Piezoelectric based Tonpilz Transducer is a mechatronics control device that works on high-power sound propagation to navigate or detect objects under the water. In order to analyze the design and performance, we generate a mathematical model of such apparatus by applying the finite element method, which yields a large-scale sparse index-I descriptor system. We also study low-rank Gramian factors based on Balanced Truncation to obtain the reduced-order model for efficient design on the limited frequency domain. The low-rank Gramian factors are obtained by solving a pair of frequency-limited Lyapunov equations. We have modified the low-rank Alternative Direction Implicit method to solve the Lyapunov equations for retaining sparsity and ensuring the preservation of the structure of the system matrices. Numerical analyses are conducted to validate the proposed techniques, and the reduced order physical model is regenerated for a comparative physical analysis with the full dimensional physical model.