Physical optics modeling of Sky coverage for TMT NFIRAOS with advanced LQG controller

We have implemented the linear quadratic Gaussian (LQG) controller in our physical optics sky coverage simulator (MAOS) for the Thirty Meter Telescope (TMT) Narrow Field InFrared Adaptive Optics System (NFIRAOS) aimed for improved correction of tip/tilt and plate scale modes. The LQG controller has a built-in capability to correct narrow frequency vibrations that are above the closed loop bandwidth of the system and is a very desirable solution for this application. The LQG controller is tuned with the combined power spectral density (PSD) of turbulence, wind shake, and vibration computed from the telemetry. We will show how LQG performs for various telescope/instrument vibration spectral (such as broadband or drifting peaks). We will also show the performance and sky coverage of LQG in comparison with single or double integrator controllers for correcting low order atmospheric turbulence with a set of up to three tip/tilt(/focus) natural guide star wavefront sensors. We found that the LQG controller reduces the median sky coverage wavefront error by 25 nm in quadrature.