This paper focuses on developing the dynamic model and motion control of an electro-hydraulically actuated Rapid Compression Expansion Machine (RCEM) with a unique feature of real time trajectory control. For combustion research aimed at investigation of influence of piston trajectory on combustion kinetics, the ability to control piston trajectory is an important requirement which is not offered by current RCEMs. Moreover, the feature of trajectory control offers ultimate flexibility in terms of RCEM operation. While any change in the compression ratio or compression time of most current RCMs has to be realized mechanically, the same can be accomplished by a controlled trajectory RCEM merely by altering the reference trajectory fed to the controller. However, high speed operation and high force requirement for piston motion presents a major challenge for the actuation system of controlled trajectory RCEM. The dynamic model used for the design of a high bandwidth actuator which can provide large actuation force, and the high speed motion control designed to ensure precise reference trajectory tracking by the piston are presented here.