Motion optimization in a free piston energy converter using direct collocation method

The free piston energy converter is a type of power unit consisting of an internal combustion engine and a linear electrical machine. Due to the lack of mechanical linkages which constrain the position and speed of the free piston, a motion controller is required to controlling the movement of piston. The use of direct collocation method to solve piston motion optimal control problem is described in this paper. Via discretization the state variables and control variables at the collocation points, the optimal control problem is transformed into a nonlinear programming problem. Then, the desired input for each stroke can be calculated by solving this nonlinear programming problem. Simulation results indicate that the proposed method leads to stable piston motion.