Active shape control of a deformable mirror in an adaptive optics system

A new control methodology for active shape control of dynamic flexible structures is presented. This method is based on the direct optimal control approach developed for discrete systems. In this method, the algebraic equations of motion of a flexible structure are derived and used for the controller design. The algebraic optimal control laws are derived in an explicit form for a general time varying distributed parameter system with piezoelectric inclusions. The essence of the approach is based on using space-time assumed mode expansions of the generalized coordinates and inputs, which is a Rayleigh-Ritz method extended to both space and time dimensions in conjunction with variational work-energy principles that govern the physical system. An optimal tracking controller was designed for shaping the surface of the deformable mirror used in an adaptive optics system. The desired surface trajectory (over time) can be supplied analytically. This data is curve fitted for direct use. One feature of this method is that it accommodates the dynamic behavior of the structure instead of considering only the static shape control.