A proportional integral derivative (PID) controller is most widely used to control industrial processes. Tuning a PID controller is an important task for obtaining the desired closed loop specifications (rise time, settling time, peak time, overshoot and steady state error). This paper presents different PID tuning formulas for a third order process. They are based on the knowledge of the ultimate gain, ultimate period and minimization of integral squared error (ISE) and integral absolute error (IAE).The performance of various tuning methods has been compared by applying a step input to the given process. Simulation results show that tuning a PID controller with Ziegler Nichols (ZN) tuning method results in less rise time (tr), peak time (tP), and integral squared error (ISE). The Relay Auto tuning method is applicable when less ISE is required while Modulus Optimum (MO) tuning method is applicable when less settling time (tS) and less overshoot is required and Computational Optimization (CO) method is helpful when the desired closed loop specifications are decided by the designer. The robustness factors gain margin (GM), phase margin (PM), gain crossover frequency, phase crossover frequency and stability are considered. The proposed approach is implemented in MATLAB.