CN108319136B - Tether tension control method based on model prediction - Google Patents
Tether tension control method based on model prediction Download PDFInfo
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Abstract
The invention relates to a tether tension control method based on model prediction. Secondly, establishing an unknown quality identifier of the captured rail waste by using a recursive least square method. Then, a relative motion state observer based on the overtorque sliding mode is established. Finally, a model predictive tension controller is designed. The invention has the following advantages: the method has the advantages that firstly, unknown quality parameters and unobservable state quantities are considered, and the method is more practical compared with the existing controller; and secondly, by adopting model predictive control, the method can stabilize the tension in an ideal range under the condition that an actuating mechanism is constrained.
Description
Technical Field
The invention belongs to the research of maneuvering orbital transfer of a tethered spacecraft, and relates to a tethered tension control method based on model prediction.
Background
The use of space tethered robots for orbital trash removal by towing has received attention for their high flexibility and safety.
Before removal is carried out, the space mobile platform releases the rope robot to approach and catch the rail rubbish. After the catching is finished, the space mobile platform and the target body are connected into a combination body with the rigidity and flexibility through a tether. In subsequent drag transfers, tether tension has a significant effect on the formation configuration of the combination. If the tension is unstable, such as large amplitude oscillation or even slack, the captured track trash and the tether can be entangled. This winding, in turn, exacerbates the instability in tether tension, pulling the two end spacecraft toward each other, resulting in a collision. Therefore, how to efficiently stabilize tether tension is critical to maintaining formation flight.
For this reason, scholars at home and abroad have proposed a number of strategies in terms of tether tension stabilization, such as: the swinging characteristic and the stability control of a space tether dragging system published in the journal of Beijing university of aerospace are combined with tether tension compound control by using a position-retaining and damping control to eliminate the swinging of a target body and keep the relative distance between satellites. In the publication "Twist application method of thermal stroke for training space deployment" of ASCE-journal of Aerospace Engineering, impedance control is used to stabilize the tether tension. However, none of their strategies takes into account the problem of actuator saturation. With existing tension control strategies, the reel used to unwind and unwind the tether is an effective and commonly used tension control actuator. In each control cycle, the reel should unwind and unwind the tether within a certain range. However, once such a tether take-up and pay-off constraint is added to existing tension controllers, the tether tension will be unstable to varying degrees.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a tether tension control method based on model prediction, which can stabilize tension in tether retraction constraint and release and does not influence the design of a platform track, so that the method has higher practicability.
Technical scheme
A tether tension control method based on model prediction is characterized by comprising the following steps:
step 1, establishing a dynamic model of an assembly orbit:
the platform mass center orbital plane internal transfer dynamic model:
wherein r is the distance between the platform centroid and the geocentric, alpha is the true peripherial angle of the platform centroid, mu is the gravity constant of the earth, and m is1The mass of the platform, F is the thrust of the platform along the local horizontal line, T is the tension of the tether, and beta is the inner angle of the orbital plane of the tether and is defined as the included angle between the orbital plane of the tether and the local horizontal line;
relative dynamics model of two-end spacecraft:
wherein d is the centroid distance of the spacecraft at the two ends, m2Is the track trash quality;
step 2, establishing an unknown track garbage quality identifier:
let in the relative dynamics modelThe rope tension after being released is as follows: u (k) ═ y (k) Θ (k)
Wherein U (k) ═ T is the tension measurement value,
where U (k) is the tension measurement, k is the iteration order,is an estimated value of the quality of the rail refuse,andrespectively, the in-plane angular velocity and the in-plane angle estimate from a state observer. Establishing an iterative relationship between U (k), Y (k) and theta (k) by using a recursive least square method:
where k is the order of iteration and λ is a forgetting factor, usually taking a constant close to 1
Step 3, establishing a nonlinear full-dimensional state observer:
order toFor the true state of the relative kinetic model,in order to be an estimate of the state X,in order to estimate errors, a nonlinear full-dimensional state observer is established by utilizing an overtorque sliding mode:
wherein the content of the first and second substances,
wherein δ is a1f+，γ＝a2(f+)1/2，a1And a2Is a normal number around 1. f. of+Is a deviation of the modelThe supremum limit of (a) is,
step 4, establishing a nonlinear model predictive controller:
discretizing the relative dynamic model of the two-end spacecraft in the step 1 by using first-order difference
Where Δ τ is the sampling time and i is the sampling order;
establishing a tension model of a tether:
where EA is the tether stiffness coefficient,/0Is the length of the undeformed tether, ctIs the damping coefficient of the tether, and delta l (i) is the retracting length of the tether in the current control;
defining a desired tether tension command:
defining a performance indicator function:
wherein Q and R are weight coefficients, u ═ Δ l is the tether take-up and pay-off rate, and N is the predicted step number;
designing system constraints:
model predictive controller utilizing tether tension command TrefTension measurement value U (k), state estimation valueAnd a quality estimateAs input to the controller, an optimal tether take-up and pay-off rate is generated, which is integrated with the initial length l of the tether when the tether is undeformed0Adding to obtain the actual undeformed ropeLong acting on the system to complete the whole control process.
