KR101380791B1 - Method for compensating friction of stabilization controller using reference angular velocity trajectory - Google Patents

Abstract

The specification relates to a friction compensating method using a standard angular speed trajectory of a stabilization controller which is loaded in all kinds of platforms and compensates disturbance and traces, and stabilizes an unknown moving object. In case of the friction compensating method using the standard angular speed trajectory of the stabilization controller which is loaded in a platform whereby there is disturbance in roll/pitch/yaw and traces and stabilizes a moving object; the friction compensating method using the standard angular speed trajectory of the stabilization controller according to the embodiment disclosed in the specification comprises: a step (1) of calculating a standard angular speed trajectory of an azimuth; a step (2) of calculating a standard angular speed trajectory of a high angle; a step (3) of performing friction compensation of the azimuth using the standard angular speed trajectory of the azimuth; and a step (4) of performing friction compensation to the high angle using the standard angular speed trajectory of the high angle. [Reference numerals] (AA) Center of gravity of platform; (BB) Platform flat surface; (CC) Blow system; (d_1) Yaw; (d_2) Pitch; (d_3) Roll; (DD) Target distance; (EE) Target; (x_3) Azimuth axis; (x_G) North; (y_G) East; (z_6) High angle axis; (z_G) Top

Description

Friction Compensation Method Using the Reference Angular Velocity Trajectory of Stabilization Controller {METHOD FOR COMPENSATING FRICTION OF STABILIZATION CONTROLLER USING REFERENCE ANGULAR VELOCITY TRAJECTORY}

The present specification relates to a friction compensation method using a reference angular velocity trajectory of a stabilization controller.

In general, the frictional force acting on the drive of a mechanical system is one of the most difficult non-linear features in precisely controlling the mechanical system. The friction force can be described primarily as a function of the drive speed of the shaft. The friction force does not exist in the absence of the speed of the drive shaft, but the friction force increases exponentially as the speed begins to develop slightly. At this time, the frictional force increases rapidly in the region where the applied force is almost no speed due to the static friction. When the speed of the drive shaft increases more than the speed range in which the static frictional force acts, the frictional force decreases temporarily. This is called the Stribeck Effect. As the speed of the drive shaft increases further, the frictional force increases in proportion to the speed as it passes through the speed range where the stripback effect is applied. This is a friction force generated by the lubrication present in the drive shaft and is called viscous friction. The strong nonlinear nature of the friction makes it difficult to control the drive shaft precisely, which can lead to poor control accuracy, chattering due to vibration, and even chaos output.

Although methods of compensating the frictional force by mathematically modeling the frictional force and including it in the model-based controller have been studied, it is difficult to model the frictional force accurately mathematically. Due to the presence of the characteristic change, friction compensation is poorly performed under these uncertain conditions.

It is also possible to minimize the above uncertainties and implement friction compensation methods. However, even in this case, in the case of the industrial robot that repeats and traces the previously planned trajectory indefinitely, the friction compensation method according to the characteristics of the trajectory can be applied. However, in the case of a sensor system or a strike system that is mounted on various platforms such as a car, a ship, or an aircraft and tracks unknown targets moving while compensating for disturbances, that is, rolls, pitches, and yaw, the attitude information and target information of the platform Friction compensation becomes very difficult because it needs to control and generate reference angle / angular velocity trajectory in real time using the

An object of the present disclosure is to provide a friction compensation method using a reference angular velocity trajectory in a stabilization controller mounted on various platforms to compensate for disturbance of a platform and to track and stabilize unknown moving targets.

The friction compensation method using the reference angular velocity trajectory of the stabilization controller according to the embodiment disclosed in the present specification uses a reference angular velocity trajectory in a stabilization controller mounted on a platform having a roll / pitch / yaw disturbance to track and stabilize a moving target. A method for compensating friction, the method comprising: (1) calculating a reference angular velocity trajectory of an azimuth; (2) calculating a reference angular velocity trajectory of the elevation; (3) performing azimuth friction compensation using the azimuth reference angular velocity trajectory; (4) performing the elevation friction compensation using the elevation reference angular velocity trajectory.

