In this work, adaptive Generalized Predictive Control (GPC) was investigated at the optimal operating conditions for a pilot plant binary packed distillation column, The studies were made. experimentally and theoretically. The dynamic behavior of the distillation column has been simulated using backmixing model and solved by utilizing Hermite Polynomials within the finite clement procedure;The control of the overhead product temperature was examined for both experimental and theoretical works. Perturbations in feed composition were utilized as the disturbance and the reboiler heat duty was-selected as the manipulated variable. Pseudo Random Binary Sequence (PRBS) signal and Bierman algorithm were used to estimate the relevant parameters of the system model for GPC. Generally theoretical and experimental control results were in god agreement with each other.