Advantageous effects
The invention provides a tether tension control method based on model prediction. Secondly, establishing an unknown quality identifier of the captured rail waste by using a recursive least square method. Then, a relative motion state observer based on the overtorque sliding mode is established. Finally, a model predictive tension controller is designed.
The invention has the following advantages: the method has the advantages that firstly, unknown quality parameters and unobservable state quantities are considered, and the method is more practical compared with the existing controller; and secondly, by adopting model predictive control, the method can stabilize the tension in an ideal range under the condition that an actuating mechanism is constrained.
Drawings
FIG. 1: model prediction tension controller structure diagram
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
a spatial tether tension model prediction control method is characterized by comprising the following steps:
step 1, establishing a dynamic model of an assembly orbit:
A. platform mass center orbital plane internal transfer dynamic model
Wherein r is the distance between the platform centroid and the geocentric, alpha is the true peripherial angle of the platform centroid, mu is the gravity constant of the earth, and m is1The mass of the platform, F is the thrust of the platform along the local horizontal line, T is the tension of the tether, and beta is the inner angle of the orbital plane of the tether and is defined as the included angle between the orbital plane of the tether and the local horizontal line.
B. Relative dynamics model of two-end spacecraft
Wherein d is the centroid distance of the spacecraft at the two ends, m2Is the track trash quality.
Step 2, establishing an unknown track garbage quality identifier
Let in the relative dynamics modelThe rope tying tension can be released as follows: u (k) ═ y (k) Θ (k)
Wherein U (k) ═ T is the tension measurement value,
where U (k) is the tension measurement, k is the iteration order,is an estimated value of the quality of the rail refuse,andrespectively, the in-plane angular velocity and the in-plane angle estimate from a state observer. Establishing an iterative relationship between U (k), Y (k) and theta (k) by using a recursive least square method:
where λ is a forgetting factor, and usually takes a constant close to 1.
Step 3, establishing a nonlinear full-dimensional state observer
Order toFor the true state of the relative kinetic model,in order to be an estimate of the state X,to estimate the error. The following state observer was built using the overtorque sliding mode.
Wherein the content of the first and second substances,
wherein δ is a1f+，γ＝a2(f+)1/2，a1And a2Is a normal number around 1. f. of+Is a deviation of the modelThe supremum limit of (a) is,
step 4, establishing a nonlinear model predictive controller
First, the B model in step 1 is discretized using a first order difference.
Where Δ τ is the sampling time and i is the sampling order.
Secondly, a tension model is established
Where EA is the tether stiffness coefficient,/0Is the length of the undeformed tether, ctIs the damping coefficient of the tether, and Δ l (i) is the retraction length of the tether at this time of control. The desired tether tension command is defined as follows:
then, the performance indicator function is defined as follows:
and Q and R are weight coefficients, u-delta i is the tether retraction rate, and N is the predicted step number.