In the friction compensation method using the reference angular velocity trajectory of the stabilization controller according to the embodiment of the present specification, the azimuth friction compensation is performed using the azimuth reference angular velocity trajectory, and the stabilization controller is performed by performing the high angle friction compensation using the elevation reference angular velocity trajectory. Friction compensation can be performed.

1 is a diagram illustrating a general kinematic structure and coordinate system of a stabilizer driving device mounted on a platform.
2 is an exemplary view showing the uncertainty of the nonlinear frictional force, the invariant frictional characteristic region, the friction compensation torque operating region and the magnitude thereof.
3 is a diagram showing the frictional force characteristics when the friction compensation method is not applied and applied.
4 is a diagram illustrating azimuth control error results when the azimuth friction compensation method is not applied.
5 is a diagram illustrating azimuth control error results when azimuth friction compensation method is applied.
FIG. 6 is a diagram illustrating an elevation control error result when the elevation friction compensation method is not applied. FIG.
7 is a view showing the results of the elevation control error when applying the high-angle friction compensation method.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings, wherein like reference numerals are used to designate identical or similar elements, and redundant description thereof will be omitted. The suffix "module" and " part "for the components used in the following description are given or mixed in consideration of ease of specification, and do not have their own meaning or role. In the following description of the embodiments of the present invention, a detailed description of related arts will be omitted when it is determined that the gist of the embodiments disclosed herein may be blurred. In addition, it should be noted that the attached drawings are only for easy understanding of the embodiments disclosed in the present specification, and should not be construed as limiting the technical idea disclosed in the present specification by the attached drawings.

The present invention proposes a friction compensation method using a reference angular velocity trajectory in a stabilization controller mounted on various platforms to compensate for disturbance of the platform and to track and stabilize unknown moving targets. The stabilization controller controls the azimuth and elevation drive shafts to match the targets that trigger the gaze of the sensor system or the striking system while compensating for disturbances, roll / pitch / yaw, occurring on the platform. Friction compensation torque acts on the azimuth and elevation drive shafts. Since frictional force is mainly a function of the angular velocity of the shaft, a reference angular velocity trajectory is generated and friction compensation is performed based on this.

First, a method of calculating the reference angular velocity trajectory will be described.

1 is a diagram illustrating a general kinematic structure and coordinate system of a stabilizer driving device (controller) mounted on a platform.

은 플랫폼의 요(Yaw)운동,

는 피치(Pitch),

는 롤(Roll)이다. 그리고 각속도인 요 각속도(Yaw rate)는

으로 나타내고, 피치 각속도(Pitch rate)는

으로, 롤 각속도(Roll rate)은

으로 표현한다. 플랫폼의 요, 피치, 롤과 그 속도 값은 오일러 값으로써 플랫폼 장착된 관성항법창치로부터 전송받는다. 관성항법장치는 플랫폼의 무게중심(Center of Gravity)에 위치하며 북쪽을 x, 서쪽을 y, 위쪽을 z방향으로 정한다. 이를 NWU(North West Up) 좌표계라고 정의한다.As shown in FIG. 1, the lower part of the platform plane is a part related to the platform, such as an automobile, a trap or an aircraft, and the upper part of the platform plane is related to a sensor or a striking system, and the azimuth drive axis and the elevation drive axis are shown. It is composed. The rigid body movement of the platform is described in three degrees of freedom.

Is the yaw movement of the platform,

Is the pitch,

Is a roll. And the yaw rate, the angular velocity

Where pitch angular velocity is

Roll rate is

Express as The yaw, pitch, roll and speed values of the platform are transmitted from the platform-mounted inertial navigation instrument as Euler values. The inertial navigation system is located at the center of gravity of the platform and defines the north as x, the west as y, and the upper z direction. This is defined as NWU (North West Up) coordinate system.

