CN108319136A - A kind of tether tension control method based on model prediction - Google Patents

Abstract

The invention relates to a tether tension control method based on model prediction. Firstly, an orbital dynamics model of an assembly is established. Secondly, the unknown mass identifier of captured orbital junk is established by using the recursive least squares method. Then, a relative motion state observer based on supertorsion sliding mode is established. Finally, a model predictive tension controller is designed. The present invention has the following advantages: 1. Considering unknown quality parameters and unobservable state quantities, it is more practical than existing controllers; Stabilize the tension within the ideal range under the conditions.

Description

A Tether Tension Control Method Based on Model Prediction

technical field

The invention belongs to the research on maneuvering orbit change of tethered spacecraft, and relates to a tether tension control method based on model prediction.

Background technique

The dragging and removal of orbital debris using space tethered robots has attracted much attention due to its high flexibility and high safety.

Before the implementation of removal, the space maneuvering platform first releases the tethered robot to approach and capture the orbital debris. After the capture is completed, the space maneuvering platform and the target are connected by a tether to form a combination of rigidity and flexibility. During the subsequent drag transfer, the tether tension has a significant impact on the formation configuration of the assembly. If the tension is unstable, such as a large vibration or even relaxation, it will cause the captured orbital garbage and the tether to be entangled. This entanglement, in turn, exacerbates the instability of the tether tension, which pulls the two spacecraft toward each other, causing a collision. Therefore, how to effectively stabilize the tension of the tether is the key to maintaining formation flight.

For this, scholars at home and abroad have proposed many strategies in terms of tether tension stability, for example: "Swing characteristics and smooth control of space tether drag system" published in "Journal of Beihang University", using retention and damping Controls combined tether tension compound control to eliminate target swing and maintain relative distance between stars. In the "Twist suppression method of tethered towing for spinning space debris" published on "ASCE-Journal of Aerospace Engineering", impedance control is used to stabilize the tension of the tether. However, none of their strategies considered the saturation of the actuator. For the existing tension control strategy, the reel used to retract and release the tether is an effective and commonly used tension control actuator. In each control cycle, the reel should retract and release the tether within a certain range. However, once this rope length retraction constraint is added to the existing tension controller, the tension of the tether will be unstable to varying degrees.

Contents of the invention

technical problem to be solved

In order to avoid the deficiencies of the prior art, the present invention proposes a tether tension control method based on model prediction, which can stabilize the tension within the constraints of tether retraction and release without affecting the design of the platform track, so it has high practicality. sex.

Technical solutions

A tether tension control method based on model prediction, characterized in that the steps are as follows:

Step 1. Establish the orbital dynamics model of the assembly:

In-plane transfer dynamics model of platform centroid orbit:

Among them, r is the distance between the center of mass of the platform and the center of the earth, α is the true anomaly angle of the center of mass of the platform, μ is the gravitational constant of the earth, m ₁ is the mass of the platform, F is the thrust of the platform along the local horizontal line, T is the tension of the tether, β is the interior angle of the tether track, defined as the angle with the local horizontal line;

The relative dynamics model of the spacecraft at both ends:

Among them, d is the center-of-mass distance of the spacecraft at both ends, and _m2 is the mass of orbital garbage;

Step 2. Establish an unknown track garbage mass identifier:

Let the relative dynamics model Solve the tension of the tether as:

Among them, U(k) is the tension measurement value, k is the iteration order, is the orbital junk mass estimate, and are the in-plane angular velocity and in-plane angle estimates obtained by the state observer, respectively. The iterative relationship between U(k), Y(k) and Θ(k) is established using the recursive least squares method:

Among them, k is the iteration order, λ is a forgettable factor, usually a constant close to 1

Step 3. Establish a nonlinear full-dimensional state observer:

make is the true state of the relative dynamics model, is the estimate of state X, To estimate the error, a nonlinear full-dimensional state observer is built using the supertorsion sliding mode:

in,

Wherein, δ=a ₁ f ⁺ , γ=a ₂ (f ⁺ ) ^1/2 , a ₁ and a ₂ are normal numbers around 1. f ⁺ is the model bias suprema,

Step 4. Establish a nonlinear model predictive controller:

Use the first-order difference to discretize the relative dynamics model of the spacecraft at both ends in step 1

Among them, Δτ is the sampling time, i is the sampling order;

Create a tension model for the tether:

Among them, EA is the stiffness coefficient of the tether, l ₀ is the undeformed length of the tether, c _t is the damping coefficient of the tether, and Δl(i) is the retractable length of the tether during this control;

Define the desired tether tension command:

Define the performance index function:

Among them, Q and R are weight coefficients, is the tether retraction rate, N is the number of predicted steps;

Design system constraints:

The model predictive controller uses the tether tension command T _ref , tension measurement value U(k), state estimation value and quality estimates As the input of the controller, the optimal tether retraction rate is generated, and the rate is integrated and then added to the undeformed initial rope length l ₀ to obtain the actual undeformed rope length to act on the system to complete the entire control process.

