Constraint enforcement of piston motion in a free-piston engine

Precise control of piston turnaround location is essential for reliable free-piston engine (FPE) operation. In this paper we derive a discrete-time, control-oriented, implicit model that describes FPE clearance height behavior by applying an energy balance to the Otto cycle. We then design a state feedback controller using dynamic inversion that stabilizes the FPE system and ensures reference tracking. To compensate for a single time step output delay we add a Smith predictor and use Newton´s method to forecast piston position. As demonstrated with a physics-based model, the proposed controller successfully stabilizes the FPE and tracks clearance set points. However, abrupt hydraulic load changes can cause the piston to travel outside a safe operating range. To enforce constraints on piston motion, we augment the system with a reference governor that manages hydraulic load transitions. The reference governor uses Newton´s method applied to the implicit control-oriented model for prediction in conjunction with a bisection search algorithm to calculate the maximum possible load increase, that if held constant, will satisfy the constraints for all future time steps. Model uncertainty can be accounted for by tightening constraints. When implemented on the physics-based FPE model, the reference governor successfully enforces a piston turnaround position constraint of ± 0.5 mm from a nominal set point during a load change.