Sliding Mode Control Strategies for Spacecraft Rendezvous Maneuvers

Transcription

1 Osaka University March 15, 2018 Sliding Mode Control Strategies for Spacecraft Rendezvous Maneuvers Elisabetta Punta CNR-IEIIT, Italy

2 Problem Statement First Case Spacecraft Model Position Dynamics Attitude Dynamics Actuation Systems Sliding Mode Control First Order Sliding Mode - Position Second Order Sliding Mode - Attitude Simulation Results Remarks Rendezvous Maneuvers Sliding Mode Control Spacecraft Systems

3 Spacecraft Systems

4 Position Dynamics uncertainties control The position vector The force vector in the LVLH frame The force vector in the body frame The transformation matrix between body and LVLH frames The control matrix

5 Attitude Dynamics Quaternions uncertainties control The angular velocities vector of the Chaser The angular velocities vector of the RW The moment of inertia of the RW The control matrix

6 Mono-directional Actuation System for Position Control The actuation system for position control exploits thrusters. The thrusters can exert mono-directional on-off actions. The control design will specify thrusters number and disposition. Mono-directional Action Non-modulated On-off Action Fixed Limited Switching Frequency The inverse of the constant allowed switching frequency for the is the maximum thruster.

7 Thrusters (I) The thrusters produce forces and moments that have to be considered for the evaluation of the spacecraft dynamics. The task of the thruster model is to convert On/Off command into thrust and moment variation according to their shoot direction and their location wrt the CoM. Forces Thrusters +X 1X 3X -X 2X 4X +Y 2Y 3Y -Y 1Y 4Y +Z 3Z 4Z -Z 2Z 1Z 7 Two thrusters have to switched on simultaneously to provide the necessary force to move the spacecraft.

8 Thrusters (II) Thrusters are characterized by predictable, accurate and repeatable performance but they cannot be modulated. The maximum thrust is provided when the thrusters is switched on. An electronic device on thrusters permit to halve the maximum thrust but can be activated only one time. Discontinuous Action Mono-directional Action Fixed Limited Switching Frequency Non-modulated On-off Action Bias and random errors are considered for the thruster errors in magnitude. Directional cosines for the shoot errors. 8

9 Thrusters (III) Forces Thrusters +X 1X 3X -X 2X 4X +Y 2Y 3Y -Y 1Y 4Y +Z 3Z 4Z -Z 2Z 1Z Component-wise directions of the Control Vectors Two thrusters have to switched on simultaneously to provide the necessary force to move the spacecraft. The number of pairs of thrusters used to fully actuate the system is 12 (6 pairs). The thrusters of the pair are always switched on together and exert the nominal force on the Chaser

10 Actuation System for Attitude Control The actuation system for attitude control exploits reaction wheels. The RW actuators can exert bi-directional continuous actions. Three reaction wheels, driven by electric motors powered by the spacecraft electrical power supply, are used. Bi-directional Actions Saturated on the maximum torque Continuous Actions A saturation on the maximum torque provided by the RW.

11 Spacecraft Rendezvous Maneuvers

12 Rendezvous Maneuvers (I) Spacecraft Systems Rendezvous Maneuvers Approaching Maneuver Cone

13 Rendezvous Maneuvers (II) Spacecraft Systems Rendezvous Maneuvers Approaching Maneuver Cone

14 First and Second Order Sliding Mode Control Strategies for Spacecraft Rendezvous Maneuvers

15 Spacecraft Rendezvous Maneuvers First Order Sliding Mode Control

16 Position Tracking First Order SMC First Order SMC n = number of thrusters, T max = maximum thrust Sliding Output Component-wise directions of the Control Vectors Two thrusters have to switched on simultaneously to provide the necessary force to move the spacecraft.

17 Multi-Input Sliding Mode Control: Switching Logic Component-Wise Switching Logic

18 Desired Position, Velocity and Control Switching Frequency Control Switching Frequency Position and Velocity Reference

19 Spacecraft Rendezvous Maneuvers Second Order Sliding Mode Control

20 Attitude Tracking Second Order SMC Super-Twisting SMC Sliding Output Desired Attitude The desired attitude implies that LVLH and Body Frames are aligned

21 Simulation Results

22 Simulation Results (II) Different cases are analyzed in function of the switching frequencies of the thrusters and of the distance between the two bodies. The external disturbances are considered for all the simulations. The thruster errors are included in some simulations. For all the simulations the performance indicators are the final R bar, the fuel consumption and the total time required for complete the maneuver. 22

