LIGO Document T1000242-v1
- Given the quantity of multi-stage suspensions planned for Advanced LIGO, hierarchical control loops will be everywhere. Stability theory for linear single-input-single-output (SISO) systems is well developed and straight forward. While hierarchical control is not SISO, rather MISO (multi-input-single-output), SISO stability theory can be extended to this MISO case. It is shown that although the stability criteria of MISO systems are the same as those for SISO systems, there are subtleties to consider. Suggestions on how to handle these subtleties to simplify the design process and produce robust practical controllers are given.
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