Predictive Cost Adaptive Control for Harmonic Disturbance Rejection in Systems with Underdamped, Undermodeled, and Undersampled Dynamics

Lightly damped modes that lie within or outside the controller bandwidth of an attitude control system are challenging. As an active control strategy for harmonic disturbances, the present paper applies predictive cost adaptive control (PCAC) to a system with a rigid-body mode and a lightly damped mode that is unmodeled and possibly aliased. PCAC is applied to the specific case of resonance, where the frequency of the exogenous harmonic disturbance coincides with the peak-amplification frequency of the system. LQG control with and without an internal model and with known and uncertain modal frequency provides a baseline for comparison with PCAC, which uses online identification and requires no prior knowledge of the system dynamics or disturbance spectrum. The numerical comparison accounts for the intersample behavior of the lightly damped mode.