만큼 회전 구동한다. 방위각 축으로부터 고각 축까지는 z축 방향으로 거리 d 만큼 이동하고, x축으로 거리 e만큼 이동한다. 그리고 고각 축에서

만큼 회전 구동을 한다. 고각 축으로부터 표적까지는 y축으로 거리 f만큼, 그리고 x축으로 g만큼 이동하면 시선과 표적이 만나게 된다. 여기서

은 방위각 축의 기준 각도이며,

는 고각 축의 기준 각도이다. 이 기준 각도와 각속도로 방위각과 고각축을 구동하였을 때, 표적은 시선 좌표계 L의 x축 선상에 존재한다. 즉 표적을 시선 좌표계의 x축에 위치시키게 되면 플랫폼의 외란을 보상하는 동시에 센서 혹은 타격체계의 시선과 표적이 일치하게 된다.Place the origin of inertial coordinate system G and the origin of platform coordinate system A at the center of gravity of the platform. There is a distance offset from the center of gravity of the platform to the point where the striking system or sensor system is mounted, a distance a in the x-axis and a distance b in the z-axis. And the distance c in the z-axis direction from the mounting point of the striking / sensor system to the azimuth drive shaft. And the azimuth axis

Drive as much rotation. The distance from the azimuth axis to the elevation axis moves by the distance d in the z-axis direction and by the distance e in the x-axis. And at the elevation axis

Rotate as much as you want. Moving from the elevation axis to the target by the distance f in the y-axis and g in the x-axis meets the eye and the target. here

Is the reference angle of the azimuth axis,

Is the reference angle of the elevation axis. When driving the azimuth and elevation axes at this reference angle and angular velocity, the target is on the x-axis line of the visual coordinate system L. In other words, if the target is located on the x-axis of the gaze coordinate system, the disturbance of the platform is compensated for and the line of sight of the sensor or the strike system coincides with the target.

로 나타내는데 고정된 B 좌표계의 위치벡터 P를 이동된 A 좌표계로 변환시키는 역할을 한다. 변환행렬은

행렬을 사용하고 오일러 각을 이용한다. x,y,z축에 대한 각각의 회전 변환 행렬은 수학식 1과 같다.In FIG. 1, the cylindrical axis is a revolute joint and the rectangular parallelepiped is a prismatic joint. In FIG. 1, there are five rotational axes and one linear axis, and three rotational axes below the platform mean yaw / pitch / roll of the platform, and two rotational axes existing on the upper part of the platform plane are azimuth and elevation. And one linear axis is the distance g from the visual coordinate system to the target. The transformation matrix for each coordinate system

It converts the position vector P of the fixed B coordinate system into the moved A coordinate system. The transformation matrix is

Use matrices and Euler angles. Each rotation transformation matrix for the x, y, z axis is represented by Equation 1.

는

를 의미하며,

는

를 나타낸다. 그리고 병진운동에 대한 변환행렬은 수학식 2와 같다.here,

The

Means,

The

. And the transformation matrix for the translational motion is shown in equation (2).

와 속도벡터

는 x축이 진북을 향하는 관성좌표계(NWU)에서 표적의 위치와 속도를 표시한 벡터이며 수학식 3과 같다.Position vector

And speed vector

Is a vector representing the position and velocity of the target in the inertial coordinate system (NWU) with the x-axis facing true north, as shown in Equation 3.

When the velocity information of the target acquired in the NWU coordinate system G is converted into the platform coordinate system A, it is expressed by Equation 4.

는 관성항법장치로부터 얻는다. 기준 각속도 궤적을 생성하려면 플랫폼 좌표계 A에서 기술된 위치벡터

를 시선 좌표계 L로 한 번 더 변환시켜야한다. 시선좌표계 L에서 표현된 표적 정보는 아래의 수학식 5와 같은 변환식을 통해서 구할 수 있다.Euler Angle

Is obtained from the inertial navigation system. To generate the reference angular velocity trajectory, the position vector described in platform coordinate system A

To be transformed into the gaze coordinate L once more. Target information expressed in the visual coordinate system L may be obtained through a conversion equation such as Equation 5 below.

