The use of a hybrid analog-digital architecture that connects one RF chain to multiple antennas through phase shifters is an energy-efficient solution for multiuser multiple-input multiple-output (MU-MIMO) systems. However, designing the hybrid precoder is challenging due to its nonconvex objective functions and constraints. Existing algorithms struggle with high computational complexity or poor performance, which often result from slow or no convergence. This study proposes a solution that leverages model-driven deep learning (DL) to maximize the spectral efficiency of MU-MIMO systems through hybrid precoding. The optimization problem is first transformed into a weighted minimum mean square error optimization. Then, it is combined with manifold optimization and DL to improve performance and simplify the process. The algorithm is designed to be robust in changing environments and utilizes DL to address imperfect channel state information. Simulation results show that the proposed method outperforms existing algorithms, is robust in changing system parameters, and can even outperforms fully digital precoding with the same number of antennas.