Beneficial effect

In the tether tension control method based on model prediction proposed by the present invention, firstly, an orbital dynamics model of the assembly is established. Secondly, the unknown mass identifier of captured orbital junk is established by using the recursive least squares method. Then, a relative motion state observer based on supertorsion sliding mode is established. Finally, a model predictive tension controller is designed.

The present invention has the following advantages: 1. Considering unknown quality parameters and unobservable state variables, it is more practical than existing controllers; Stabilize the tension within the ideal range under the conditions.

Description of drawings

Figure 1: Structure diagram of model predictive tension controller

Detailed ways

Now in conjunction with embodiment, accompanying drawing, the present invention will be further described:

A space tether tension model predictive control method, characterized in that the steps are as follows:

Step 1. Establish the orbital dynamics model of the assembly:

A. Platform centroid-orbit in-plane transfer dynamics model

Among them, r is the distance between the center of mass of the platform and the center of the earth, α is the true anomaly angle of the center of mass of the platform, μ is the gravitational constant of the earth, m ₁ is the mass of the platform, F is the thrust of the platform along the local horizontal line, T is the tension of the tether, β is the interior angle of the tether track, defined as the angle with the local horizontal line.

B. Relative dynamics model of spacecraft at both ends

Among them, d is the center-of-mass distance of the spacecraft at both ends, and _m2 is the mass of orbital junk.

Step 2. Establish an unknown track garbage mass identifier

Let the relative dynamics model The tether tension that can be solved is

Among them, U(k) is the tension measurement value, k is the iteration order, is the orbital junk mass estimate, and are the in-plane angular velocity and in-plane angle estimates obtained by the state observer, respectively. The iterative relationship between U(k), Y(k) and Θ(k) is established using the recursive least squares method:

Among them, λ is a forgettable factor, which is usually a constant close to 1.

Step 3. Establish a nonlinear full-dimensional state observer

make is the true state of the relative dynamics model, is the estimate of state X, for the estimation error. The following state observer is established by using the supertwisted sliding mode.

in,

Wherein, δ=a ₁ f ⁺ , γ=a ₂ (f ⁺ ) ^1/2 , a ₁ and a ₂ are normal numbers around 1. f ⁺ is the model bias suprema,

Step 4. Build a nonlinear model predictive controller

First, the B-model in step 1 is discretized using the first-order difference.

Among them, Δτ is the sampling time, i is the sampling order.

Second, build a tension model

Among them, EA is the stiffness coefficient of the tether, l ₀ is the undeformed length of the tether, c _t is the damping coefficient of the tether, and Δl(i) is the retractable length of the tether during this control. Define the desired tether tension command as follows:

Then, define the performance index function as follows:

Among them, Q and R are weight coefficients, is the tether retraction rate, and N is the number of predicted steps.

Finally, the design system constraints are as follows:

The control flow is shown in Figure 1. Firstly, the position sensor measures the coordinates [x,y] ^T within the track plane of the track garbage relative to the platform, and the tension sensor measures the tension of the tether. Second, the state observer according to the position coordinates and Estimated Velocity Information for Orbital Junk in is the quality identifier based on state estimation information Estimated mass of orbital debris identified from tether tension measurements. Then, the model predictive controller uses the tension command, tension measurement value, state estimation value and quality estimation value to generate the optimal tether retraction rate, which is integrated and then added to the tether undeformed initial rope length l ₀ to obtain the actual undeformed tether The length of the deformed rope acts on the system to complete the entire 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, α 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, β 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:

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. And (3) establishing an iterative relationship among 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,

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, c_tIs the damping coefficient of the tether, and delta l (i) is the retraction 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,the tether take-up and pay-off rate, N is the predicted step number;

designing system constraints:

model predictive controller utilizing tether tension command T_refTension measurement value U (k), state estimation valueAnd a quality estimateAs an input to the controller, an optimal tether pay-off and take-up rate is generated, which is integrated with the initial undeformed tetherLength of rope l₀Adding to obtain the actual length of the undeformed rope to act on the system, and finishing the whole control process.