Sensing of displacement using only inertial measurement devices (IMDs) such as rate gyros and accelerometers is an active research topic with many diverse applications in biomechanics, human motion, earthquake engineering, robotics and mixed reality interfaces.

The main challenge in using integration to obtain velocity or position data from IMDs is DC drift in measurements. Even very small DC offsets in acceleration measurements lead to significant errors that increase linearly in single integration and parabolically in double integration. This severely complicates the problem of sensing static (DC) displacements using IMDs. Nevertheless, a significant amount of literature has focused on improving absolute (both static and dynamic) displacement estimations in spite of DC offsets.

We use a different approach to tackle the drift problem and achieve real-time displacement measurements sufficiently accurate for modeling and feedback control. We avoid the static displacement sensing problem by constraining our measurements to sense only dynamic displacements. This constraint puts a limitation on the applications in which our approach can be used; however, many important applications are still possible, such as frequency domain system identification and active vibration suppression, among others.

Within this project, we built a two-stage critically damped op-amp based analog integrator circuit, interspaced with high-pass filters for eliminating DC offsets before and after each integration step. We tested the accuracy of both digital (rectangular and trapezoidal) and analog integration methods under varying sampling rates. We then conducted frequency domain system identification of a speaker with and without encoder attachment. Finally, we controlled the displacement of the speaker with a PD controller based on only acceleration measurements, experimentally verifying the accuracy of the obtained model as well as of the displacements sensed via both integration methods.