Stable Inverse Control for Discrete Time Systems Using Second Order Holds

Spacecraft often perform high-accuracy tracking maneuvers where feedback control is constrained by limited bandwidth. Feedforward control, obtained by inverting the system dynamics, generates command inputs that reproduce desired trajectories and, in digital implementations, requires discrete-time inverses. This paper develops a lifted input–output formulation for second-order hold (SOH) discretizations that characterizes the discrete dynamics governing stable inversion. A rank-structure analysis shows that nonminimum-phase zeros of the SOH model induce rank deficiency in the lifted operator, revealing the mechanism of unstable discrete-time inverses. Simulations on a fourth-order flexible spacecraft confirm comparable tracking accuracy to zero-order-hold (ZOH) with reduced intersample error and control effort.