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

2. 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

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

4. 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

5. 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

6. 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

7. 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

8. Hanford 2k Optical Layout
Matthew Evans, March 2004

9. 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

10. 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