Designing pneumatically actuated deformable mirrors: control of circular plates with varying thickness

This contribution focuses on the optimal design and pneumatic deformation control of thin circular plates with spatially-varying thickness. The work is motivated by pneumatically actuated deformable mirrors, which are used to compensate for wavefront disturbances in adaptive optics. To achieve the required deformation profiles with high precision, the equilibrium deformation is optimized with respect to the plate's thickness. For designing an asymptotic tracking control, the finite relative degree of the distributed parameter system is exploited. Since the nonlinear pressure dynamics actuate the governing partial differential equation (PDE) in a distributed way, finite-order feedback linearization can be applied. In addition, static nonlinear effects in the pneumatic valve and infinite-dimensional internal dynamics have to be taken into account. Finally, we demonstrate the controller's performance by means of simulations.