KR20140094313A - Friction compensator and compensating method using thereof - Google Patents

Abstract

A purpose of present invention is to provide a friction compensator via command torque shaping, which changes a discontinuous characteristic of friction near zero speed of a reaction wheel into smooth continuous properties by using a command torque shaping method to reduce jerk disturbance torque. To achieve the purpose mentioned above, the friction compensator according to an embodiment of the present invention, functioning as a friction compensator for a torque generation driver for posture stabilization and orientation conversion of an object, comprises: a friction estimation unit for estimating friction force using the speed of a wheel of the torque generation driver and command torque calculated by an object posture controller; and a command torque shaping unit for substituting the friction force estimated by the friction force estimation unit into a shaping function to output shaping torque.

Description

[0001] The present invention relates to a frictional force compensator and a frictional force compensating method using the frictional compensator,

The present invention relates to a frictional force compensator and a frictional force compensating method using the frictional force compensator. More particularly, the present invention relates to a frictional force compensator capable of reducing jerk disturbance torque in an artificial satellite or the like, and a frictional force compensating method using the same.

Reaction wheels, momentum wheels and control moment gyroscopes are motor application devices with rotors with high moments of inertia, such as satellites, ships, And is used as a torque generating actuator for stabilizing and redirecting a vehicle and a floating platform such as an automobile, an aircraft, and a missile.

For example, a reaction wheel is a device that generates a control torque by an action / reaction rule using a servomotor, attaches a wheel having a certain moment of inertia to the end of the motor shaft, and controls the speed of the wheel by a servo to generate a continuous control torque do.

Specifically, as shown in Figs. 18 and 19, a motor 11 and a flywheel 12 having a high moment of inertia are used to rotate the flywheel 12 mounted on the motor shaft at a high speed In the rotated state, the physical generated torque generated through the acceleration / deceleration according to the external command torque is transmitted to the satellite to stabilize the posture from the disturbance or to rotate the satellite in a specific direction to perform the mission. Therefore, the flywheel speed and direction of rotation change constantly according to control commands. Through this, the reaction wheel generates the generated torque, and then, through the satellite dynamics, the attitude sensor, and the attitude controller, the command torque for controlling the attitude of the satellite is input to the reaction wheel.

However, the reaction wheel has a friction force specific to the motor due to the bearings provided therein, and is generally expressed as a function of the flywheel speed. A typical Stribeck friction model is defined as a nonlinear function using a viscous friction coefficient, a coulomb friction coefficient, and a stiction friction coefficient.

In terms of satellite attitude control, reaction wheels are generally described by a combination of MOI (Moment Of Inertia), integrator, and frictional force function. The reaction torque τ _ω generated from the reaction wheel is defined as the difference between the command torque τ _c for the reaction wheel and the frictional torque τ _f from the frictional force function.

[Equation 1]

Where J is the MOI of the reaction wheel, and Ω is the reaction wheel speed.

In particular, the frictional force function is considered a Stryckic frictional force model, which is a general form of nonlinearity of the reaction wheel.

&Quot; (2) "

&Quot; (3) "

Where F _υ is the viscous frictional force, F _c is the Coulomb frictional force, F _s is the static frictional force (ie, stiction), Ω _s is the Stryvek velocity, and n _s is a constant. To calculate the jerk disturbance from the frictional force function, the time derivative of τ _f is:

&Quot; (4) "

&Quot; (5) "

)은 임펄스(impulse) 함수 성분 즉, Ω=0 에서 δ(Ω)을 가진다. 휠 속도 0을 지나는 동안

에서 원치 않는 임펄스 저크 효과를 보상하기 위하여 τ_c에 더해지는 성형 토크(τ_s)를 정의하면, 보상된 반작용 토크(τ)는 다음과 같다.Jerk disturbance (

) Has an impulse function component, i.e.,? (?) At? = 0. While passing the wheel speed 0

Defining the shaping torque (τ _s ) to be added to τ _c to compensate for the unwanted impulse jerk effect, the compensated reaction torque (τ) is

&Quot; (6) "

는 보상된 마찰력 토크이다.here,

Is the compensated frictional torque.

If the flywheel is rotating in one direction, it is common to compensate for the frictional forces through the flywheel speed feed feedback controller. However, when the flywheel changes its direction of rotation around the zero speed, jerk disturbance torque is generated due to discontinuous characteristics of the static frictional force and the coulomb frictional force, thereby deteriorating the precision attitude control performance of the satellite .

