Zero Placement for Discrete Time Systems

Spacecraft sensors often perform tracking maneuvers and require precision tracking. Feedback control design can struggle to achieve the desired bandwidth and meet performance objectives. One solution to bypass this is using inverse control ideas, finding the input needed to produce the desired output given a model and desired output. However, this approach usually fails for discrete time systems due to unstable input commands. This paper proposes a new approach to stable inverse theory using a zero placement algorithm analogous to modern control theory’s pole placement methods. The new inverse theory addresses limitations of the existing theory in the literature, by incorporating additional zero order hold inputs between addressed time steps. The input needed to produce the desired output can be made stable. This stable inverse theory can be applied to feedback control design, overcoming limitations and achieving zero error above the bandwidth. It enables spacecraft sensors to perform more precise tracking, especially for repeated tracking of specific trajectories. The inverse model result can be used in Iterative Learning Control to converge to a stable inverse result in hardware, eliminating model errors and repeating disturbances.