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 $\mp$ 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.

本文重点介绍使用非接触式磁传感器的智能执行器中的位置估计。长行程执行器中的磁位置估计涉及非线性非单调测量方程，并且需要使用多个磁传感器。通过开发一种用于计算最佳传感器位置的方法和一种用于基于LMI的观察者设计技术的改进方法，可以解决这些挑战。首先，由于输出非线性的非单调性，因此显示了该应用缺乏具有全局稳定性的恒定增益观测器。因此，将开关增益观察器设计为确保全局稳定性。第二，在执行器位置范围内，可观察性矩阵的最小奇异值用作优化传感器位置并确定需要使用的传感器数量的度量。尽管零范数问题的公式是非凸的，并且计算量很大，但优化问题却被放宽为凸形，并使用随机舍入算法进行了求解。广泛的实验结果被提出对所开发的估计算法的性能。非线性观察者将两个传感器放置在合理但非最佳的位置，可以提供 广泛的实验结果被提出对所开发的估计算法的性能。非线性观察者将两个传感器放置在合理但非最佳的位置，可以提供 广泛的实验结果被提出对所开发的估计算法的性能。非线性观察者将两个传感器放置在合理但非最佳的位置，可以提供$\mp$与扩展的卡尔曼滤波器相比，位置估计的误差为2％，并且具有出色的鲁棒性。将最佳传感器位置与两个传感器一起使用可将估计误差降低到小于1％，并有助于满足所需的性能规格。使用三个具有最佳位置的传感器可导致小于0.5％的峰值位置误差。