This paper presents an analytic Proportional-Integral (PI) controller design for a servo motor speed control under given control performance demands. When designing the classical linear controllers, standard 2nd order systems are often considered to simplify the design problems. Realistically, however, most of the systems are usually non-standard 2nd order systems and assuming them as standard 2nd order systems could sometimes cause designing mismatches. To solve this issue, this study derived analytical PI controller formulas, where the control gains were determined by applying Genetic Algorithm (GA) with the aim of approaching the desired performances including overshoot and settling time as close as possible. A numerical simulation is also performed to attest the results. The main contributions of this paper include the accuracy of achieving the control performance demands by taking the exact analytical solutions, eliminating the model discrepancies between the exact closed-loop model and the standard 2nd order system, and the proposed method can be extended to a wide variety of process control topics.