23 Simulation Results (I) A 6 DOF simulation is considered for evaluation of the tracking performance of the proposed controller. The Target CoM is located at the origin of the LVLH frame and is 500 m far from the Chaser. The maneuver starts with a speed equal to 0.15 m/s at an orbit altitude of 650 km. Spacecraft geometrical and inertial data [4] : Low thrust produces low spacecraft accelerations and guarantees low fuel consumption and high precision. [4] Guglieri, G., Quagliotti, F., Pellegrino, P., and Saluzzi, A., Analysis of Automated Rendezvous and Docking Operations, AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, Hawaii,

24 Simulation Results: Forces

25 Simulation Results: Moments

26 Simulation Results: Case A

27 Simulation Results: Case B

28 Simulation Results: Case C

29 Remarks

30 Remarks Sliding mode controllers are discontinuous and must guarantee that the system trajectories reach and maintain a motion on the desired sliding manifold. Global stability and robustness to system uncertainties. A first order sliding mode controller is implemented, reducing the fuel consumption and guaranteeing tracking in terms of positions and speeds. A second order sliding mode controller is designed as for the attitude control of the spacecraft. 30

31 Simplex Sliding Mode Control Strategies for Spacecraft Rendezvous Maneuvers

32 Problem Statement Second Case Spacecraft Model Position Dynamics Attitude Dynamics Actuation Systems Sliding Mode Control Simplex Sliding Mode - Position Second Order Sliding Mode - Attitude Simulation Results Conclusions Rendezvous Maneuvers Sliding Mode Control Spacecraft Systems

33 Spacecraft Systems

34 Position Dynamics uncertainties control The position vector The force vector in the LVLH frame The force vector in the body frame The transformation matrix between body and LVLH frames The control matrix

35 Attitude Dynamics Quaternions uncertainties control The angular velocities vector of the Chaser The angular velocities vector of the RW The moment of inertia of the RW The control matrix

36 Mono-directional Actuation System for Position Control The actuation system for position control exploits thrusters. The thrusters can exert mono-directional on-off actions. The control design will specify thrusters number and disposition. Mono-directional Action Non-modulated On-off Action Fixed Limited Switching Frequency The inverse of the constant allowed switching frequency for the is the maximum thruster.

37 Actuation System for Attitude Control The actuation system for attitude control exploits reaction wheels. The RW actuators can exert bi-directional continuous actions. Three reaction wheels, driven by electric motors powered by the spacecraft electrical power supply, are used. Bi-directional Actions Saturated on the maximum torque Continuous Actions A saturation on the maximum torque provided by the RW.

38 Spacecraft Rendezvous Maneuvers

39 Rendezvous Maneuvers Spacecraft Systems Rendezvous Maneuvers Approaching Maneuver Cone

40 Spacecraft Rendezvous Maneuvers Sliding Mode Control Design

41 Simplex of Vectors

42 Multi-Input Sliding Mode Control: Switching Logics Component-Wise Switching Logic Simplex-Based Switching Logic

43 Position Tracking Simplex SMC The thrusters configuration is designed to have a zero moment in the ideal case. The minimum number of control directions required to fully actuate the system is 4 and it is sufficient if and only if the 4 directions form a simplex of vectors in. The total number of required thrusters is 8. The thrusters of the pair are always switched on together and exert the nominal force on the Chaser

44 Position Tracking Simplex SMC Simplex SMC Sliding Output Simplex of Vectors

45 Desired Position, Velocity and Control Switching Frequency Control Switching Frequency Position and Velocity Reference

46 Attitude Tracking SMC Super-Twisting SMC Sliding Output Desired Attitude The desired attitude implies that LVLH and Body Frames are aligned

47 Simulation Results

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52 Conclusions

53 Conclusions SMC for simultaneous position tracking and attitude control of a rendezvous maneuver (approaching phase) between two spacecraft. Position tracking: simplex SMC considers different phases of the approaching maneuver based on the Chaser distance from the Target. Attitude control: Second Order SMC algorithm designs continuous control signals for the reaction wheels. Simplex First Order Sliding Mode Simplex SMC permits to reduce the number of thrusters, the fuel consumption and the switching frequency required to control the spacecraft. The control strategy is implemented in an on-board algorithm with minimum computational effort. Results.

54 Aerospace Applications (E. Capello, F. Dabbene, G. Guglieri, E. Punta, R. Tempo) Rendezvous and Docking Maneuvers via Sliding Mode Controllers [1] E. Capello, F. Dabbene, G. Guglieri, E. Punta, R. Tempo, Rendez-Vous and Docking Position Tracking via Sliding Mode Control, American Control Conference-ACC 2015, Chicago, IL, USA, July 1 3, [2] E. Capello, F. Dabbene, G. Guglieri, E. Punta, R. Tempo, Rendez-Vous and Docking Maneuvers via Sliding Mode Controllers, Journal of Guidance, Control, and Dynamics, vol. 40, no. 6, 2017.