (

) Shows the completeness of the commands of the EI input molding machine and the second input molding machine. Here, the area A is the short command and the area B is the interference command, which shows the largest residual displacement. The C region is a long command, and the second input molding machine shows better performance than the EI input molding machine. The allowable residual error range is 5%, indicated by black dotted lines.

)에 따른 제2 입력성형기와 EI 입력성형기의 간섭 커맨드와 긴 커맨드(long command)에서 잔류변위를 나타낸다. B 영역은 간섭 커맨드로서, 가속도가 제한된 램프 형태의 명령이 완성되지 않아 EI 입력성형기의 경우 큰 잔류변위가 나타난다. 또한 제2 입력성형기의 경우 5%의 허용 잔류변위를 1% 정도 오버슈트(overshoot)되는 현상이 나타난다. C 영역은 긴 커맨드로서, 가속도가 제한된 램프 형태의 명령이 완성되는 영역으로 이상적인 EI 입력성형기의 경우 불규칙적으로 잔류변위가 나타난다. 반면 제2 입력성형기의 경우 전반적으로 허용 잔류변위의 크기가 동일한 잔류변위가 나타난다. 14 shows the line length (

Residual displacement in the interference command and the long command of the second input molding machine and the EI input molding machine according to Area B is an interference command, and a ramp-type command with limited acceleration is not completed, so a large residual displacement appears in an EI input molding machine. In addition, in the case of the second input molding machine, a phenomenon of overshooting the allowable residual displacement of 5% by about 1% appears. The C region is a long command, and is a region in which a ramp-type command with limited acceleration is completed. In the case of an ideal EI input molding machine, the residual displacement is irregular. On the other hand, in the case of the second input molding machine, the residual displacement having the same magnitude of the allowable residual displacement appears in general.

와 감가속도

에 따른 제2 입력성형기와 EI 입력성형기의 차이를 보여준다. 가속도와 감가속도의 범위는 0.3 ~5m/s²로 설정하였으며, 제2 입력성형기의 경우 전체적으로 0.01cm의 잔류변위를 허용하지만 EI 입력성형기의 경우 0.17cm의 잔류변위가 나타났다. 이때 가속도와 감가속도의 크기가 같으면 램프형 구동기에 대한 제2 입력성형기와 EI 입력성형기의 잔류변위 저감 성능이 같아진다. 또한 가속도

와 감가속도

의 값이 커질수록 선형 구동기와 유사한 구동을 하기 때문에 오차가 감소함에 따라 잔류변위 자체도 줄어든다. 따라서 램프형 구동기에 대한 설계시 가속도와 감가속도의 크기를 고려해야 한다. 15 acceleration

And deceleration

Shows the difference between the second input molding machine and the EI input molding machine. The range of acceleration and deceleration was set at 0.3 ~ 5m / s ² , and the residual displacement of 0.01cm was allowed for the second input molding machine, but 0.17cm for the EI input molding machine. At this time, if the magnitude of acceleration and deceleration is the same, the residual displacement reduction performance of the second input molding machine and the EI input molding machine for the ramp driver is the same. Also acceleration

And deceleration

As the value of is increased, the residual displacement itself decreases as the error decreases because the driving is similar to that of the linear driver. Therefore, the magnitude of acceleration and deceleration should be considered when designing a lamp-type actuator.

와 지속시간

에 따른 제2 입력성형기와 EI 입력성형기의 차이를 보여준다.

는 0.5 ~3m/s² ,

는 2~5(sec)로 시뮬레이션을 진행하였다. 특성상 잔류오차를 허용하지만 EI 입력성형기의 경우 제2 입력성형기에 비해 잔류 오차의 크기가 미세하게 높으며 가속도

가 낮은 구간에서는 잔류변위의 크기가 0.25cm 가량 증가하고 가속도의 크기가 클수록 선형 구동기와 유사한 구동을 하기 때문에 오차가 더욱 줄어든다.16 is the acceleration

And duration

Shows the difference between the second input molding machine and the EI input molding machine.

Is 0.5 to 3 m / s ² ,

Was simulated with 2 to 5 (sec). Due to the nature, residual error is allowed, but the EI input molding machine has a slightly higher residual error and acceleration than the second input molding machine.