In order to solve such a problem, there has been proposed a method of linearizing nonlinearity by additionally inputting a dither signal having a small amplitude and a high frequency in the vicinity of the zero speed of the flywheel to the command torque of the reaction wheel U.S. Patent No. 5,020,745 'Reaction Wheel Friction Compensation Using Dither', 1991). However, this method has a limitation in performance since it is not a method to fundamentally compensate the frictional force by generating a high-speed shaking signal.

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems and provides an instruction torque generating apparatus and a control method thereof capable of reducing discontinuity of jerk disturbance torque by making a discontinuous characteristic of a frictional force near a reaction wheel speed constant as a smooth continuous characteristic, And to provide a friction force compensator using a molding technique.

Further, the present invention includes other objects that can be achieved from the construction of the present invention described later, in addition to the objects explicitly mentioned.

In order to achieve the above object, a frictional force compensator according to an embodiment of the present invention is a frictional force compensator for a torque generating actuator for stabilizing an orientation of an object and changing a direction, A friction estimation unit for estimating a friction force using the command torque calculated by the friction torque estimator, and a command shaping unit for outputting a shaping torque by substituting the friction force estimated by the friction force estimator into a molding function, .

In addition,

(여기서, k₁, k₂, Ω_c는 양의 설계 매개변수)이며,

(Where k ₁ , k ₂ , Ω _c are positive design parameters)

이고,

ego,

(여기서, F_υ는 점성 마찰력, F_c는 쿨롬 마찰력, F_s는 정지 마찰력, Ω_s는 스트리벡 속도, n_s는 상수)이다.

(Where F _υ is the viscous frictional force, F _c is the Coulomb friction force, F _s is the static frictional force, Ω _s is the Stryvek velocity, and n _s is a constant).

Regression, least squares, and Kalman filter optimization algorithms are applied to the estimation of the frictional force by the frictional force estimator.

Also, the torque generating actuator corresponds to any one of a reaction wheel, a momentum wheel, and a control moment gyroscope.

Meanwhile, a method of controlling the attitude of the object using the frictional force compensator may include the steps of: generating the combined torque by combining the command torque from the attitude controller and the forming torque from the frictional force compensator, And feedback to the torque generating driver.

According to the present invention having the above configuration, the present invention reduces the Jerk disturbance of the static frictional force discontinuity to a predetermined level. In particular, the commnand shaper has a closed form solution and can be applied in real time in orbit.

Further, in the present invention, in order to compensate for the jerk disturbance due to the discontinuous frictional force discontinuity from the reaction wheel, the proposed command molding machine is constituted by a parabolic function as a basis function so that the sudden change of the generated torque continuously So that the control error value can be effectively stabilized in the satellite attitude control system.

Also, the present invention can be applied to a linear regression algorithm for real-time frictional force estimation in posture control of a satellite or the like.

 On the other hand, the effects of the present invention are not limited to those described above, and other effects that can be derived from the constitution of the present invention described below are also included in the effects of the present invention.

Figure 1 shows a Stryvek frictional force model.
Figure 2 shows the effect of frictional force compensation using a parabolic commander, specifically Figure 2 (a) shows the compensated frictional force in the reaction wheel, and Figure 2 (b) shows the jerk reduction in the reaction wheel.
Figure 3 shows a block diagram of a friction compensator for a reaction wheel.
Figure 4 shows a typical relationship between the reaction wheel speed and the control error value.
Figure 5 shows a pyramidal mounting arrangement of four reaction wheels (RW) in a satellite body frame.
6 shows a block diagram of a satellite attitude control system with a reaction wheel.
Figure 7 shows a control error without frictional force compensation.
Figure 8 shows the body rate without friction force compensation.
Figure 9 shows the reaction wheel speed without friction force compensation.
Figure 10 shows the reaction wheel torque without friction force compensation.
Figure 11 shows a control error with frictional force compensation.
Figure 12 shows the body rate with frictional force compensation.
Figure 13 shows the reaction wheel speed with frictional force compensation.
Figure 14 shows the reaction wheel torque with frictional force compensation.
Figure 15 shows shaping torque with frictional force compensation.
16 shows an estimate of the viscous frictional force with frictional force compensation.
17 shows an estimate of the coulomb frictional force with frictional force compensation.
Figure 18 shows the main configuration of the reaction wheel.
Figure 19 shows an example of a conventional satellite attitude control system based on a reaction wheel.

Hereinafter, a frictional force compensator (hereinafter referred to as a "frictional force compensator") according to an embodiment of the present invention will be described in detail with reference to the drawings.

