CN109814377A

CN109814377A - Two-dimensional swing control method of space tether assembly based on linearized feedback control

Info

Publication number: CN109814377A
Application number: CN201910104449.5A
Authority: CN
Inventors: 郭吉丰; 鄢雨辰; 王班; 周传平; 冯长水
Original assignee: Zhejiang University ZJU; Hangzhou Electronic Science and Technology University
Current assignee: Zhejiang University ZJU; Hangzhou Electronic Science and Technology University
Priority date: 2019-02-01
Filing date: 2019-02-01
Publication date: 2019-05-28
Anticipated expiration: 2039-02-01
Also published as: CN109814377B

Abstract

本发明公开了一种基于线性化反馈控制的空间绳系组合体二维摆动控制方法。建立空间固定直角坐标系，根据拉格朗日方程建立得到空间绳系组合体的摆动动力学模型，建立线性化反馈控制的摆角抑制控制方式、速度反馈控制方式、位置反馈控制方式，分别处理获得摆角、速度、位置的控制量并复合计算获得总控制量带入到摆动动力学模型中进行控制。本发明方法实现空间绳系组合体二维摆动控制，具有控制器设计简单、工程可实现性强及控制效果好等优点。The invention discloses a two-dimensional swing control method for a space rope assembly based on linearized feedback control. Establish a space fixed Cartesian coordinate system, establish the swing dynamics model of the space rope assembly according to the Lagrangian equation, and establish the linearized feedback control swing angle suppression control mode, speed feedback control mode, and position feedback control mode, and deal with them separately. The control quantities of swing angle, speed and position are obtained and the total control quantity obtained by compound calculation is brought into the swing dynamics model for control. The method of the invention realizes the two-dimensional swing control of the space rope assembly, and has the advantages of simple controller design, strong engineering practicability and good control effect.

Description

Space rope system assembly two-dimensional wiggle control method based on Linearization Feedback control

Technical field

The present invention relates to the control of space rope system assembly more particularly to a kind of space ropes based on Linearization Feedback control It is assembly two-dimensional wiggle control method.

Background technique

Space rope system system refers to the flight system that multiple satellites or spacecraft composition are connected using flexible tether.Two-body Rope system system is generally made of two spacecrafts with the long hawser that the two is connected as typical space rope system.Two-body rope system It is to carry out the basis that rope is network analysis.It is largely ground currently, scholars have been carried out using two-body rope system's acquisition procedure as research object Study carefully, develops a set of control method based on rope length rate control, thruster control, tether tension force, Torque Control etc., Good effect is achieved in the researchs such as attitude stabilization, tether folding and unfolding stabilization.For the periodic motion occurred in two-body rope system, have Document points out that the amplitude of in plane vibration is several times as much as the amplitude of out-of-plane vibration, outside opposite pivot angle often provide reached it is stable it is assumed that because The elimination for aiming at pivot angle in face of this many research concern, and be plane fortune by the periodic motion approximating assumption of two-body rope system It is dynamic.But in fact, inside and outside swing in face that rope is assembly intercouples, the present invention is thus with dragging under the suspended state of space Dragging rope system assembly is research object, carries out the space rope system assembly two-dimensional wiggle control of task based access control platform Acceleration Control Research.

Summary of the invention

The two-dimensional wiggle problem that rope is assembly is pulled for space, the purpose of the present invention is to provide one kind based on linear The space rope system assembly two-dimensional wiggle control method for changing feedback control is that a kind of controller design is simple, engineering realizability The advantages that strong and control effect is good.

In order to achieve the above object of the invention, as shown in Fig. 2, the step of the technical solution adopted by the present invention is as follows:

Step 1), perpendicular to XY axis is established in the plane of drag direction, constructs XYZ three-dimensional flute using drag direction as Z axis Karr coordinate system is as the fixed rectangular coordinate system in space；It is established to obtain the swing of space rope system assembly according to Lagrange's equation Kinetic model are as follows:

Wherein: (x, y, z) is the mass center O of task platform₀In the three-dimensional coordinate of the fixed rectangular coordinate system in space, m is target The quality of star, tether length of the l between task platform and target satellite, F_TIndicate tether tension, θ O₀O₁In the throwing of XZ plane Pivot angle in angle, that is, space rope system assembly face between shadow and cone center line,For O₀O₁Projection and O in XZ plane₀O₁ Between angle, that is, space rope system assembly face outside pivot angle, O₁For the mass center of target satellite；A little indicate that single order is led on letter It counts, the two o'clock on letter indicates second dervative；

Step 2) is during dragging, task platform mass center O₀Acceleration in the Z-axis directionIt is fixed with tether length l It is constant, with task platform mass center O₀Acceleration in the x and y directionsController design is carried out as control input quantity, Following pivot angle, which is established, according to Linearization Feedback control inhibits control mode:

Wherein, u_ax,u_ayRespectively indicate the X-axis and Y direction Acceleration Control amount for realizing swinging angle control, k_pθ、k_dθRespectively The ratio and differential coefficient of the PD control device of pivot angle θ in face,Respectively pivot angle outside facePD control device ratio Coefficient and differential coefficient；

Step 3) is inputted by speed difference as speed closed loop, speed feedback valueFrom to task platform mass center O₀ AccelerationIntegral, consider from swinging angle control, before the control amount in speed closed loop link is introduced as disturbance To channel, following speed feedback control mode is established:

Wherein, u_vx、u_vyRespectively indicate the X-axis and Y direction Acceleration Control amount of the control of realization task platform speed； k_pvx、k_ivxAnd k_dvxProportionality coefficient, integral coefficient and the differential coefficient of speed by PID controller respectively on X axis coordinate component, k_pvy、k_ivyAnd k_dvyProportionality coefficient, integral coefficient and the differential coefficient of speed by PID controller respectively on Y axis coordinate component； Δv_xFor the velocity error on X axis coordinate component, Δ v_yFor the velocity error on Y axis coordinate component, t indicates the time；

Step 4) is inputted by position difference as position closed loop, and location feedback value (x, y) is to task platform mass center O₀Velocity amplitudeIntegral, control and consider from angle, the control amount in position closed loop link introduces forward path as disturbance, Establish following position feedback control mode:

Wherein, u_sx、u_syThe X-axis and Y direction Acceleration Control amount of the control of realization task position of platform are respectively indicated, k_psx、k_isxAnd k_dsxProportionality coefficient, integral coefficient and the differential coefficient of position PID controller respectively on X axis coordinate component, k_psy、k_isyAnd k_dsyProportionality coefficient, integral coefficient and the differential coefficient of speed by PID controller respectively on Y axis coordinate component； Δ x is the velocity error on X axis coordinate component, and Δ y is the velocity error on Y axis coordinate component；

The u that step 5) obtains step 2) processing_ax、u_ay, the obtained u of step 3) processing_vx、u_vyAnd step 4) is handled The u arrived_sx、u_syIt is updated to the X-axis for obtaining realization task platform courses in following complex controll calculation formula and Y direction accelerates Spend control amount u_xAnd u_y:

u_x=u_ax-u_vx-u_sx、u_y=u_ay-u_vy-u_sy

By u_xAnd u_yIt is brought into the swing kinetic model that step 1) obtains and replaces task platform mass center O respectively₀In X and Y Acceleration in axis directionAnd then it realizes that space rope system assembly disappears in the two dimension of X/Y plane and puts control.

The space rope system assembly be placed in vacuum it is agravic under the conditions of, space rope system assembly include task platform and Target satellite is connected between task platform and target satellite by tether, drives target satellite to move along drag direction by task platform, Tether thinks to be rigid body for nonelastic ungauged regions under dragging process, and target satellite is in the flatness and reciprocator fortune perpendicular to drag direction Dynamic, the movement of the dragging point of control method active control task platform through the invention carries out the fortune of the flatness and reciprocator to target satellite It is dynamic disappear putting control.

The task platform substantially can be the mobile device with displacement driving power, such as air-jet device, boat Its device, target satellite are satellite.

The invention has the advantages that:

Pulling rope the present invention provides simple, effective space is assembly swing control method, can be by task Acceleration of the platform in the direction x, y realizes that the two dimension of space rope system assembly disappears and puts control.The simple, control response with control Fastly, the advantages that strong robustness, Project Realization facilitate.The method is suitable for the control of the space rope system system of general occasion.