In the low section, the residual displacement increases by about 0.25cm, and the larger the magnitude of the acceleration, the more similar the driving of the linear driver, the error is reduced.

과 가속도

에 대한 강건성을 보여주는 그림으로서, 줄길이는 0.8m, 가속도는 1m/s²로 설정하였다.17 is the length of the line

And acceleration

As a figure showing the robustness, the string length is set to 0.8m and the acceleration is set to 1m / s ² .

In the case of the second input molding machine, the size of the residual displacement increased when the error of the acceleration exceeded the set acceleration while maintaining the shape of the hump shape. In the case of the EI input molding machine, the shape of the hump does not appear and the residual displacement has a size of 0.02.

As a result of the numerical simulation, it was confirmed that the first input molding machine and the second input molding machine are more robust than the ZVD input molding machine and the EI input molding machine, and the residual displacement control performance is increased.

In addition, to verify the performance of the first input molding machine and the second input molding machine of the present invention, the experimental verification was performed using the mini-bridge crane as shown in FIG.

19 shows the hardware and software components constituting the mini bridge crane utilized for experimental verification. In a hardware component, a programmable logic controller (PLC) is connected to a computer by a wireless local area network to perform the proposed algorithm, and the speed command generated by the PLC is sent to a bridge, trolley motor drive. . The drive uses the command coming from the PLC as the speed setting point of the motor. The motor drive uses a synchronous AC motor and consists of a communication module and control driver for the motor. The software components CFC, SCL and WinCC software are used in the system operating program for uploading and downloading experimental data. The VS 720 family of vision sensors is a vision program written through Spectation software that is used to measure the magnitude of payload vibrations.

The pi gain and acceleration and braking are adjusted in the motor control driver to track the command as accurately as possible considering the imbalance acceleration and braking of the actuator.

In this performance evaluation, we set the system to p gain of 0.25 and i gain of 10ms.

,

,

,

,

그리고

로 수치적 성능평가 때와 비슷하게 설정하였다.20 shows that the error between the command entered and the command executed in the actual mini bridge crane is within the range of ± 2cm / s ² . The design parameters of the first input molding machine and the second input molding machine

,

,

,

,

And

This is similar to the numerical performance evaluation.

The first input molding machine and the second input molding machine were experimentally verified based on the change of molding machine parameters and residual deflection using a mini bridge crane.

With respect to the accuracy of the speed command, it can be understood from FIG. 21 that the error of the speed command generated by the experimental apparatus affects the residual displacement. As shown in FIG. 21, the time response of the first input molding machine shows better performance in reducing residual displacement than the ZVD input molding machine as shown in FIG. 21.

In the case of the first input molding machine, the magnitude of the residual displacement is generally close to zero when compared to the ZVD input molding machine, and a part with a slight error occurs according to the velocity error of FIG. 20. In case of ZVD input molding machine, residual displacement of amplitude about 1.2cm appears periodically.

In the case of the second input molding machine of FIG. 21, there are some errors in allowing the residual displacement. However, the second input molding machine is close to the size of the designed allowable residual displacement.

,

,

,

,

로 설계하였다. FIG. 22 is a sensitivity curve for system modeling error of row length L. FIG. The design variables for the experiment

,

,

,

,

Designed as.

크기 만큼 잔류변위가 나타난다. 전체적으로 제1 입력성형기와 제2 입력성형기가 ZVD 입력성형기와, EI 입력성형기보다 강건함을 보인다.Overall, the simulation results and some errors occur due to the initial speed error of FIG. 21 and the external environment during the experiment. Experimental results are averaged data from a number of experiments. In case of EI input molding machine, it is out of the designed allowable residual displacement and the size of hump type is small. In most system modeling errors of the ZVD input molding machine, the residual displacement is higher than that of the first input molding machine. However, the magnitude of the residual displacement is 0, and the allowable

Residual displacement appears by magnitude. Overall, the first input molding machine and the second input molding machine are more robust than the ZVD input molding machine and the EI input molding machine.

