The recently developed pitch-controllable text-to-speech (TTS) model, i.e. FastPitch, was conditioned for the pitch contours. However, the quality of the synthesized speech degraded considerably for pitch values that deviated significantly from the average pitch; i.e. the ability to control pitch was limited. To address this issue, we propose two algorithms to improve the robustness of FastPitch. First, we propose a novel timbre-preserving pitch-shifting algorithm for natural pitch augmentation. Pitch-shifted speech samples sound more natural when using the proposed algorithm because the speaker's vocal timbre is maintained. Moreover, we propose a training algorithm that defines FastPitch using pitch-augmented speech datasets with different pitch ranges for the same sentence. The experimental results demonstrate that the proposed algorithms improve the pitch controllability of FastPitch.