Detailed description of the invention

Fig. 1 is space rope system assembly swinging model of the invention.

Fig. 2 is control method block diagram of the invention.

Fig. 3 is pivot angle time history diagram inside and outside face of the invention.

Fig. 4 is towing point acceleration time history diagram of the invention.

Fig. 5 is towing point Velocity Time course figure of the invention.

Fig. 6 is hitch position time history diagram of the invention.

In figure: 1, task platform, 2, tether, 3, target satellite.

Specific embodiment

Present invention will be further explained below with reference to the attached drawings and examples.

Specific implementation initially sets up the swing kinetic model for space rope system assembly.

As shown in Figure 1, establishing rectangular coordinate system in space (x, y, z), task platform mass center is equivalent to towing point, space rope It is that the towing point coordinate of assembly is set as O₀(that is, mass center of task platform 1), towing point can be freely motor-driven.Target satellite quality is M, center-of-mass coordinate O₁.It is connected between target satellite 3 and towing point by tether 2, tether rope length is l, and tether tension is F_T。

O₀O₁Angle between the projection and cone center line of XZ plane is pivot angle θ in face, O₀O₁In the projection of XZ plane With O₀O₁Between angle be pivot angle outside faceEstablish Lagrange's equation.

The simplified model of two-body rope system --- dumbbell model is to regard spacecraft as particle, and tether is the kinematic system of rigid body, It is as follows to the hypothesis of dumbbell model:

(1) tether 2: tensioning does not consider tether quality and damping；

(2) task platform and target satellite (spacecraft): it is considered as particle, does not consider volume to the work of space rope system assembly With；

(3) mass center: the mass center of space rope system assembly is located at a certain position of tether according to Mass Distribution.

(4) potential energy field: space rope system assembly is in the suspended state of space complete agravity, puts aside gravity gradient ?.

Task platform mass center O₀Coordinate is (x, y, z), target satellite mass center O₁Coordinate is (x_m, y_m, z_m), wherein

The system total kinetic energy T of space rope system assembly are as follows:

Wherein, x_m、y_m、z_mIt is expressed as the three-dimensional coordinate of target satellite mass center；

Based on space rope system assembly be in the suspended state of complete agravity it is assumed that system without potential energy field.Then system has Some potential energy V are as follows:

V=0 (2)

Calculate LagrangianL:

Pivot angle θ in face, pivot angle outside face are taken respectivelyRope length l is that generalized coordinates substitutes into Lagrange's equation, is then taken in face Pivot angle θ is generalized coordinates q₁It establishes equation, take pivot angle outside faceFor generalized coordinates q₂It establishes equation, rope length l is taken to be generalized coordinates q₃ Equation is established, and handles together the swing kinetic model for obtaining space rope system assembly in terms of above three:

Then according to the method for the present invention step 1)~5) the specific embodiment experimental conditions implemented afterwards are as follows:

It will disappear and put controller u_x、u_yIt is applied to progress numerical simulation verifying in rope system coal-rock combination body.Enable long change of ropeEmulation is as shown in table 1 using the numerical value of physical parameter and primary condition.

1 simulation parameter of table

If target velocityTarget position (x_d,y_d)=(0,0).Disappear pendulum control simulation result such as Fig. 3 institute Show: pivot angle is stablized by initial ± 30 ° and ± 23 ° near 0 ° respectively under the pendulum control input type that disappears inside and outside face, disappears and puts control (3.14) stabilization of pivot angle inside and outside face is realized.Fig. 4 is control input, and input value range is in (- 1m/s²,1m/s²) in；Speed is rung It should respond as shown in Figure 5, Figure 6 with distance, be returned near origin by adjustment process rear haulage point.In response process, distance is most Big instantaneous value is -0.32m, and speed maximum instantaneous value is 0.25m/s, ensure that the motion range of towing point and quick movement are rung It answers.

