The Primary Mirror Active Control System (ACS) of the W.M. Keck Telescope has as its main function the maintenance of
the mirror figure of the 36-segment primary mirror under the changing effects of gravity, temperature, and other low frequency
perturbations. The ACS is a multivariate control loop that can be represented in a diagonalized form, provided that segment
actuator motions only excite oscillations in its corresponding whiffletree (tying an actuator to a mirror segment), with
no coupling to the other whiffletrees in the same segment mirror. Since whiffletree oscillations are expected to occur at frequencies
above the bandpass of the control system, the assumption is expected to be valid for the purpose of analyzing the
stability and response of the ACS under the expected low frequency perturbations.
The results of a one-dimensional simulation, justified by the diagonalized form of the problem, will be presented showing
the conditions for stability, the system response to desired changes and the advantages of using feed-forward. A verification
of the theoretical results will be presented for an actual actuator coupled to a sensor controlled by a one-dimensional version
of the ACS software.
Also based on the diagonalized form, a study of noise coupling, equivalent system bandwidth and matrix noise magnification
factor will be presented. The effect of the feed-back control loop on the telescope mis image radius caused by sensor
noise will be calculated.