CN116788527A - Underdrive rope system assembly racemization control method based on layered sliding mode - Google Patents
Underdrive rope system assembly racemization control method based on layered sliding mode Download PDFInfo
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- CN116788527A CN116788527A CN202310208114.4A CN202310208114A CN116788527A CN 116788527 A CN116788527 A CN 116788527A CN 202310208114 A CN202310208114 A CN 202310208114A CN 116788527 A CN116788527 A CN 116788527A
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- 239000012634 fragment Substances 0.000 claims abstract description 6
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- 230000010355 oscillation Effects 0.000 claims abstract 2
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- 238000013459 approach Methods 0.000 claims description 4
- 238000013461 design Methods 0.000 claims description 4
- 230000036544 posture Effects 0.000 abstract 2
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- 230000000694 effects Effects 0.000 description 6
- 230000010485 coping Effects 0.000 description 2
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G4/00—Tools specially adapted for use in space
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G1/00—Cosmonautic vehicles
- B64G1/10—Artificial satellites; Systems of such satellites; Interplanetary vehicles
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Abstract
The invention discloses an underdrive rope assembly racemization control method based on a layered sliding mode, which is suitable for pose control of an assembly system formed after space fragments are captured by a flexible rope net. The invention provides a layered sliding mode-based combined body posture control method, which is used for supplementing and perfecting a dynamic model of a combined body by considering uncertainty of dynamic parameters of space fragments, errors in measurement of initial postures of targets and existence of external interference force. The method stabilizes the entire underactuated tether assembly system by torque applied to an actively controlled service satellite while applying radial propulsion to inhibit oscillation of the service satellite in the radial direction in order to increase the stability efficiency of the system. The control method provided by the invention simplifies the control input parameters, and the space debris can be racemized by the tether only through the attitude adjustment of the service satellite. Compared with the traditional proportional differential controller, the control performance and the robustness of the control method are better.
Description
Technical Field
The invention discloses an underdrive rope assembly racemization control method based on a layered sliding mode, which is suitable for pose control of an assembly system formed after space fragments are captured by a flexible rope net.
Background
Space debris poses a threat to satellites in normal service in orbit. The flexible rope net is a space debris active cleaning technology with great development prospect at present. After the flying net captures the space debris, the service satellite and the space debris form a rope combination body together with the rope net. The tether assembly has the following characteristics: 1) The system comprises a rigid service satellite, space debris and a flexible flying net, and is a rigid-flexible coupled complex system; 2) The spatial debris is a non-cooperative target, and the tethered assembly dynamics model is accompanied by uncertainty; 3) The space debris loses power and the tethered assembly is only dependent on the service satellite with control input devices installed for motion control, a typical under-actuated system.
The dynamic model of the tethered assembly is affected by the uncertainty of the dynamic parameters of the space debris, the spin initial attitude error of the space debris, and external disturbances. On the basis of perfecting the uncertainty description of the dynamic model, the invention adopts the gesture control based on the layered sliding mode method, and compared with the proportional differential gesture control, improves the efficiency and the precision of racemization control, and shows good robustness. Meanwhile, radial propulsion control is applied in an auxiliary mode, radial swing of a service satellite is restrained, and racemization stability control of the rope system assembly is accelerated.
Disclosure of Invention
The invention aims to provide an underdrive rope system assembly racemization control method based on a layered sliding mode, which is used for coping with uncertainty of space debris dynamic parameters, initial attitude errors and external interference on the basis of ensuring good control efficiency and control precision of a control system, and has good robustness and improved racemization stability.
An underdrive rope system assembly racemization control method based on a layered sliding mode comprises the following steps:
step 1: a kinetic model of the tethered assembly is established. And taking uncertainty of non-cooperative space debris dynamic parameters, space debris spin initial attitude errors and external interference into consideration, and supplementing and perfecting a dynamic model. On the basis, expressing a dynamic model in the form of a state space equation;
step 2: and (3) defining a layered sliding mode surface based on the dynamic model established in the step (1), designing a sliding mode surface approach law, deducing a control law of a sliding mode control method, and realizing racemization control of the rope system assembly.
Step 3: on the basis of the gesture control in the step 2, a radial swing suppression controller is designed, and a given control target is set to enhance the racemization stabilizing capability of the rope combination body.
