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A sensing estimation scheme is presented that combines analog and threshold sensing on a piezoelectric microactuator for calibration of microscale inertial sensors. Using a variation of the Kalman filter, an asynchronous threshold sensor improves state estimates obtained from less reliable analog sensor measurements of microactuator motion. The resulting velocity estimates are compared with estimates without threshold sensing, and related to feasible calibration performance for gyroscopes. Results show that incorporating threshold sensors in a projected low-noise environment based on capacitive sensing will produce high-accuracy velocity measurements at certain fixed angles, with an approximately 80% reduction in angular velocity estimation error. Experimental testing with noisier, more variable piezoelectric sensing shows improved estimation accuracy at all velocities and positions when threshold detections are added. In simulation, the addition of feedback control is shown to further improve estimation accuracy.

The force transmitted from the front tires to the steering rack of a vehicle, called the rack force, plays an important role in the function of electric power steering (EPS) systems. Estimates of rack force can be used by EPS to attenuate road feedback and reduce driver effort. Further, estimates of the components of rack force (arising, for example, due to steering angle and road profile) can be used to separately compensate for each component and thereby enhance steering feel. In this paper, we present three vehicle and tire model-based rack force estimators that utilize sensed steering angle and road profile to estimate total rack force and individual components of rack force. We test and compare the real-time performance of the estimators by performing driving experiments with non-aggressive and aggressive steering maneuvers on roads with low and high frequency profile variations. The results indicate that for aggressive maneuvers the estimators using non-linear tire models produce more accurate rack force estimates. Moreover, only the estimator that incorporates a semi-empirical Rigid Ring tire model is able to capture rack force variation for driving on a road with high frequency profile variation. Finally, we present results from a simulation study to validate the component-wise estimates of rack force.