에 따른 시스템 모델링 오차에 대한 강건성을 나타낸 것이다. 실험시 변수는

,

,

,

,

로 설계하였다. 실험 결과는 다수의 실험을 통한 평균적인 데이터이다.23 is an acceleration that is one of the main variables of the ramp-type driver

It shows the robustness against system modeling error. Variables in the experiment

,

,

,

,

Designed as. Experimental results are averaged data from a number of experiments.

ZVD input molding machine and EI input molding machine are almost unaffected by the residual displacement due to acceleration, and overall error is slightly different from the simulation result due to the initial speed error of Fig. 21 and the external environment during the experiment, but similar residual displacement is maintained. It is.

일 때, 잔류변위가 0이어야 하지만 약간의 오차가 발생하며 이를 기준으로 점점 시스템 모델링 오차의 변화에 따라 잔류 변위가 발생한다. 실험결과는 전반적으로 0.1cm의 크기가 나타난다. 제2 입력성형기의 경우

만큼의 잔류변위를 허용함으로 0.3cm의 크기가 발생하며, 전반적으로 수치적 시뮬레이션과 실험적 시뮬레이션 결과가 크게 다르지 않음을 확인할 수 있다.The ZVD input molding machine generally has a residual displacement of 0.2 cm and the EI input molding machine generally has a residual displacement of 0.3 to 0.4 cm.

In this case, the residual displacement should be 0, but a slight error occurs. Based on this, the residual displacement gradually occurs as the system modeling error changes. Experimental results show that the overall size is 0.1cm. In case of 2nd input molding machine

As the residual displacement is allowed, the size of 0.3cm is generated, and it can be seen that the numerical and experimental simulation results are not significantly different.

The description of the presented embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the scope of the invention. Thus, the present invention should not be limited to the embodiments set forth herein but should be construed in the broadest scope consistent with the principles and novel features set forth herein.

Claims (4)

Vector using displacement vectors for residual displacements in the form of phasor vectors using equations modeling the loads on the pendulum system in the motion of the flexible system

,

,

Obtaining
Using the three vectors, the time t ₂ and t ₃ of the impulse for reducing the residual vibration during the movement of the flexible system are calculated by the following equation,

In order to reduce the residual vibration after the movement of the flexible system as described above, t ₅ , t ₆ for the stop motion is obtained by the following equation,

[In the above equation,

: Natural frequency of the pendulum system

Is the desired speed that can be the maximum speed of the actuator

Is the acceleration that defines the velocity function.

:

This means the pulse duration, which means the duration of the start operation.]
The linear-based robustness of the ramp-type actuator is characterized by reducing the residual vibration by using the t _2, t _3, t ₅ , t ₆ as an input command for the movement of the flexible system with limited acceleration and transient displacement. Input molding machine.
The method of claim 1,

As summarized
Based on Zero Vibration Derivate (ZVD) input molding machine,
In the above equation, T is the period of the flexible system,

And a linear input robust input molding machine for a ramp type driver, which is designed for the case of ζ = 0.
Vector using displacement vectors for residual displacements in the form of phasor vectors using equations modeling the loads on the pendulum system in the motion of the flexible system

,

,

Obtaining
Using the three vectors, the time t ₂ and t ₃ of the impulse for the starting motion for reducing the residual vibration during the movement of the flexible system are calculated by the following equation,

,
In order to reduce the residual vibration after the movement of the flexible system as described above, t ₅ , t ₆ for the stop motion is obtained by the following equation,

[In the above equation,

: Natural frequency of the pendulum system

Is the desired speed that can be the maximum speed of the actuator

Is the acceleration that defines the velocity function.

:

This means the pulse duration, which means the duration of the start operation.]
The linear-based robustness of the ramp-type actuator is characterized by reducing the residual vibration by using the t _2, t _3, t ₅ , t ₆ as an input command for the movement of the flexible system with limited acceleration and transient displacement. Input molding machine.
The method of claim 3, wherein

As summarized
Based on the Extra Insensitivity (EI) input molding machine,
In the above equation, T is the period of the flexible system,

Is a percentage (%) of the residual displacement size in the unshaped to which the input molding method is not applied, and is a linear-based robust input molding machine for a ramp type driver, which is designed for the case of ζ = 0.

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