Meanwhile, the present frictional force compensator is a frictional force compensator for a torque generating actuator for stabilizing and redirecting an object, wherein the object is a vehicle including a variety of vehicles such as a satellite, a ship, a submersible vehicle, an aircraft, a missile, ), And the torque generating actuator may be a reaction wheel, a moment wheel, a control moment gyro, etc. For convenience of explanation, the reaction wheel for controlling the satellite will be described as an example.

As shown in FIG. 3, the present friction force compensator 500 includes a friction force estimator 600 and a command torque shaper 700.

Specifically, the friction estimation 600 calculates the frictional force F by using the wheel speed? Of the reaction wheel 200 and the command torque? _C calculated by the attitude controller 100 of the satellite, . In this case, optimization algorithms such as regression, Least Square, and Kalman Filter can be applied for estimation.

Command torque molding machine (command shaping) (700) outputs the molding torque (torque shaping) (τ _s) by the frictional force (F) estimated by the frictional force estimator 600 assigned to the forming function. The forming function used here is composed of the frictional force function and the secondary forming function. The shaping torque? _S is applied to the torque input of the reaction wheel 200 together with the command torque? _C of the attitude controller 100 to smooth the discontinuous frictional force characteristic as a continuous characteristic while the flywheel 200 passes the zero speed (smooth).

Specifically, the frictional force compensation using the command torque forming is performed as follows.

First, using a parabolic function as a basis function, the shaping torque? _S is proposed as follows.

&Quot; (7) "

(Where k ₁ , k ₂ , Ω _c are positive design parameters). Then, the compensated torque and the derivative value for? Are obtained as follows.

&Quot; (8) "

&Quot; (9) "

및

)을 만족시키는 k₁ 및 k₂를 구해야 한다.To determine k ₁ , k ₂ at a given Ω _c (»Ω _s ), the following boundary conditions (Ω = Ω _c

And

K _{< /} RTI _> And k ₂ .

&Quot; (10) "

The unique solution of Equation (10) is calculated as a closed form as shown below.

&Quot; (11) "

Figure 2 shows the compensated torque and jerk reduction at different Ω _c in the frictional force model. The command molder can be applied to the real-time estimation of the frictional force model, solving linear equations in which the solution is obtained in closed form.

인 경우, 마찰력 모델은 명령토크 및 측정된 휠 속도를 사용하여 추정된다. {τ_s(k), Ω(k)}, k={1, 2,…, N}을 샘플링된 일련의 명령토크와, 도 4에 도시된 바와 같이 인공위성 자세기동 구간(즉, │Ω(k)│> Ω_c) 동안 통상적으로 사다리꼴 파형(trapezoidal wave form)인 측정된 휠 속도 변화로 정의한다. 그러면, 수학식 7로부터│Ω(k)│> Ω_c 에서 τ_s(k) = 0 이므로, 시간 k에서 순간적 마찰 토크는 수학식 1로부터 다음과 같이 구해진다.

, The frictional force model is estimated using the command torque and the measured wheel speed. {τ _s (k), Ω (k)}, k = {1, 2, ... , N} and the measured wheel torque, which is typically a trapezoidal wave form during the satellite attitude maneuver interval (i.e., Ω (k) │> Ω _c ) as shown in FIG. 4 Speed change. Then, from Equation (7), Ω (k) │> Ω _c Since? _s (k) = 0, the instantaneous frictional torque at time k is obtained from Equation (1) as follows.

&Quot; (12) "

Ω(k)}, k={1, 2,…, N}를 가진 선형 회귀법(linear regression)을 사용하여, 아래와 같이 계산된다.(Where? T is the data sampling time). The estimates of F _υ and F _c are then {

Ω (k)}, k = {1, 2, ... , N}, using the linear regression.

&Quot; (13) "

와 함께 수학식 11을 사용하면, 추정된 마찰력 매개변수는 인공위성 안정화 구간(│Ω(k)│< Ω_c) 동안 사용되는 수학식 7의 성형 토크를 구성하는데 사용된다.
Finally,

, The estimated frictional force parameter is used to construct the shaping torque of Equation (7) used during the satellite stabilization period ([Omega] (k) < [Omega] _c ).

Hereinafter, the operation of the present invention will be described by taking as an example satellite control using four reaction wheels (RW # 1, RW # 2, RW # 3, RW # 4).

The satellite attitude control system consists of a PID controller, a command shaper interlocked with the friction force estimator, a reaction wheel, satellite dynamics, and kinematics, as shown in FIG. The simulation parameters are listed in Table 1.

