The control and design optimization of a Free Piston Engine Generator (FPEG) has been found to be difficult as each independent variable changes the piston dynamics with respect to time. These dynamics, in turn, alter the generator and engine response to other governing variables. As a result, the FPEG system requires an energy balance control algorithm such that the cumulative energy delivered by the engine is equal to the cumulative energy taken by the generator for stable operation. The main objective of this control algorithm is to match the power generated by the engine to the power demanded by the generator. In a conventional crankshaft engine, this energy balance control is similar to the use of a governor and a flywheel to control the rotational speed. In general, if the generator consumes more energy in a cycle than the engine provides, the system moves towards a stall. If the generator consumes less energy, then the effective stroke, compression ratio and maximum translator velocity must rise steadily from cycle-to-cycle until the heat transfer losses stop the increase. Moreover, when stiff springs are added to the FPEG system, the dynamics becomes more sinusoidal and more consistent with increasing spring stiffness. To understand the behavior of proposed control and cycle-to-cycle variations, a comprehensive FPEG numerical model with a 1 kW target electric power was developed in MATLAB®/Simulink. An FPEG system corresponding to that numerical model has been operated in the laboratory. This MATLAB®/Simulink numerical model has been used to examine the sensitivity of FPEG dynamics and performance parameters to the changes in design and operating inputs. A difficulty during the modeling is associated with the cycle-to-cycle energy balance, and this difficulty is also reflected in the real-world FPEG control. Therefore, the authors have devised a control strategy similar to the real world intended control methodology. In this numerical model, two different feedback control methodologies were implemented and investigated. These control methodologies were applied to regulate the generator load with selected control or input variables, namely peak pressure, mid-stroke piston velocity, trapped compression ratio and dead center set points. The controllers with optimized coefficients demonstrated the feasibility of energy balance management during the transient operation. Based on the simulation results, the controllers with compression ratio, peak pressure and dead center clearance set points as control variables demonstrated stable FPEG operation whereas the mid-stroke velocity failed to achieve the steady-state operation due to deviation in the piston dynamics. The simulation results from this study will be used as the pathway for improving and optimizing the experimental FPEG design.