Here, the transformation matrix is shown in Equation 6.

이다.here,

to be.

과

의 속도가 0 이어야한다. 수학식 5에서 y방향의 속도가 0이어야 하기 때문에 둘째 행을 쓰면 수학식 7과 같다.To match the line of sight with the target, we need to

and

The speed should be zero. In Equation 5, since the velocity in the y direction should be 0, the second line is written as Equation 7.

Therefore, the reference angular velocity trajectory can be obtained from Equation 7 as shown in Equation 8.

Since the velocity in the z-axis direction should also be zero in the visual coordinate system L, the third term of Equation 5 is rewritten as Equation 9.

In Equation 9, the reference angular velocity trajectory of the elevation may be calculated as in Equation 10.

here,

Hereinafter, the friction compensation method will be described with reference to FIGS. 2 to 7.

2 is an exemplary view showing the uncertainty of the nonlinear frictional force, the invariant frictional characteristic region, the friction compensation torque operating region and the magnitude thereof.

과 고각 기준 각속도 궤적

를 이용하여 기준 각속도 궤적값이 일정한 속도 문턱값(Threshold)

보다 크면 마찰력과 반대방향으로 모터토크

를 일정하게 가해준다. 만약 축의 속도가 위와 반대인 경우, 다시 말해 기준 각속도 궤적값이

보다 작으면 축에 작용하는 마찰력과 반대방향으로

의 토크를 일정하게 가해준다. 기준 각속도 궤적이

이상이 되거나

보다 작게 되면 마찰력과 반대방향으로 일정한 토크를 가해 줌으로써 비선형 마찰력의 크기를 줄일 수 있도록 하는 방법이다. As shown in Fig. 2, there is an uncertainty region of the friction characteristic because the friction characteristic is large in variation. However, even if the characteristic change is taken into account, a region in which the friction characteristic does not change is present in a rectangular shape as shown in FIG. 2. Therefore, by using this constant region of frictional characteristics, friction can be compensated by applying a constant torque to the motor in the opposite direction to the frictional force when the frictional force is applied. Azimuth reference trajectory

Angular velocity trajectory

Speed threshold with constant reference angular velocity trajectory

Greater than motor torque in the direction opposite to the friction

It is added regularly. If the velocity of the axis is opposite to the above, that is, the reference angular velocity trajectory

If it is smaller than the friction force acting on the shaft

Constant torque is applied. Reference angular velocity trajectory

Become abnormal

If it is smaller, the nonlinear frictional force can be reduced by applying a constant torque in the opposite direction to the frictional force.

3 is a diagram showing the frictional force characteristics when the friction compensation method is not applied and applied.

As shown in Fig. 3, the dotted line indicates the friction characteristics when the friction compensation method is not applied, and the solid line indicates the friction characteristics when the friction compensation method is applied.

The method for performing azimuth friction compensation using the reference angular velocity trajectory of the azimuth angle,

(조건1)이면 방위각 마찰력과 반대방향으로 마찰보상 토크(Friction compensation torque)(

)를 적용하며,

If (Condition 1), Friction compensation torque in the direction opposite to azimuth friction

),

(조건2)이면 방위각 마찰력과 반대방향으로 마찰보상 토크(

)를 적용하며, 상기 조건 1과 2를 만족하지 않으면 방위각 마찰보상 토크를 적용하지 않는다.

(Condition 2), friction compensating torque in the direction opposite to azimuth friction

), And does not apply azimuth friction compensation torque unless conditions 1 and 2 are satisfied.

Method for performing high-angle friction compensation by using the high-angle reference angular velocity trajectory,

(조건1-1)이면 고각 마찰력과 반대방향으로 마찰보상 토크(

)를 적용하며,

(Condition 1-1), friction compensation torque (

),

(조건2-1) 이면 고각 마찰력과 반대방향으로 마찰보상 토크(

)를 적용하며, 상기 조건 1-1과 2-1를 만족하지 않으면 고각 마찰보상 토크를 적용하지 않는다.