Advantages of the invention
The invention mainly relates to an underdrive rope system assembly racemization control method based on a layered sliding mode, which realizes racemization stable control of the rope system assembly. The advantages are that: firstly, the uncertainty factors existing in the tethered assembly are considered to comprise the uncertainty of the space debris parameters, the initial spin attitude error of the space debris and external interference, so that an assembly dynamics model is improved; secondly, the moment provided by the service satellite is the control input of the rope system assembly, and on the basis of guaranteeing the racemization effect, the hardware equipment of the system is simplified; third, the layered sliding mode attitude controller has improved control efficiency and control accuracy compared to proportional-differential attitude controllers, while coping with a tether assembly model containing uncertainty, and has greater robustness.
Drawings
FIG. 1 is a tether assembly formed after capture
FIG. 2 is a diagram of a tethered assembly configuration with initial attitude error considerations
FIG. 3 illustrates the racemization effect of a model accurate lower space debris in an embodiment
FIG. 4 is a graph showing the angular velocity distribution of the spatial debris under the uncertainty of the parameters in the embodiment
FIG. 5 shows the effect of spatial debris racemization under external disturbance due to attitude error in the embodiment
Detailed Description
Referring to fig. 1 to 5, the technical scheme adopted by the invention comprises the following contents:
1. establishing dynamic model of rope combination
1.1 Complex dynamics model
The dynamic model of the tether assembly formed after the flying net is captured is shown as a figure 1, and comprises a service satellite, space debris and a tether, wherein the dynamic model of the service satellite and the space debris is built by adopting a Newton's Euler method, and the tether adopts a mass spring model.
A. Service satellite dynamics model
F+T 0 ＝m S a S (1)
Wherein F= [ F ] x F y ]Is the propelling force in the track motion direction provided by the propeller, ensures the tensioning of the tether, T 0 ＝[T 0x T 0y ]Is the tension vector on the main rope, a S ＝[a Sx a Sy ]Is the linear acceleration of the service satellite, m S 、J S The mass and the moment of inertia of the service satellite are respectively, and the connection point of the main tether on the service satellite is O 1 P 0 ＝[-l S 0]Wherein l S Is one half of the length of the service satellite,is a rotation matrix that converts vectors from an inertial coordinate system to a service satellite volume coordinate system, where θ S Is the rotation angle of the service satellite, M C Is the torque input provided by the propulsion, momentum wheel, etc. devices on the service satellite.
B. Space debris dynamics model
T 1 +T 2 ＝m T a T (3)
wherein ,T1 ＝[T 1x T 1y ]，T 2 ＝[T 2x T 2y ]Respectively the tension vectors, a, on the two sub-tethers T ＝[a Tx a Ty ]Is the linear acceleration of the space debris, m T 、J T The mass and the rotational inertia of the space debris are respectively, and the connection points of the rope net and the space debris are respectively O 2 P 1 ＝[l T w T ]，O 2 P 2 ＝[l T -w T], wherein lT 、w T Half the length and width of the space debris respectively,is a rotation matrix that converts vectors from an inertial coordinate system to a spatial chip coordinate system, where θ T Is the angle of rotation of the spatial debris.
C. Tether dynamics model
Where k is the stiffness of the tether, l i For the deformed length of each tether, l i0 For the undeformed natural length of each tether Δl i ＝[Δl xi ,Δl yi ] T Is the elongation of each tether.
1.2 supplementing model uncertainty
A. Taking the uncertainty of the dynamic parameters of the space debris into consideration, the improved dynamic equation is as follows:
where δ is the boundary value for correcting the nominal inertia coefficient.
B. Taking into account the initial attitude error of the space debris, the resulting composite configuration is shown in FIG. 2, with the initial attitude angle defined as follows:
α T ＝π/4·η (7)
wherein eta is a random number between 0 and 1.
The initial attitude angle change causes the change of the connection point of the tether and the space debris, and the connection point of the tether and the space debris is defined as follows in an inertial coordinate system:
wherein ,converting a position vector of a connecting point from a space fragment body coordinate system to a rotation matrix of an inertial coordinate system, setting an x-direction coordinate of the connecting point in the inertial coordinate system as d, and calculating to obtain a position vector of the connecting point in the body coordinate system as follows: />
C. Considering the external interference D-N (0,0.0001) received by the space debris 2 ) N·m, the modified kinetic equation is as follows:
1.3 expressing the kinetic model in the form of a state equation:
wherein ,
f 1 ＝(O 2 P 1 ×(R -1 (θ T )·T 1 )+O 2 P 2 ×(R -1 (θ T )·T 2 ))/J T ,
f 2 ＝(O 1 P 1 ×(R -1 (θ S )·T 0 ))/J S ,
u 1 ＝0,u 2 ＝M C ,b 2 ＝1/J s .
