Year: 2022
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Cao, Di, Cowan, Noah J., Freudenberg, James S.
Institutions: Johns Hopkins University, University of Michigan
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4307207259