(Condition 2-1) If it is, the friction compensation torque in the direction opposite to the

) Is applied, and the elevation friction torque is not applied unless the above conditions 1-1 and 2-1 are satisfied.

4 to 7 show experimental results of a stabilization controller mounted on a platform having actual roll / pitch / yaw disturbances to track a target.

4 shows the control error before applying the azimuth friction compensation method, and FIG. 5 shows the control error after applying the azimuth friction compensation method. 4 and 5, the result of the control error for the azimuth angle, the maximum error value is "1" when the control error is not applied to the friction compensation method, but after the friction compensation method is applied, the maximum error value is large. Decrease to "0.5" level.

6 shows the control error when the high-angle friction compensation method is not applied, and FIG. 7 shows the control error when the high-angle friction compensation method is applied. 6 and 7, which are the result of the control error for the elevation, show that the maximum error value is "2" when the control error is not applied to the friction compensation method, but the maximum error value is large when the friction compensation method is applied. Decreases to "1".

As described above, the friction compensation method using the reference angular velocity trajectory of the stabilization controller according to the embodiment of the present invention performs azimuth friction compensation using the azimuth reference angular velocity trajectory, and uses the high angle reference angular velocity trajectory to compensate for the high angle friction. By performing this, friction compensation of the stabilization controller can be performed.

It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. Therefore, the embodiments disclosed in the present invention are intended to illustrate rather than limit the scope of the present invention, and the scope of the technical idea of the present invention is not limited by these embodiments. The scope of protection of the present invention should be construed according to the following claims, and all technical ideas falling within the scope of the same shall be construed as falling within the scope of the present invention.

Claims (5)

A method of compensating friction using a reference angular velocity trajectory in a stabilization controller mounted on a platform where roll / pitch / yaw disturbances exist, for tracking and stabilizing a moving target,
(1) calculating a reference angular velocity trajectory of the azimuth angle;
(2) calculating a reference angular velocity trajectory of the elevation;
(3) performing azimuth friction compensation using the azimuth reference angular velocity trajectory;
(4) performing an elevation friction compensation using the elevation reference angular velocity trajectory,
Reference angular velocity trajectory of the azimuth using the roll / pitch / yaw angle and angular velocity information of the platform and the position and velocity of the target

How to calculate,

Calculated by the formula, where

The

Lt; / RTI >

The

Lt; / RTI >

Represents the reference angle of the azimuth axis,

Is the position in the x direction in the platform coordinate system A, a is the distance from the platform center to the azimuth drive axis in the x axis direction,

Is the target position in the y-axis direction in platform coordinate system A,

Wow

The friction compensation method using a reference angular velocity trajectory of the stabilization controller, characterized in that the target speed represented by the platform coordinate system A. delete The reference angular velocity trajectory of claim 1, wherein the platform uses the roll / pitch / yaw angle and angular velocity information of the platform and the position and velocity of the target.

How to calculate,

Calculated by the formula,
here,

Lt;

Is the position in the z direction of the target in the platform coordinate system A, h is the distance in the z direction from the center of gravity of the platform to the position of the elevation axis, and e represents the distance in the x direction from the azimuth axis to the elevation axis. Friction compensation method using reference angular velocity trajectory of stabilization controller. The method of claim 3, wherein the azimuth friction compensation is performed by using the azimuth reference angular velocity trajectory.

If (Condition 1), Friction compensation torque in the direction opposite to azimuth friction

),

(Condition 2), friction compensating torque in the direction opposite to azimuth friction

), And does not apply azimuth friction compensation torque if the conditions 1 and 2 are not satisfied. The method of claim 4, wherein the performing of the high angle friction compensation using the high angle reference angular velocity trajectory comprises:

(Condition 1-1), friction compensation torque (

),

(Condition 2-1) If it is, the friction compensation torque in the direction opposite to the

), And the high angle friction compensation torque is not applied if the conditions 1-1 and 2-1 are not satisfied, and the friction compensation method using the reference angular velocity trajectory of the stabilization controller is applied.

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