Generalized Predictive Control Using Second-Order Hold Discretization

Generalized Predictive Control (GPC) enables anticipative tracking by optimizing future control actions over a prediction horizon, but its performance depends critically on the accuracy of the discrete-time model. Second-Order Hold (SOH) discretization offers improved dynamic fidelity for systems with smooth state evolution or flexible modes. This paper presents a GPC formulation that directly incorporates SOH-discretized models without altering the standard GPC structure. Numerical simulations on a fourth-order spacecraft model with rigid-body and flexible dynamics demonstrate that SOH-based GPC achieves near-perfect tracking of low-frequency trajectories while maintaining feasible control effort. These results highlight the potential of SOH-discretized GPC for precision spacecraft attitude control.