In this study, Proportional Integral Accelerator (PIA) controller parameters are obtained using Random Search (RS) optimization algorithm by compromising between Reference to Disturbance Rate (RDR) criteria and control error. Thus, robustness performance of PIA controller against the input disturbance is investigated. First, the robustness of the system controlled by the PIA against input disturbance is theoretically demonstrated. Then, the performance analysis of the PIA control system whose parameters obtained by RS optimization is examined with application examples in Matlab/Simulink environment