The European Solar Telescope (EST) is a European collaborative project to build a 4m class solar telescope in the Canary Islands, which is now in its design study phase. The telescope will provide diffraction limited performance for several instruments observing simultaneously at the Coudé focus at different wavelengths. A multi-conjugated adaptive optics system composed of a tip-tilt mirror and several deformable mirrors will be integrated in the telescope optical path. The secondary mirror system is composed of the mirror itself (Ø800mm), the alignment drives and the cooling system needed to remove the solar heat load from the mirror. During the design study the feasibility to provide fast tip-tilt capabilities at the secondary mirror to work as the adaptive optics tip-tilt mirror is also being evaluated.