Mean value modelling of diesel engine airpath and model predictive control of EGR-VGT systems

In this PhD thesis, a mean value model (MVM) of a turbocharged Diesel engine airpath having exhaust gas recirculation (EGR) and variable geometry turbine (VGT) systems and a model predictive controller (MPC) which aims to decrease NOx emissions and fuel consumption are designed. The engine modelled, simulated and controlled in the thesis is a 12.7 litre 6 cylinder Diesel engine with EGR-VGT systems. Fuel flow, EGR actuator signal and VGT actuator signal are the model inputs, load moment is disturbance and engine rotational velocity, the moment produced, EGR gas ratio in the intake manifold and oxygen to fuel ratio in the cylinders are model outputs. EGR gas ratio in the intake manifold and oxygen to fuel ratio in the cylinders are used as feedback signals for the MPC controller. The reason of using oxygen to fuel ratio instead of air to fuel ratio, which is usually used in engine systems, is the exhaust gas that is sent to combustion chamber by the EGR system's still containing oxygen and the amount of oxygen's being more important than the amount of air. The reason of not using mass air flow through the compressor (MAF) and intake manifold air pressure (MAP), they are also used generally in the literature, is that the designed controllers in this study are aimed to decrease pumping moment for decreasing the fuel consumption and EGR gas ratio in the intake manifold and oxygen to fuel ratio in the cylinders's having a direct relation with pumping moment. The mathematical model used in this study is obtained by mean value modelling (MVM), which is a method used for obtaining mathematical Diesel engine airpath models. MVM uses thermodynamic equations with empirical relationships and first order nonlinear differential equations expressing engine and turbocharger dynamics and changes in pressure and mass flows in manifolds. The system is simulated by the model equations using "Matlab-Simulink" software. The air getting into the system is compressed through the compressor. Then the air is cooled passing through the heat exchanger after the compressor outlet. After that, the air is mixed with the exhaust gas coming from EGR system and the mixture is sent to cylinders passing through the intake manifold. Some amount of the exhaust gas getting out of the cylinders after combustion process is taken into the EGR system, passed through the EGR cooler and EGR valve, mixed with the fresh air and sent back to the intake manifold. The other amount of the exhaust gas rotates the turbocharger by passing through the VGT and thrown to the atmosphere. Engine moment obtained from the engine in this study is the difference of pumping and friction moments from the gross indicated moment. Engine rotational velocity is obtained by solving a differential equation dependent on engine moment and load moment. Manifold pressures and oxygen ratios are modelled by differential equations derived from the conservation of mass and ideal gas laws. Exhaust manifold temperature is calculated by using Seiliger cycle method. Turbocharger rotational velocity is calculated by solving a differential equation obtained from the Newton's second law and dependent on powers of turbine and compressor. EGR actuator dynamics and VGT actuator dynamics are modelled by linear differential equations. States of the system are given below: - Engine rotational velocity - Intake manifold pressure - Exhaust manifold pressure - Intake manifold oxygen ratio - Exhaust manifold oxygen ratio - Turbocharger rotational velocity - EGR actuator states (two states) - VGT actuator state The model predictive controllers designed in this study are aimed to keep the NOx emissions below 0.4 gr/kWh, which is the criterion of Euro 6 standards, and minimize the fuel consumption of the engine. Nonlinear working region of the engine is divided into nine subregions and different linear MPC controllers are designed for each subregion. Decision of which controller will be chosen to control the system is done by a switching algorithm that is a function of engine speed and the amount of fuel. EGR valve ratio and VGT angle are the control inputs to the system and EGR gas ratio in the intake manifold and oxygen to fuel ratio in the cylinders are feedback signals. Engine rotational velocity and fuel input are used as input signals to the switching algorithm. Different linear models are obtained for each subregion and each subregion has different reference values. Linearization points are determined for each subregion and system identification methods have been used about these points to obtain linear models. To determine linearization points, fuel input, engine rotational velocity, EGR input and VGT input values has to be specified for each point. To decide what values engine rotational velocity and fuel input to take, nonlinear region is divided into subregions which are equal in size and the values at middle points of the subregions are assigned as the linearization values. While deciding the values of EGR input and VGT input, linearization points' being reference points for MPC has been taken into consideration, because EGR input and VGT input are used as the control signals. In this situation, maps are constructed to find the linearization points. Suitable points, which are confirming the control objectives, have been chosen from the maps and EGR input and VGT input values have been determined. After determining linearization points, "Matlab System Identification Toolbox" is used to obtain linear state space models for each subregion. Provided that fuel input and engine rutational velocity constant, PRBS (Pseudorandom binary sequence) inputs of EGR and VGT actuators in +-10% bandwidth are used as input signals to the nonlinear model. "Two inputs-two outputs" linear state space models are obtained by using the EGR gas ratio in the intake manifold and oxygen to fuel ratio in the cylinders results. To show the validity of the linear models obtained, the comparison of the results of nonlinear and linear simulations for the same PRBS inputs are analyzed and crosscorelation test is applied. After obtaining linear models, "Matlab Model Predictive Toolbox" is used to design the MPC controllers. The values of prediction horizon, control horizon and weights are determined. The constraints of the MPC controllers are 0%-80% for EGR input and 20%-100% for VGT input. Results show that MPC controller can decrease NOx emissions in seven of nine subregions while keeping the same amount in two of them. Moreover, it seems that fuel consumption can be decreased in six of nine subregions. System can be brought to reference point and put into steady state in a short time. This situation is a sign of MPC's having a powerful tracking performance. Results show MPC's being superior than classical mapping approach by adjusting the transient response and standard approach (PID) by taking into consideration the interaction between the states of the whole system. Moreover, MPC performance was compared with two different controller performances from literature and it was seen that MPC had a better performance than the other controllers. So MPC method seems to be a good choice of controlling Diesel engine airpaths that have EGR and VGT systems. As future work, an MPC controller is planned to be designed for Diesel engines that have low and high pressure EGR and VGT systems, controlling fuel amount is planned for automatic pilot and dynamic positioning systems and again controlling fuel input of more than one engine for running them together interactively.