Hierarchical Control Theory for Advanced LIGO

Document #:

LIGO-T1000242-v2

Document type:

T - Technical notes

Abstract:

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.

Files in Document:

• T1000242-v2.pdf (1.6 MB)

Topics:

• Commissioning

Authors:

• Brett Shapiro

Keywords:

hierarchical control aLIGO

Notes and Changes:

-v2 includes minor changes which fix typos, reformats some figures, and clarifies ambiguous notation.

Referenced by:

• LIGO-G1200632-v3: Towards Applied Heirarchical Control
• LIGO-G1200692-v3: Hierarchical Control Notes – Blending Style
• LIGO-G1400135-v1: Hierarchical Control of Toy Double Pendulum for Practice (HIFO-XY)
• LIGO-G1700563-v1: CSWG Workshop at the March 2017 LVC meeting