Lock Acquisition Real and Simulated observable Not experimentally observable Matthew Evans, March 2004

Lock Acquisition with a Linear Controller Controller are characterized by their “threshold velocity”. ideal Coil Magnet Optic I V 150mA ~10mN realistic Realistic actuation modeling plays a critical role in control design. Matthew Evans, March 2004

Error Signal Linearization arbitrary unit arbitrary unit arbitrary unit Matthew Evans, March 2004

Evolution of Lock Acquisition Code From Simulation to the Real World Develop in simulation Port to real-time system (In LIGO, the code written for the simulation is used, without modification, to control the interferometer.) Requires well defined, yet flexible, interface Robustness to Imperfections Algorithms developed in the relatively perfect world of simulation must anticipate the imperfections of reality Anticipation is often problematic, so the ability to change, test, and load new code quickly is very helpful. Measurement Bootstrapping Lock acquisition algorithms require information about the interferometer This information must be measurable in states which can be attained without the desired information. It may be useful to locking states not on the path to the operating state (single arm, interferometer without power recycling, etc.) Matthew Evans, March 2004

Making an Interferometer “Lockable” Understanding the Interferometer During LA Additional detectors and A2D channels may be required for LA (e.g., to measure power levels related to the sensing matrix). Diagnostic, calibration and switching software may be necessary to integrate the LA algorithm into the control software. Maintaining Signal Integrity Typically, the power in the interferometer varies greatly over the course of lock acquisition. Noise, saturation and offset problems not present in the operating state appear during lock acquisition. Alignment Wave-front-sensing is not available during lock acquisition. Large impulsive drive forces are applied, inevitably exciting angular motion. Optical lever feedback, or some other local control system, is needed to achieve robust alignment control. Matthew Evans, March 2004

Conclusion Lock acquisition is best thought about in the interferometer design phase. The LIGO1 interferometers have all been locked using a generalize signal linearization scheme. Many possible refinement exist Multiple acquisition paths and destination states Robust state estimation with redundant signals Imperfect mode-overlap compensation Smooth state switching Trajectory extrapolation and guided lock acquisition Alignment lock acquisition Matthew Evans, March 2004

The Fabry-Perot Cavity The simplest optical resonator, the Fabry-Perot cavity, consists of only two mirrors and is sufficient to demonstrate many of the principals of lock acquisition. Linear control theory can be used to hold the cavity near resonance. Matthew Evans, March 2004

Hanford 2k Optical Layout Matthew Evans, March 2004

Sensing Matrix For the F-P cavity the sensing equation is . “Error Signal Linearization” is a particular application of a more general rule: the correct control matrix is the inverse of the sensing matrix. For LIGO I the sensing equation is approximately where and . Unfortunately, the sensing matrix is not always easy to invert. In fact, “Multi-Step Locking” results from singularities in the sensing matrix. Matthew Evans, March 2004

Multi Step Locking State 1 : Nothing is controlled. This is the starting point for lock acquisition. State 2 : The power recycling cavity is held on a carrier anti-resonance. In this state the sidebands resonate in the recycling cavity. State 3 : One of the ETMs is controlled and the carrier resonates in the controlled arm. State 4 : The remaining ETM is controlled and the carrier resonates in both arms and the recycling cavity. State 5 : The power in the IFO has stabilized at its operating level. This is the ending point for lock acquisition. Matthew Evans, March 2004