Multi-input digital frequency stabilization of monolithic lasers

Embedded Model Control: Outline of the theory

“…Alternatively, by modelling w(i) as a DT zero-mean, white noise with bounded covariance and assuming zero initial state as in (5), D can be interpreted as a vector of zero-mean, random processes having the root spectral density rolling off not faster than −20(n w −1) dB/dec from low to high frequencies. The latter interpretation favours d synthesis from experimental data as in [4,6]. Zero initial conditions in (5) imply the past state x d (i < 0) is not to be kept from one control run to another, which asks for the initial state to be recovered along with time delay and errors.…”

“…(2) The second inequality simplifies Control Law design (see Section 3.2.2), as an oversized command, n z < n u , would require an ad hoc apportionment strategy as in [4], while the downsize case, n z > n u , would ask for performance restriction.…”

“…Since then, EMC has been fully developed and applied to different applications, the most recent being [2][3][4][5][6]19]. The present theory outline revises, simplifies [1] and prepares for a paper showing a standard application: web winding [17].…”

A self-analyzing double-loop digital controller in laser frequency stabilization for inter-satellite laser ranging

“…Most importantly, it has been studied that the analog circuits have a much more significant long-term drift 11 which is crucial for the measurements at low frequency range that we are interested in. Recently, digital controllers have been used for laser frequency stabilizations in various applications [12][13][14][15][16] and have exhibited excellent performances.…”

A scalable, self-analyzing digital locking system for use on quantum optics experiments

“…This makes a digital system easily reproducible, as well as having the ability to add complex logic which would be difficult to include with analog circuits alone (for examples see Ref.s [3] and [4]). Using the added power of digital control has lead many to develop novel methods for frequency stabilizing lasers (for example see Ref.s [5][6][7][8][9][10]). Quantum optics is one branch of science which can benefit from digitization and computer control.…”