Transport is an integral part of society and one of its basic prerequisites. Society is now facing a transition as it must go from dependence on fossil fuels to sustainability. Despite large investments by the vehicle manufacturers, the transition needs to be accelerated for the two-degree (Celsius) target to be reached, which requires new innovations and solutions. 

The development of computers has led to efficient software being available today to numerically solve optimization problems, which enables mathematical modeling and optimization as a systematic problem-solving method. However, taking advantage of the numerical solvers requires specialized knowledge and is a barrier for many engineers. To overcome this and make the problem-solving methodology available, tools that bridge the gap between the engineer’s problem and the numerical solvers are needed. 

The dissertation covers the complete chain from problem to solution, with methods and tools that support the problem-solving process. Software for optimal control is investigated with the aim of making the numerical solvers available to the user. The result is a design based on the introduction of a domain-specific programming language. It makes it possible to automatically reformulate the user’s problem into a form that the computer can handle, while making the program more user-friendly by reducing the difference between the problem domain and the computer’s domain. The result has been developed together with the software Yop, which is used by engineers and researchers nationally and internationally to solve control engineering problems, in academia as well as in industry. 

The software is used to investigate whether an electrified powertrain can be made more efficient by equipping the diesel engine with a larger and more efficient turbocharger, at the expense of increased inertia. The result indicates a gain and that the increased inertia can be compensated by the electric motor. As part of the work, a diesel engine model has been developed, where it has been investigated how relevant effects for turbocharger selection can be included in a way suitable for optimal control. The result is a validated and dynamic diesel engine model that has been made available to the research community through publications and open-source code.  

Accurate simulation of the numerical optimal control in software environments where call to simulation routines is explicit, for instance Matlab and SciPy. A discussion on the simulation aspects of numerical optimal control, how it may fail, and how such erroneous results can be detected using accurate simulation. The key contribution is how to accurately include a piecewise constant control input in the simulations, which is discussed in detail, including code examples. The technique is demonstrated on an example problem which show how simulation can be used to analyze optimal control problems with uncertainty, but also demonstrates how erroneous simulation may lead to erroneous conclusions.

A dynamic heavy-duty Euro 6 diesel engine model for energy optimal control is developed. The modeling focus ison accuracy in the entire engine operating range, with attention to the region of highest efficiency and physically plausible extrapolation. The effect of the air-to-fuel ratio on combustion efficiency is studied, and it is demonstrated how this influences the energy optimal transient control. A convenient, physics-based, method for pressure sensor bias estimation is also presented.

The pursuit of lower fuel consumption and stricter emission legislation has made a simulation- and optimization-based development methodology important to the automotive industry. The keystone in the methodology, is the system model. But for the results obtained using a model to be credible, the model has to be validated. The paper validates an open-source, meanvalue engine model of a 13 liter CI inline 6 cylinder heavyduty engine, and releases it as open-source.

When electrifying the powertrain, there arises an opportunity to revise the traditional turbocharging trade-off between fuel-economy and transient performance. With the help of electrification, it might be possible to make the trade-off in favor of fuel economy, since transient response can be improved by the electric machine. The paper investigates this trade-off by looking at three turbocharger selections. A conventionally dimensioned turbocharger, an efficiency optimized turbocharger with maintained flow capacity, and an efficiency optimized turbocharger with increased flow capacity. The concepts are evaluated on the following cases: stationary operation, engine tip-in performance, vehicle acceleration performance, and on road fuel economy performance. The investigation is based on a validated mean value engine model of a six cylinder inline CI engine, and on a validated driveline and vehicle model of a heavy-duty truck. The evaluations are made with the help of simulations and numerical optimal control. The results show that there is a fuel saving potential, and that the transient response is improved by the electric machine.

Turbochargers stand for the dominating dynamics in engines and in the design, analysis, and optimization of new engines, it becomes more and more important to analyze system interactions and dynamics. In the development process, modeling, simulation, and optimization have evolved from being used in research to being stan- dard tools for engineers and play an important role in the engine development. To be successful in the process, one needs to both have component models, and methods and tools where system models can be built, analyzed, and optimized. The component models should also have capabilities to extrapolate behavior outside the nominal re- gion since design explorations can go to extreme points while searching for optimal solutions.

The first part of the chapter summarizes the compressor and turbine maps and how they can be used in simulation models. A generic model structure for compressors and turbines that fit into an engine modeling and simulation framework is described. Then the Ellipse compressor flow model and the Enthalpy based efficiency model will be described, they have been developed so that they can be integrated in a simulation environment and also used in optimization. Their main features are that they are ca- pable of extrapolating compressor behavior outside the normal range of the map in a physically sane way. In addition to this, a tuning method has been developed that takes a normal manufacturer map and returns all model parameters for compressor flow and efficiency models. Thereafter, compact turbine flow and efficiency models will be described.

Then the attention is turned to simulation and optimization applications where compressor models are used. First an engine experiment where compressor surge oc- curs is modelled and used to illustrate the extrapolation capabilities using the models presented. Then the scope is turned to control and optimization of turbocharger opera- tion on an engine, where the focus will be on a VGT controlled diesel engine equipped with EGR. First the steady state mapping of the engine is demonstrated, then optimal control of the turbo operation is investigated using modern computer tools for dynamic optimization. 

The diesel engine remains one of the key components in the global economy, transporting most of the worlds goods. To cope with stricter regulations and the continuous demand for lower fuel consumption, optimization is a key method. To enable mathematical optimization of the diesel engine, appropriate models need to be developed. These are preferably continuously differentiable, in order to be used with a gradient-based optimization solver. Demonstration of the optimization-based methodology is also necessary in order for the industry to adapt it. The paper presents a complete mean value engine model structure, tailored for optimization and simulation purposes. The model is validated using measurements on a heavyduty diesel engine. The validated model is used to study the transient performance during a time-optimal tip-in, the results validate that the model is suitable for simulation and optimization studies.