Abstract
Motivated by an application in metrology for speed up of measurement devices, the following problem is considered: given output observations of a stable linear time-invariant system with known dc gain, generated by a step input, find the input. If a model of the data generating process is available, the input estimation problem is solved as an equivalent state estimation problem for an autonomous system. Otherwise, the input estimation problem is reduced to standard system identification problems: (1) identification from step response data and (2) autonomous system identification. The link to autonomous system identification suggests a data-driven solution, i.e., an algorithm for computation of the input value without identifying a representation of the system. The data-driven algorithm is a structured low rank approximation problem.
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Notes
- 1.
The dc (or steady-state) gain of a linear time-invariant system, defined by an input/output representation with transfer function H, is G=H(0) in the continuous-time case and G=H(1) in the discrete-time case. As the name suggest the dc gain G is the input-output amplification factor in a steady-state regime, i.e., constant input and output.
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Markovsky, I. (2012). Fast Measurements of Slow Processes. In: Low Rank Approximation. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-2227-2_7
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DOI: https://doi.org/10.1007/978-1-4471-2227-2_7
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