论文标题

传感器延迟的最佳估计

Optimal Estimation with Sensor Delay

论文作者

Cao, Di, Cowan, Noah J., Freudenberg, James S.

论文摘要

鉴于植物进行延迟的传感器测量,有几种补偿延迟的方法。一种明显的方法是解决该问题在国家空间中,其中$ n $维的植​​物状态被$ n $ dimensional(padé)的近似值增强,可提供(最佳)国家估计的反馈相对于分离原则。使用此框架,我们显示:(1)估计的植物状态的反馈部分颠倒了延迟; (2)最佳(Kalman)估计器分解为$ n $(PADé)不可控制状态,其余的$ n $ eigenValues是减少订购卡尔曼过滤器问题的解决方案。此外,我们表明,在植物干扰和测量噪声之间的估计误差(全州估计器的)误差的权衡仅取决于减少订单的卡尔曼滤波器(可以独立于延迟构建); (3)基于州估计的控制方案的微妙修改版本与史密斯预测指标非常相似。这种修改的状态空间方法与其史密斯预测变量类似物(包括无法稳定最不稳定的植物)有一些局限性,这些局限性在使用未修改状态估计框架时会得到缓解。

Given a plant subject to delayed sensor measurement, there are several approaches to compensate for the delay. An obvious approach is to address this problem in state space, where the $n$-dimensional plant state is augmented by an $N$-dimensional (Padé) approximation to the delay, affording (optimal) state estimate feedback vis-à-vis the separation principle. Using this framework, we show: (1) Feedback of the estimated plant states partially inverts the delay; (2) The optimal (Kalman) estimator decomposes into $N$ (Padé) uncontrollable states, and the remaining $n$ eigenvalues are the solution to a reduced-order Kalman filter problem. Further, we show that the tradeoff of estimation error (of the full state estimator) between plant disturbance and measurement noise, only depends on the reduced-order Kalman filter (that can be constructed independently of the delay); (3) A subtly modified version of this state-estimation-based control scheme bears close resemblance to a Smith predictor. This modified state-space approach shares several limitations with its Smith predictor analog (including the inability to stabilize most unstable plants), limitations that are alleviated when using the unmodified state estimation framework.

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