The goal of this paper is to investigate the use of a very simple direct adaptive controller in the guidance of a large, flexible launch vehicle. The adaptive controller, requiring no on-line information about the plant other than sensor outputs, would be a more robust candidate controller in the presence of unmodeled plant dynamics than a model-based fixed gain linear controller. NASA’s seven-state FRACTAL academic model for ARES I-X was employed as an example launch vehicle on which to develop the controller.
To better understand the difficult dynamic issues, we started with a simplified model that incorporated the inherent instability of the plant and the nonminimum phase nature of the dynamics: an inverted pendulum with an attachable slosh tank. We formulated controllers for this simplified plant with slosh dynamics using control algorithms developed only on a reduced–order model consisting of the rigid body dynamics without slosh. The controllers must be designed to reject three different persistent input disturbances: persistent pulse, step, and sine. We assumed that only position feedback was available, and that rates would have to be estimated.
For comparison, a fixed gain linear controller was developed using the well-known Linear Quadratic Gaussian methodology employing state estimation to obtain rate estimates. For a stable adaptive controller, we used direct adaptive control theory developed by Balas, et al. For this theory we need CB > 0 and a minimum-phase open-loop transfer function. We employed a new transmission zero selection method to develop a blended output shaping matrix which would satisfy these conditions robustly. We used approximate differentiation filters to obtain rates for the adaptive controller. Again for comparison, we redesigned the LQG controller to use the same blended output matrix and filters.
Following the work on the pendulum, the same method was applied to develop an adaptive controller for the FRACTAL launch vehicle model. An adaptive controller stabilizes a rigid body version of FRACTAL over a very long timeline while exceeding all reasonable state and output limits.
Convergence results for an averaged LQR problem with applications to reinforcement learning