Embedded model control: Submicroradian horizontality of the nanobalance thrust-stand

Pendulum tilt, with respect to local gravity, is affected by the tilt and lateral acceleration of the supporting structure. A differential pendulum, such as the Nanobalance thrust-stand, would be immune only in the ideal case of perfectly balanced pendulums. In the actual case, the equivalent tilt must be zeroed in the measuring bandwidth by an active control system. This paper outlines requirements, technology, modeling, and robust control strategies to ensure instrument horizontality, achieving submicroradian accuracy in a frequency band from 0.1 mHz to 1 Hz. Control strategies, including the coordination of slow and fast motors, have been designed and implemented following the embedded model control methodology. The results of commissioning tests are given and discussed, pointing out the limits of the available technology.