A Load Balance Optimization Approach for the GMT Primary Mirror Support Actuator System

The Giant Magellan Telescope (GMT) primary mirror active support system incorporates pneumatic force actuators to hold the mirror and to control its surface. This paper describes an optimization approach to transform the required control demand into the primary mirror support forces. Based on a quadratic cost function, the method performs a trade-off between the optical surface deflection and a weighted norm of the support forces. An iterative algorithm is proposed to handle actuator operational limits, without resorting to the more sophisticated techniques, such as quadratic programming methods. Such iterative procedure redistributes the control demand over the available degrees of freedom and can handle straightforwardly known actuator failures. Simulation results based on finite-element analysis data indicate relevant improvements in the gravity print-through achieved with the force balance algorithm used so far, using comparable actuators force magnitudes.