In this work, we study codebook designs for full-dimension multiple-input multiple-output (FD-MIMO) systems with a multi-panel array (MPA). We propose novel codebooks which allow precise beam structures for MPA FD-MIMO systems by investigating the physical properties and alignments of the panels. We specifically exploit the characteristic that a group of antennas in a vertical direction exhibit more correlation than those in a horizontal direction. This enables an economical use of feedback bits while constructing finer beams compared to conventional codebooks. The codebook is further improved by dynamically allocating the feedback bits on multiple parts such as beam amplitude and co-phasing coefficients using reinforcement learning. The numerical results confirm the effectiveness of the proposed approach in terms of both performance and computational complexity.