Magnetic position estimation using optimal sensor placement and nonlinear observer for smart actuators

Abstract This paper focuses on position estimation in smart actuators using non-contacting magnetic sensors. Magnetic position estimation in long-stroke actuators involves nonlinear non-monotonic measurement equations and the need to use more than one magnetic sensor. These challenges are addressed by developing a methodology for computing optimal sensor placement and an improved methodology for a LMI-based observer design technique. First, the lack of a constant gain observer with global stability for this application is shown due to the non-monotonic nature of the output nonlinearity. A switched-gain observer is therefore designed to ensure global stability. Second, the minimum singular values of the observability matrix over the range of actuator positions are utilized as a metric for optimizing sensor location and deciding on the number of sensors that need to be utilized. While a zero-norm problem formulation is non-convex and computationally expensive, the optimization problem is relaxed into a convex form and solved using a randomized rounding algorithm. Extensive experimental results are presented on the performance of the developed estimation algorithms. A nonlinear observer with two sensors placed at reasonable but non-optimal locations is shown to provide ∓ 2% error in position estimation and superior robustness properties compared to an extended Kalman filter. The use of optimal sensor locations with two sensors reduces the estimation error to less than 1% and helps meet desired performance specifications. Utilizing three sensors with optimal locations results in less than 0.5% peak position errors.