2. layered slip-form controller design
2.1 definition of the layered slip plane
wherein ,z1 ，z 2 Two sub-slip mould surfaces, s is an integral slip mould surface, c 1 、c 2 Alpha is a weight coefficient greater than zero, and the value of the desired state variable is set to x 1d ＝x 2d ＝x 3d ＝x 4d ＝0。
2.2 sliding mode switching law design
To avoid jitter problems caused by frequent switching, a saturation function is introduced to establish a switching law:
ds/dt＝-ε·sat(s)+f(x 1 ,x 2 ,x 3 ,x 4 ) (12)
where ε is the approach rate and other functions are defined as follows:
where Δ is the slip boundary value of the overall slip plane.
Where γ is the scaling factor of the control input and is a fraction between 0 and 1.
2.3 deriving the sliding mode control law as
3. Thrust controller for suppressing radial swing
3.1 defining position error to obtain propulsion control law
wherein ,yS Andradial position and velocity, y, respectively, of the service satellite d and />The desired values of the radial position and velocity of the service satellite, respectively.
Y C ＝-k 3 ·e 1 -k 4 ·e 2 (17)
wherein ,k3 and k4 Is a control gain with positive value, Y C Is the radial force input generated by the impeller.
3.2, setting control targets as follows:
wherein ,ysb Is the switching boundary, y pb Is a convergence location boundary.
Thereby, the racemization control of the rope combination is realized.
Examples
According to the underdrive rope system assembly racemization control method based on the layered sliding mode, the rope system shown in fig. 1 is taken as an object to be unfolded and verified, and parameters of the rope system are shown in table 1. The initial condition of the state variable of the tether assembly is [ x 1 ,x 2 ,x 3 ,x 4 ]＝[0,0.5,0,0]The desired state quantity target is [ x 1d ,x 2d ,x 3d ,x 4d ]＝[0,0,0,0]。
Table 1 parameters of the tethered assembly
The control method and the proportional differential control method provided by the invention are respectively utilized to carry out racemization control on the rope combination, and the racemization effect of space debris in the combination is shown in figure 3. The result shows that the angular velocity of the space debris enters into a five percent error band at 78s by the proportional differential control, and the angular velocity of the space debris enters into a five percent error band at 55s by the control method provided by the invention, so that the racemization efficiency of the space debris is improved, the control precision is 1.2 DEG/s in terms of the control precision, and the precision achieved by the proportional differential control is 0.5 DEG/s in the limited simulation time of 100 s.
Under the condition of inaccurate space debris dynamic parameters, the racemization effect of the space debris in the combination is shown in fig. 4, and the result shows that when the correction coefficient delta changes within plus or minus 0.3, the accuracy of proportional differential control fluctuates within a large range of 0.4-7 DEG/s within a finite simulation time of 100s, while the robustness of the control method provided by the invention is stronger, and the control accuracy fluctuates within a small range of 0.2-0.8 DEG/s. Under the condition of considering the initial attitude error of the space debris and the external interference, the racemization effect of the space debris in the combined body is shown as shown in fig. 5, and the robustness of the control method provided by the invention is stronger, and the angular velocity of the space debris can enter into an error band of five percent before proportional differential control for more than 30 s.
Claims (1)
1. The underdrive rope system assembly racemization control method based on the layered sliding mode is characterized in that space fragments can be racemized through the ropes only through attitude adjustment of a service satellite, so that stability of an assembly system is realized. The method comprises the following specific steps:
step 1: establishing a tethered assembly dynamics model, supplementing an uncertainty description of a plurality of parameters involved in the model, and expressing the dynamics model in a state space, comprising the sub-steps of:
step 1.1: establishing dynamic model of rope combination
A. Service satellite dynamics model
F+T 0 ＝m S a S (1)
Wherein only the motion in the track plane is considered, f= [ F x F y ]Is the propelling force of the propeller in the motion direction of the service satellite in the orbit plane so as to ensure the tensioning of the tether, T 0 ＝[T 0x T 0y ]Is the tension vector on the main rope, a S ＝[a Sx a Sy ]Is the linear acceleration of the service satellite, m S 、J S The mass and the moment of inertia of the service satellite are respectively, and the connection point of the main tether on the service satellite is O 1 P 0 ＝[-l S 0]Wherein l S Is one half of the length of the service satellite,is a rotation matrix that converts vectors from an inertial coordinate system to a service satellite volume coordinate system, where θ S Is the rotation angle of the service satellite, M C Is the torque input provided by the propulsion, momentum wheel, etc. devices on the service satellite.
