In this paper, the problem of controlling synchronous machines driving high pulsed, constant-power loads (CPLs) with fast ramp rates is investigated. Using a PI controller to provide offset-free tracking of the generator voltage in steady state, we design controllers using Model Predictive Control which act as a reference governor to ensure power quality constraints are met during transients. However, it is shown that a standard linear MPC algorithm creates a steady state offset due to model mismatch at off-nominal power levels resulting in loss of power quality. This problem is corrected by creating multiple linear models of the generator dynamics linearized around the nominal and high power operating points. We then demonstrate that a Hybrid Model Predictive Control algorithm (using the constrained piecewise affine prediction model) exhibits zero offset during the high power pulse. The Hybrid MPC algorithm also keeps the generator voltage within the required constraints. This approach has the benefit of correcting the model mismatch issue without using a computationally expensive nonlinear Model Predictive Control algorithm. Future work will focus on implementing and testing this hybrid MPC controller on a generator via explicit MPC techniques.