Observable mathematical model of DDM (Direct Dirve Motor) was suggested. The motor that operates the object system directly is called DDM. DDM has many strong points, however, it has a significant disadvantage, that it is more sensitive to the external force than the motor with reduction gear. In other word, if the force is applied, air gap of the motor can be perturbed. This causes not only difficulty in motor control but also even more serious problem, such as the breakdown of motor. However, if the air gap variation can be estimated, it can help prevent these problems. DDM should be modeled to estimate the air gap variation. The type of researched DDM is PMSM (Permanent Magnet Synchronous Motor) and precedent model of PMSM includes only characteristics of electro-magnetic system and rotational motion. However, suggested model should also include characteristics of translational motion of rotor to estimate the air gap variation. Also, this model should satisfy observability condition, because state observer is designed based on this model.