Control Design for a Second Order Dynamic System : Two-Stage Turbocharger

This paper proposes a formal approach to the study of the dynamic behavior of a two stage turbocharger on a Diesel engine. It uses a reduced model that was developed for control purposes in previous publications. The system is second order, with one actuator. The control problem is single input single output, the setpoint being the product of the two states. A difficulty of the control problem is that a constraint on one state must be respected. The Poincaré Bendixon theory for the study of systems in the phase plane is used to study this problem. It gives a proof that the system globally converges to unique equilibrium state, and that a simple feedback control strategy results in trajectories that respect the state constraint.