Methods and systems for controlling multi-body vehicles with fuel slosh

1. A method for stabilizing a vehicle with fuel slosh, the method comprising:

providing a controller for a multi-body assembly, the controller formed by a method comprising:

selecting vehicle configuration and velocity as states of a rigid body;

writing equations of motion for the multi-body assembly;

determining velocity states that are unactuated;

defining a decoupling transformation from the unactuated velocity states; and

transforming the equations of motion using the decoupling transformation such that unactuated states are decoupled from actuated states; and

coupling a slosh state estimator to the controller such that the slosh state estimator is in operative communication with an input to the controller and an output from the controller.

2. The method of claim 1 , wherein the slosh state estimator is formed by a method comprising:

selecting vehicle configuration and velocity as states of a rigid body;

writing equations of motion for the multi-body assembly;

determining a velocity state that needs to be observed;

defining a decoupling transformation from the velocity state that needs to be observed; and

transforming the equations of motion using the decoupling transformation such that an observer state is decoupled from other measured states.

3. The method of claim 1 , wherein the vehicle comprises a multi-body launch vehicle.

4. The method of claim 3 , wherein the method provides inner loop control of the multi-body launch vehicle.

5. The method of claim 3 , wherein an attitude dynamic of the multi-body launch vehicle is underactuated.

6. The method of claim 3 , further comprising modeling a booster body as a first rigid body, an engine body as a second rigid body, and a fuel slosh as a third rigid body.

7. The method of claim 6 , further comprising providing a control input comprising an angle of engine thrust.

8. The method of claim 7 , wherein the angle of engine thrust comprises an engine gimbal torque value.

9. The method of claim 6 , further comprising providing a control input comprising an angle of engine thrust and an angle of auxiliary thrusters.

10. The method of claim 6 , further comprising providing a control input comprising an angle of engine thrust and a magnitude of engine thrust.

11. The method of claim 1 , wherein the method uses a dynamic inversion-based nonlinear control algorithm that accounts for coupled dynamics of interconnected rigid bodies.

12. The method of claim 1 , wherein the slosh state estimator provides an estimate of fuel slosh dynamics to the controller.

13. A system for stabilizing a vehicle with fuel slosh, the system comprising:

a controller having a control input and a control output, the control output in communication with the vehicle; and

a slosh state estimator in operative communication with the control input and the control output of the controller, the slosh state estimator comprising:

a reduced order observer module;

a first input to the observer module, the first input in operative communication with the control output;

at least one output from the observer module, the output in operative communication with the control input;

a summing device in operative communication with the output from the observer module and an output from the vehicle;

an observer gain module in operative communication with the summing device; and

a second input to the observer module, the second input in operative communication with the gain module.

14. The system of claim 13 , wherein the output from the observer module is in operative communication with a signal selector.

15. The system of claim 13 , wherein the output from the observer module is in operative communication with an integrator.

16. A computer readable medium having instructions stored thereon for implementing a method for providing a controller for use in stabilizing a vehicle with fuel slosh, the controller formed by a method comprising:

selecting vehicle configuration and velocity as states of a rigid body;

writing equations of motion for the multi-body assembly;

determining velocity states that are unactuated;

defining a decoupling transformation from the unactuated velocity states; and

transforming the equations of motion using the decoupling transformation such that unactuated states are decoupled from actuated states.

17. The computer readable medium of claim 16 , further comprising providing a slosh state estimator formed by a method comprising:

selecting vehicle configuration and velocity as states of a rigid body;

writing equations of motion for the multi-body assembly;

determining a velocity state that needs to be observed;

defining a decoupling transformation from the velocity state that needs to be observed; and

transforming the equations of motion using the decoupling transformation such that an observer state is decoupled from other measured states.

18. The computer readable medium of claim 17 , wherein the method further comprises modeling a booster body as a first rigid body, an engine body as a second rigid body, and a fuel slosh as a third rigid body.

19. The computer readable medium of claim 18 , wherein the method further comprises providing a control input comprising an angle of engine thrust.

20. The computer readable medium of claim 19 , wherein the control input further comprises an angle of auxiliary thrusters or a magnitude of engine thrust.