Optimal Estimation with Sensor Delay Yields Smith-like Predictor

ABSTRACT: Delay is inevitable in motor control simply because neural transduction of information is slow. For example, visuomotor delays introduce about 110-160 ms into the feedback loop. Despite these long latencies, humans manage smooth and accurate movements with ease. It is believed that our nervous system incorporates internal models of the plant, sensory dynamics, and delay in order to compensate for the delayed feedback, and various architectures have been proposed for doing so, including the classical Smith predictor as well as state space optimal control. We adopt the latter approach, replacing the delay with a Pade’ approximation and including the Pade’ state in a state estimator. We show that the resulting compensator partially inverts the time delay. Furthermore, if the estimator is a Kalman filter, then its eigenvalues are the union of the Pade’ eigenvalues plus the eigenvalues corresponding to a lower order optimal estimation problem that does not depend on the delay. A slight rearrangements of the resulting compensator reveals a control architecture with many features in common with the Smith predictor.

This is joint work with Di Cao and Noah Cowan from Johns Hopkins University.

BIO: Jim Freudenberg has been at the University of Michigan since 1984, and is currently a Professor of Electrical Engineering and Computer Science. He is a Fellow of the IEEE. His research interests are in the theory of fundamental design limitations, and the teaching of embedded control systems.

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