The aim of this study is to prove that the dynamic behavior of tensegrity grids can be controlled. This possibility is very important, especially for deployable structures. The impact the support conditions of the structure on the existence of the immanent characteristics, such as self-stress states and infinitesimal mechanisms, and consequently on the dynamic control, is analyzed. Grids built with the modified Quartex modules are considered. A geometrically non-linear model is used, implemented in an original program written in the Mathematica environment. The results confirm the feasibility of controlling tensegrity structures characterized by the presence of the infinitesimal mechanisms. In the case that the mechanisms do not exist, structures are insensitive to the change of the initial prestress level. The occurrence of mechanisms can be controlled by changing the support conditions of the structure. The obtained results make tensegrity a very promising structural concept, applicable in many areas when conventional solutions are insufficient.