Display value Explanation J 0.05 kgm ² MOI of the reaction wheel F _v 2.5 x 10 ^-5 Nm / rpm Viscous frictional force F _c 0.01 Nm Coulomb friction F _s 0.01 Nm Static friction force Ω _c 40 rpm Compensation speed K 0.4587 Proportional control gain C 1.1875 Differential control gain T 17.6839 Integral time constant f _s 8 Hz Control sampling frequency q _c [0.2588, 0, 0, 0.9659] ^T Quaternion command
(Corresponds to 30 degrees around the rolling axis) alpha 45 deg AZ angle in pyramid shape beta 35.3 deg In the pyramid shape,

The rotational equations for rigid satellites are described as follows.

&Quot; (14) &quot;

(Where ω is the angular velocity of the satellite, h _ω is the momentum of the reaction wheel cluster, and τ _sc is the control torque of the satellite). Furthermore, the satellite MOI (I _sc ) is given in kgm ² as:

&Quot; (15) &quot;

로서 쿼터니온(quaternion)을 정의하면, 쿼터니온 운동학 미분 방정식(quaternion kinematics differential equation)은 다음과 같이 주어진다.

If we define a quaternion as a quaternion kinematics differential equation,

&Quot; (16) &quot;

From Equation (7), the quaternary base PID controller is adopted as follows in the simulation of a closed loop control system.

&Quot; (17) &quot;

Here, q _e is a quaternion error value defined as follows.

&Quot; (18) &quot;

Where q _c is the attitude command quaternion. Considering the typical pyramid mounting arrangement of the four reaction wheels, a steering matrix M _str from the satellite to the four reaction wheels and an unsteering matrix from the four reaction wheels to the satellite body (unsteering matrix) M _unstr is defined as follows.

&Quot; (19) &quot;

&Quot; (20) &quot;

Figs. 7 to 10 show the control performance in the absence of the friction force compensation, and Figs. 11 to 17 show the control performance in the friction force compensation state. If no compensation is applied to the control system, the wheel generating torque exhibits a chattering phenomenon and as a result the control error value does not converge to zero. However, if control compensation is applied, the formed torque will stabilize the steady state of the wheel due to the shaping torque, and the control error value converges to zero after 40 seconds. Furthermore, as shown in Figs. 16 and 17, the linear regression algorithm has a good estimate of the unknown frictional force coefficient.

As described above, nonlinear simulation of an attitude control system, which is composed of a quaternion-based PID controller, quaternion-based PID controller, four reaction wheels with an unknown friction model, satellite dynamics, kinematics, The effect of the present invention can be confirmed.

As described above, in the present invention, the composite torque is generated by combining the command torque from the posture controller and the formed torque from the frictional force compensator, and then the synthetic torque is fed back to the torque generation driver, It has been shown that the increase of the posture error value and the unwanted chattering phenomenon are eliminated by the execution of the command molding machine.

On the other hand, in the case of using multiple reaction wheels, the present invention can selectively and separately apply the frictional force compensator. In addition, although the secondary molding function is presented, it can be extended to higher order forming function and cosine forming function.

While the present invention has been particularly shown and described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, And all changes and modifications to the scope of the invention.

100 ... attitude controller, 200 ... reaction wheel
500 ... Frictional force compensator, 600 ... Frictional force estimator
700 ... command torque molding machine,

Claims (5)

A friction force compensator for a torque generating actuator for stabilizing the posture of an object and changing the direction thereof,
A friction estimation unit for estimating a friction force using the speed of the wheel of the torque generating actuator and the command torque calculated by the attitude controller of the object,
An instruction torque shaping unit for outputting a shaping torque by substituting a frictional force estimated by the frictional force estimator into a shaping function,
. The method of claim 1,
The shaping function may include:

(Where k ₁ , k ₂ , Ω _c are positive design parameters)

ego,

(Where F _υ is the viscous frictional force, F _c is the Coulomb friction force, F _s is the static frictional force, Ω _s is the Stryvek velocity, and n _s is a constant)
Friction force compensator. The method of claim 1,
Wherein the friction force estimator estimates the frictional force using a regression method, a Least Square method, and a Kalman filter optimization algorithm. The method of claim 1,
Wherein the torque generating actuator corresponds to one of a reaction wheel, a momentum wheel, and a control moment gyroscope. A method of controlling an attitude of an object using a frictional force compensator according to any one of claims 1 to 4,
Synthesizing the command torque from the attitude controller and the forming torque from the frictional force compensator to produce a combined torque, and
Feeding back the combined torque to the torque generating driver
&Lt; / RTI &gt;

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