Zero Placement for Inverting Discrete-time Model and its Relation with Pseudo-Inverse

Spacecraft tracking systems, such as the James Webb Space Telescope, demand high precision. Feedforward control using inverse methods can improve performance but may introduce unstable zeros in discrete-time systems, making control impractical. A prior method stabilizes the inverse by placing zeros inside the unit circle through multiple zero-order holds. This paper investigates pseudo-inverse solutions in iterative learning control, which stabilize control without explicit zero placement. By comparing zero-placement algorithms and pseudo-inverse methods, we aim to better understand their effects on system dynamics and improve feedforward control for spacecraft tracking.