Modern control of suspended test mass for precision interferometry

We are working towards stabilising a triple-pendulum-suspended mirror via modern controls techniques, such as Linear Quadratic Gaussian (LQG) control and Kalman filtering. A modern control approach is a systematic approach that allows for optimality and robustness, as well as being inherently multi-variable (multi-input multi-output, MIMO).

Schematic of the triple pendulum seismic isolation system, designed for the 10m-prototype at the AEI Hannover.

In order to demonstrate the power of such a systematic modern controls approach to the local control problem we have constructed a model triple pendulum suspension for a test mirror (design by 10m-prototype group at AEI and U Glasgow). The suspension provides seismic isolation for the interferometer mirrors by combining passive and active damping. By means of co-located sensor-actuator combinations (so-called “BOSEMs”) we are able to introduce a signal at the top suspension stage and measure the response at the upper stage directly, and at the lowest stage with two external optical levers.

There are six degrees of freedom in the system: longitudinal (the interferometer mode), pitch, yaw, tilt, roll and bounce. Based on the measurements of transfer functions from the first three dominant D.O.F. we are currently setting up a 3×3 cross-correlation matrix. This matrix describes the coupling to and from longitudinal, pitch and yaw. Once we’ve populated the matrix we need to convert it into a linear state space model (SSM) which describes the overall dynamics of the system.

Modular testmass for our triple-pendulum-suspension setup

Kalman filtering adds white Gaussian sensor/mechanical noise to the SSM and gives and (optimal) estimate of the states under consideration. We will then define a cost functional to solve the optimisation problem containing the system variables, which will lead to an optimal controller. This optimal controller will be implemented to damp the eigenmodes of the triple pendulum suspension and compensate for unwanted cross-correlations between the dominant D.O.F.. By using a variable test mass (designed in our group, see below) we will be able to test for effects of cross-couplings and non-ideal suspension setups.