# Air Systems Modeling and Control for Turbocharged Engines

**Author**: Philippe Moulin, May 5 2010

The performances of internal combustion engines are limited by the quantity of fresh air and burned gas that can be brought into the cylinder by their air system. Turbochagers enable to increase this quantity and this is the reason why they are now used commonly, often combined with other complex components. These systems generate a slow dynamics on the engine. The associated control strategies are therefore complex because they must utilize the full dynamics of a complex system. This thesis investigates the control problems of turbocharged air systems through three case studies : a fixed geometry turbocharger on a gasoline engine, a variable geometry turbine on a Diesel engine fitted with two exhaust gas recirculation circuits, and a two stage turbocharger on a Diesel engine.

The proposed approach consists in the reduction of a physical model of the system and in the design of simple control strategies based on the analysis this model. Thanks to the simplicity of both the reduced model and the control law, it is possible to prove properties of the closed loop system such as the convergence, the stability and the satisfaction of constraints. Experimental results are provided for each case study in order to demonstrate the relevance of the approach.

The first problem considered is single input single output (SISO) with constraints on the actuator. The system is non linear and first order. The control strategy is based on feedback linearization and constrained motion planning. It consists in a dynamic inversion of a physical representation of the system. Practical issues such as actuator constraints and integrator anti wind up are taken into account in both feedforward and feedback terms of the controller. The approach and the developments are then extended to more complex applications.

The second air system considered contains several subsystems with many interactions : turbocharger and exhaust gas recirculation circuits. A similar level of representation as for the first case is used for the system analysis. It is shown that the dynamics of the

exhaust gas recirculation circuits are faster than that of turbochargers and can therefore be neglected. However the static interactions between the two systems impose constraints on the turbocharger control. The control structure developed for the first example is adapted to this new control problem.

The last application is the most complex one. The control problem can be reduced to a single input single output (SISO) problem, but the system is second order and constraints must be respected on one of the states. A reduced physical second order model allows to study the trajectories of the closed loop system in the phase plane. Control strategies are thus designed to force the system to the desired trajectory while satisfying the constraints.

The thesis thus shows that different air systems control problems can be addressed with similar coherent solutions. The global approach and the chosen modeling level are generic. They can therefore be extended to future air systems control problems, but also to diagnostic problems for which they are well adapted.

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**BibTeX**:

@phdthesis{,

author = {Moulin, Philippe},

title = {Air Systems Modeling and Control for Turbocharged Engines},

school = {MINES ParisTech},

address = {Paris},

pages = {},

year = {2010},

abstract = {The performances of internal combustion engines are limited by the quantity of fresh air and burned gas that can be brought into the cylinder by their air system. Turbochagers enable to increase this quantity and this is the reason why they are now used commonly, often combined with other complex components. These systems generate a slow dynamics on the engine. The associated control strategies are therefore complex because they must utilize the full dynamics of a complex system. This thesis investigates the control problems of turbocharged air systems through three case studies : a fixed geometry turbocharger on a gasoline engine, a variable geometry turbine on a Diesel engine fitted with two exhaust gas recirculation circuits, and a two stage turbocharger on a Diesel engine.

The proposed approach consists in the reduction of a physical model of the system and in the design of simple control strategies based on the analysis this model. Thanks to the simplicity of both the reduced model and the control law, it is possible to prove properties of the closed loop system such as the convergence, the stability and the satisfaction of constraints. Experimental results are provided for each case study in order to demonstrate the relevance of the approach.

The first problem considered is single input single output (SISO) with constraints on the actuator. The system is non linear and first order. The control strategy is based on feedback linearization and constrained motion planning. It consists in a dynamic inversion of a physical representation of the system. Practical issues such as actuator constraints and integrator anti wind up are taken into account in both feedforward and feedback terms of the controller. The approach and the developments are then extended to more complex applications.

The second air system considered contains several subsystems with many interactions : turbocharger and exhaust gas recirculation circuits. A similar level of representation as for the first case is used for the system analysis. It is shown that the dynamics of the

exhaust gas recirculation circuits are faster than that of turbochargers and can therefore be neglected. However the static interactions between the two systems impose constraints on the turbocharger control. The control structure developed for the first example is adapted to this new control problem.

The last application is the most complex one. The control problem can be reduced to a single input single output (SISO) problem, but the system is second order and constraints must be respected on one of the states. A reduced physical second order model allows to study the trajectories of the closed loop system in the phase plane. Control strategies are thus designed to force the system to the desired trajectory while satisfying the constraints.

The thesis thus shows that different air systems control problems can be addressed with similar coherent solutions. The global approach and the chosen modeling level are generic. They can therefore be extended to future air systems control problems, but also to diagnostic problems for which they are well adapted.},

keywords = {Engine Control, Turbocharger Control, Nonlinear Control, Motion Planning, Feedback Linearization}}