Finally, the design system constraints are as follows:
the control flow is shown in fig. 1. First, the position sensor measures the coordinates [ x, y ] of the rail refuse in the rail plane relative to the platform]TAnd the tension sensor measures the tension of the tether. Secondly, the state observer is based on the position coordinates andestimating speed information of off-track spamWhereinThe quality identifier estimates information according to the stateAnd identifying the estimated quality of the rail waste by using the tether tension measurement value. Then, the model predictive controller utilizes the tension instruction, the tension measured value, the state estimated value and the quality estimated value to generate the optimal tether retraction rate, and the rate is integrated with the initial length l of the undeformed tether0Adding to obtain the actual length of the undeformed rope to act on the system, and finishing the whole control process.
Claims (1)
1. A tether tension control method based on model prediction is characterized by comprising the following steps:
step 1, establishing a dynamic model of an assembly orbit:
the platform mass center orbital plane internal transfer dynamic model:
wherein r is the distance between the platform centroid and the geocentric, alpha is the true peripherial angle of the platform centroid, mu is the gravity constant of the earth, and m is1The mass of the platform, F is the thrust of the platform along the local horizontal line, T is the tension of the tether, and beta is the inner angle of the orbital plane of the tether and is defined as the included angle between the orbital plane of the tether and the local horizontal line;
relative dynamics model of two-end spacecraft:
wherein d is the centroid distance of the spacecraft at the two ends, m2Is the track trash quality;
step 2, establishing an unknown track garbage quality identifier:
let in the relative dynamics modelThe rope tension after being released is as follows: u (k) ═ y (k) Θ (k)
Wherein U (k) ═ T is the tension measurement value,
where U (k) is the tension measurement, k is the iteration order,is an estimated value of the quality of the rail refuse,andthe method comprises the steps of obtaining an in-plane angular rate and an in-plane angular estimated value by a state observer respectively; establishing an iterative relationship between U (k), Y (k) and theta (k) by using a recursive least square method:
where k is the order of iteration and λ is a forgetting factor, usually taking a constant close to 1
Step 3, establishing a nonlinear full-dimensional state observer:
order toFor the true state of the relative kinetic model,in order to be an estimate of the state X,in order to estimate errors, a nonlinear full-dimensional state observer is established by utilizing an overtorque sliding mode:
wherein the content of the first and second substances,
wherein δ is a1f+，γ＝a2(f+)1/2，a1And a2Is a normal number around 1; f. of+Is a deviation of the modelThe supremum limit of (a) is,
step 4, establishing a nonlinear model predictive controller:
discretizing the relative dynamic model of the two-end spacecraft in the step 1 by using first-order difference
Where Δ τ is the sampling time and i is the sampling order;
establishing a tension model of a tether:
where EA is the tether stiffness coefficient,/0Is the length of the undeformed tether, ctIs the damping coefficient of the tether, and delta l (i) is the retracting length of the tether in the current control;
defining a desired tether tension command:
defining a performance indicator function:
wherein Q and R are weight coefficients, u ═ Δ l is the tether take-up and pay-off rate, and N is the predicted step number;
designing system constraints:
model predictive controller utilizing tether tension command TrefTension measurement value U (k), state estimation valueAnd a quality estimateAs input to the controller, an optimal tether take-up and pay-off rate is generated, which is integrated with the initial length l of the tether when the tether is undeformed0Adding to obtain the actual length of the undeformed rope to act on the system, and finishing the whole control process.
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| CN109189091B (en) * | 2018-07-25 | 2021-11-02 | 西北工业大学 | Multi-spacecraft cooperative control method based on integral sliding mode and model predictive control |
| CN109613822B (en) * | 2018-11-27 | 2022-01-18 | 上海航天控制技术研究所 | Space tether system deployment control method based on nonlinear model predictive control |
| CN110007681B (en) * | 2018-11-28 | 2020-06-26 | 北京理工大学 | Optimization method for realizing spin stability and unfolding of rope formation by using continuous propeller |
| CN110174844B (en) * | 2019-07-03 | 2021-08-10 | 西北工业大学 | Generalized order sliding mode prediction control method of remote control system |
| CN112180944B (en) * | 2020-10-22 | 2022-02-15 | 南京航空航天大学 | Rope-tied wheel type mobile robot motion control system and method |
| TWI826322B (en) * | 2023-05-18 | 2023-12-11 | 威綸科技股份有限公司 | Display apparatus having waterproof and dustproof structure |
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