For a first-order lag process with dead-time models (FOPDT) under step load disturbances, optimal parameters of proportional and integral (PI) controller are obtained through numerical optimization based on minimizing the integrated time and absolute error (ITAE), or maximizing the integral gain. The optimizations are under constrains of sensitivity functions. Then, the tuning formulas for PI controllers are adjusted according to parameters from numerical fittings of optimized values within a large scope of the ratio of the inertia time to the dead-time of processes. Finally, the process information is acquired from closed-loop tests of a two-channel relay and the process is approximately modeled with a FOPDT model in order to achieve parameter auto-tuning of controllers. The approach proposed is proved to be effective according to simulation results.