Claims

1. a two-dimensional swing control method for a space tether assembly based on linearized feedback control, is characterized in that, the steps of the method are as follows:

Step 1) Take the dragging direction as the Z axis, establish the XY axis on the plane perpendicular to the dragging direction, and construct the XYZ three-dimensional Cartesian coordinate system as the space fixed Cartesian coordinate system; according to the Lagrange equation, the space rope combination is obtained. The swing dynamics model of is:

Among them: (x, y, z) is the three-dimensional coordinate of the center of mass O ₀ of the mission platform in the space fixed Cartesian coordinate system, m is the mass of the target star, l is the length of the tether between the mission platform and the target star, F _T represents the system rope tension, θ is the angle between the projection of O ₀ O ₁ on the XZ plane and the center line of the cone, that is, the in-plane swing angle of the spatial rope assembly, is the angle between the projection of O ₀ O ₁ on the XZ plane and O ₀ O ₁ , that is, the out-of-plane swing angle of the space tether assembly, and O ₁ is the center of mass of the target star; a point on the letter represents the first derivative, the letter The two points above represent the second derivative;

Step 2) During the dragging process, the acceleration of the task platform mass center O ₀ in the Z-axis direction And the tether length l is fixed, the acceleration of the task platform center of mass O ₀ in the X and Y axis directions The controller is designed as the control input quantity, and the following sway angle suppression control method is established according to the linearized feedback control:

Among them, u _ax and u _ay respectively represent the acceleration control amount in the X-axis and Y-axis directions to realize the swing angle control, k _pθ and k _dθ are the proportional and differential coefficients of the PD controller of the in-plane swing angle θ, respectively, out-of-plane swing angle The proportional coefficient and differential coefficient of the PD controller;

Step 3) Use the speed difference as the speed closed-loop input, and the speed feedback value Acceleration from the center of mass O ₀ of the mission platform The integral of , considering the swing angle control, the control variable in the speed closed-loop link is introduced into the forward channel as a disturbance, and the following speed feedback control method is established:

Among them, u _vx and u _vy respectively represent the X-axis and Y-axis direction acceleration control quantities for the task platform speed control; k _pvx , k _ivx and k _dvx are the proportional coefficient and integral of the speed PID controller on the X-axis coordinate components, respectively Coefficient and differential coefficient, k _pvy , _kivy and k _dvy are the proportional coefficient, integral coefficient and differential coefficient of the speed PID controller on the Y-axis coordinate component respectively; Δv _x is the speed error on the X-axis coordinate component, Δv _y is Velocity error on the Y-axis coordinate component, t represents time;

Step 4) The position difference value is used as the position closed-loop input, and the position feedback value (x, y) comes from the velocity value of the center of mass O ₀ of the task platform. The integral of , considering the angle control, the control amount in the position closed-loop link is introduced into the forward channel as a disturbance, and the following position feedback control method is established:

Among them, u _sx and u _sy respectively represent the X-axis and Y-axis direction acceleration control quantities to realize the position control of the task platform, and k _psx , k _isx and k _dsx are respectively the proportional coefficient and integral of the position PID controller on the X-axis coordinate component. Coefficient and differential coefficient, k _psy , k _isy and k _dsy are the proportional coefficient, integral coefficient and differential coefficient of the speed PID controller on the Y-axis coordinate component respectively; Δx is the speed error on the X-axis coordinate component, Δy is the Y-axis Velocity error on coordinate components;

Step 5) Substitute u _ax , u _ay obtained in step 2), u _vx , u _vy obtained in step 3) and u _sx and u _sy obtained in step 4) into the following composite control calculation formula to obtain the realization task. The acceleration control quantities u _x and u _y in the X-axis and Y-axis directions of the platform control:

u _x =u _ax -u _vx -u _sx , u _y =u _ay -u _vy -u _sy

Bring u _x and u _y into the swing dynamics model obtained in step 1) to replace the acceleration of the mission platform center of mass O ₀ in the X and Y axis directions, respectively Furthermore, the two-dimensional anti-swing control of the space tether assembly is realized.

2. A two-dimensional swing control method for a space rope assembly based on linearized feedback control according to claim 1, characterized in that: the space rope assembly is placed in a vacuum without gravity, and the space rope assembly is The system combination includes a mission platform and a target star. The mission platform and the target star are connected by a tether. The mission platform drives the target star to move in the dragging direction, and the target star reciprocates in a plane perpendicular to the dragging direction.

3. A two-dimensional swing control method for a space tether assembly based on linearized feedback control according to claim 1, characterized in that: the task platform is a mobile device with its own motion driving power, and the target star for the satellite.