B. Space debris dynamics model
T 1 +T 2 ＝m T a T (3)
wherein ,T1 ＝[T 1x T 1y ]，T 2 ＝]T 2x T 2y ]Respectively the tension vectors, a, on the two sub-tethers T ＝[a Tx a Ty ]Is the linear acceleration of the space debris, m T 、J T The mass and the rotational inertia of the space debris are respectively, and the connection points of the rope net and the space debris are respectively O 2 P 1 ＝[l T w T ]，O 2 P 2 ＝[l T -w T], wherein lT 、w T Half the length and width of the space debris respectively,is a rotation matrix that converts vectors from an inertial coordinate system to a spatial chip coordinate system, where θ T Is the angle of rotation of the spatial debris.
C. Tether dynamics model
Where k is the stiffness of the tether, l i For the deformed length of each tether, l i0 For the undeformed natural length of each tether Δl i ＝[Δl xi ,Δl yi ] T Is the elongation of each tether.
Step 1.2: uncertainty description of kinetic model
A. Taking the uncertainty of the dynamic parameters of the space debris into consideration, the improved dynamic equation is as follows:
where δ is the boundary value for correcting the nominal inertia coefficient.
B. Considering the initial attitude error of the space debris, the initial attitude angle is defined as follows:
α T ＝π/4·η (7)
wherein eta is a random number between 0 and 1.
The initial attitude angle change causes the change of the connection point of the tether and the space debris, and the connection point of the tether and the space debris is defined as follows in an inertial coordinate system:
wherein ,converting a position vector of a connecting point from a space fragment body coordinate system to a rotation matrix of an inertial coordinate system, setting an x-direction coordinate of the connecting point in the inertial coordinate system as d, and calculating to obtain a position vector of the connecting point in the body coordinate system as follows: />
C. Taking into account the external interference suffered by the space debris, by Gaussian noise D-N (0,0.0001 2 ) N.m to simulate the disturbance moment suffered by the space debris, the improved kinetic equation is as follows:
step 1.3: the mathematical expression of the dynamics model in the state space is:
wherein ,
f 1 ＝(O 2 P 1 ×(R -1 (θ T )·T 1 )+O 2 P 2 ×(R -1 (θ T )·T 2 ))/J T ，
f 2 ＝(O 1 P 1 ×(R -1 (θ S )·T 0 ))/J S ,
u 1 ＝0,u 2 ＝M C ,b 2 ＝1/J s .
step 2: the design of the hierarchical sliding mode control method comprises the following substeps:
step 2.1, defining a layered sliding mode surface as follows:
wherein ,z1 ，z 2 Two sub-slip mould surfaces, s is an integral slip mould surface, c 1 、c 2 Alpha is a weight coefficient greater than zero, and the desired state variable value is set to x 1d ＝x 2d ＝x 3d ＝x 4d ＝0。
Step 2.2, the design of the sliding mode approach law is as follows:
ds/dt＝-ε·sat(s)+f(x 1 ,x 2 ,x 3 ,x 4 ) (12)
where ε is the approach rate and other functions are defined as follows:
where Δ is the slip boundary value of the overall slip plane.
Wherein, gamma is the scaling factor of the control input, and 0 < gamma < 1.
Step 2.3 deducing a control law:
step 3: a propulsion controller is designed to dampen radial oscillations. Comprises the following substeps:
step 3.1, defining position errors to obtain a propulsion control law
wherein ,yS Andis respectively a garmentRadial position and velocity of satellite, y d and />The desired values of the radial position and velocity of the service satellite, respectively.
Y C ＝-k 3 ·e 1 -k 4 ·e 2 (17)
wherein ,k3 and k4 Is a control gain with positive value, Y C Is the radial force input generated by the impeller.
Step 3.2, the propulsion control targets are:
wherein ,ysb Is the switching boundary, y pb Is a convergence location boundary.
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| CN118168561A (en) * | 2024-05-14 | 2024-06-11 | 北京航天驭星科技有限公司 | Satellite speed acquisition method and system, satellite track lifting method and control system |
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| CN118168561A (en) * | 2024-05-14 | 2024-06-11 | 北京航天驭星科技有限公司 | Satellite speed acquisition method and system, satellite track lifting method and control system |
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