Pneumatic systems exhibits many advantages including high speed and better efficiency. Servo pneumatic system enables the pneumatic system to be employed in varying position applications such as robots. There will be always a compromise between the speed and allowable overshoot in determining the parameters of the system based on the applications. In present research, a system comprising of two pneumatic cylinders attached to each other is used. A small cylinder which is used to for fine adjustments in accuracy is mounted on the rod end of the large cylinder which travels the coarse movement. This system reduces the overshoot of the system without much reduction in speed. Mathematical model of the system comprising of motion dynamics, pressure and temperature dynamics inside cylinder chambers and mass flow variation in the valves are derived from the physical laws and recent literature information. Based on the mathematical model, a simulation model of the system is created in the Matlab-Simulink software. A fuzzy based control system has been designed for servo position control of the system. The simulation model is validated using the experimental results. The energy efficiency of the system is computed from the overall power developed in the system and cumulative air power supplied to the system. The analysis of the dynamics of the system while tracking a sinusoidal signal is taken as a task for analyzing the energy efficiency of the system. The energy efficiency of the system has been analyzed for various sizes of cylinders, various supply pressure levels to both the cylinders in the system and various applied loads to the system. To reduce the number of experiments to be conducted, a Taguchi based design of experiments is carried out. A statistical analysis has been made for analyzing the variation of energy efficiency with the above parameters. From the study, external load affects the energy efficiency in a considerable way which has 54.39% of the overall contribution. The second dominant factor on influencing energy efficiency is supply pressure to cylinder A which has the contribution of 23.65%.