Constrained nonlinear high-efficiency model predictive technics for test mass capture

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This paper presents a nonlinear high-efficiency model predictive control (NHMPC) with constraints designed for the test mass (TM) capture phase of the drag-free satellite about gravitational wave observatory. To avoid collisions between test mass and satellite cavity, TM capture is the essential technology for drag-free satellite. Test mass is located inside an electrostatic suspension and locked by a clamp mechanism initially. The test masses are released with high initial offsets and velocities when the mechanism is retracted. The purpose of this phase is to guarantee the TM to be positioned at the cage center and attitude aligned with the local cage frame. Due to the low actuation authority of electrostatic suspension along with critical initial offsets and velocities, it is a challenging task to design the attitude and translation control schemes with simultaneous consideration of system performance and energy consumption. For the problem given above, the TM capture can be reformulated into a nonlinear quadratic optimal control problem with the state and input constraints. A nonlinear model predictive control (NMPC) structure is also designed to handle the noises by forming a closed loop. This control framework can realize optimality and robustness in a compromise. To improve the speed of solving high-dimensional nonlinear optimal control online for MPC, the indirect Chebyshev pseudospectral method with constraints is employed. The convergence and stability of the control loop are analyzed. Simulation examples show that the feasibility and performance of the designed control loop are verified compared with the existing methods and computation times in the millisecond range can be achieved.