The nominal performance of mechanical systems is often degraded by unknown disturbances. A two-degree-of-freedom control structure can decouple nominal performance from disturbance rejection. However, perfect disturbance rejection is unattainable when the disturbance dynamic is unknown. In this work, we reveal an inherent tradeoff in disturbance estimation subject to tracking speed and tracking uncertainty. Then, we propose two novel methods to enhance disturbance estimation: an interacting mult