We consider a fluid described by a parameterized EoS of the general form $P=(\gamma-1)\rho+p_{0}+\omega_{H}H+\omega_{H2}H^{2}+\omega_{dH}\dot{H}$ \cite{Ren}, where $p_{0}$, $\omega_{H}$, $\omega_{H2}$ and $\omega_{dH}$ are free parameters of the model, interacting with a Tachyonic field with a relativistic Lagrangian $L_{TF}=-V(\phi)\sqrt{1-\partial_{i}\phi\partial^{i}\phi}$. The acceleration of the Universe described by a scale factor $a(t)=t^{n}, (n>1)$. Under consideration of different forms of interaction the field $\phi$ and the potential $V(\phi)$ are recovered and graphical analysis performed. For illustration purposes we fixed values of parameters of the models to provide $V \rightarrow 0$ for later stages of evolution, when $t \rightarrow \infty$.