Piano cover generation aims to automatically transform a pop song into a piano arrangement. While numerous deep learning approaches have been proposed, existing models often fail to maintain structural consistency with the original song, likely due to the absence of beat-aware mechanisms or the difficulty of modeling complex rhythmic patterns. Rhythmic information is crucial, as it defines structural similarity (e.g., tempo, BPM) and directly impacts the overall quality of the generated music. In this paper, we introduce Etude, a three-stage architecture consisting of Extract, strucTUralize, and DEcode stages. By pre-extracting rhythmic information and applying a novel, simplified REMI-based tokenization, our model produces covers that preserve proper song structure, enhance fluency and musical dynamics, and support highly controllable generation through style injection. Subjective evaluations with human listeners show that Etude substantially outperforms prior models, achieving a quality level comparable to that of human composers.