Abstract This thesis considers some linear and nonlinear time series models. In the linear case, the analysis of a large number of short time series generated by a first order autoregressive type model is considered. The conditional and exact maximum likelihood procedures are developed to estimate parameters. Simulation results are presented and compare the bias and the mean square errors of the parameter estimates. In Chapter 3, five important nonlinear models are considered and their time series properties are discussed. The estimating function approach for nonlinear models is developed in detail in Chapter 4 and examples are added to illustrate the theory. A simulation study is carried out to examine the finite sample behavior of these proposed estimates based on the estimating functions.

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

<p>Having an engine model that is accurate but not too complicated is desirable when working with on-board diagnosis or engine control. In this thesis a four state mean value model is introduced. To make the model usable in an on-line automotive application it is discrete and simulated with a fixed step size solver. Modelling is done with simplicity as main object. Some simple static models are also presented. </p><p>To validate the model measuring is carried out in a Scania R124LB truck with a 12 liter six-cylinder turbo charged diesel engine. In general, for this relatively simple model, the mean errors must be considered low. The inlet manifold pressure mean error during highway driving is 3.4\%.</p>

<p>Over the last years, the emission and on board diagnostics legislations for heavy duty trucks are getting more and more strict. An accurate engine model that is possible to execute in the engine control system enables both better diagnosis and lowered emissions by better control strategies. </p><p>The objective of this thesis is to extend an existing mean value diesel engine model, to include turbo compound. The model should be physical, accurate, modular and it should be possible to execute in real time. The calibration procedure should be systematic, with some degree of automatization. </p><p>Four different turbo compound models have been evaluated and two models were selected for further evaluation by integration with the existing model. The extended model showed to be quite insensitive to small errors in the compound turbine speed and hence, the small difference in accuracy of the tested models did not affect the other output signals significantly. The extended models had better accuracy and could be executed with longer step length than the existing model, despite that more complexity were added to the model. For example, the mean error of the intake manifold pressure at mixed driving was approximately 3.0%, compared to 5.8% for the existing model. The reasons for the improvements are probably the good performance of the added submodels and the systematic and partly automatized calibration procedure including optimization.</p>

<p>VehProLib is one of many libraries being developed for the object oriented multi-domain language Modelica. The layout and the current status of the library are shown. The aims of the library are to provide the user with a number of different components with different levels of complexity. The components included range from mean value engine components to in-cylinder models. An efficient way to handle parameters using records is provided. Different bus systems are implemented and discussed. Furthermore are replaceable fluid models introduced in the library. It will be shown that Modelica is a very efficient way to create an advanced modelling library.</p>

<p>Because of new emission and on board diagnostics legislations, heavy truck manufacturers are facing new challenges when it comes to improving the engines and the control software. Accurate and real time executable engine models are essential in this work. One successful way of lowering the NOx emissions is to use Exhaust Gas Recirculation (EGR). The objective of this thesis is to create a mean value model for Scania's next generation EGR system consisting of a poppet valve and a two stage cooler. The model will be used to extend an existing mean value engine model. Two models of different complexity for the EGR system have been validated with sufficient accuracy. Validation was performed during static test bed conditions. The resulting flow models have mean relative errors of 5.0% and 9.1% respectively. The temperature model suggested has a mean relative error of 0.77%.</p>

<p>Due to stricter emission legislation, there is a need for more efficient control of diesel engines with exhaust gas recirculation(EGR). In particular, it is important to estimate the air/fuel ratio accurately in transients. Therefore a new engine gas flow model has been developed. This model divides the gas into one part for oxygen and one part for inert gases. Based on this model an observer has been designed to estimate the oxygen concentration in the gas going into the engine, which can be used to calculate the air/fuel ratio. This observer can also be used to estimate the intake manifold pressure. The advantage of estimating the pressure, instead of low pass filtering the noisy signal, is that the observer does not cause time delay.</p>

<p>Since measurements in engine test cells are closely coupled with high costs it is of interest to use physically interpretable engine models instead of engine maps. Such engine models can also be used to do off-line tests of how new or altered components affects engine performance.</p><p>In the thesis an existing mean value engine model will be extended with a model of a compressor bypass valve. A controller for that valve will also be developed. The purpose with that controller is to save torque and boost pressure but at the same time avoid having the compressor entering surge during fast closing transients in the throttle position.</p><p>Both the extension and controller is successfully developed and implemented. The extension lowers the pressure after the compressor and increases the pressure before the compressor when the bypass valve is being opened and the controller shows better results in simulations than the controller used in the research lab. By using the proposed controller, as much as 5 percent higher torque can be achieved in simulations.</p><p>Finally there is a discussion on wastegate control alternatives and the use of TOMOC for optimization of wastegate control.</p>

<p>Linear time-invariant approximations of nonlinear systems are used in many applications and can be obtained in several ways. For example, using system identification and the prediction-error method, it is always possible to estimate a linear model without considering the fact that the input and output measurements in many cases come from a nonlinear system. One of the main objectives of this thesis is to explain some properties of such approximate models.</p><p>More specifically, linear time-invariant models that are optimal approximations in the sense that they minimize a mean-square error criterion are considered. Linear models, both with and without a noise description, are studied. Some interesting, but in applications usually undesirable, properties of such optimal models are pointed out. It is shown that the optimal linear model can be very sensitive to small nonlinearities. Hence, the linear approximation of an almost linear system can be useless for some applications, such as robust control design. Furthermore, it is shown that standard validation methods, designed for identification of linear systems, cannot always be used to validate an optimal linear approximation of a nonlinear system.</p><p>In order to improve the models, conditions on the input signal that imply various useful properties of the linear approximations are given. It is shown, for instance, that minimum phase filtered white noise in many senses is a good choice of input signal. Furthermore, the class of separable signals is studied in detail. This class contains Gaussian signals and it turns out that these signals are especially useful for obtaining approximations of generalized Wiener-Hammerstein systems. It is also shown that some random multisine signals are separable. In addition, some theoretical results about almost linear systems are presented.</p><p>In standard methods for robust control design, the size of the model error is assumed to be known for all input signals. However, in many situations, this is not a realistic assumption when a nonlinear system is approximated with a linear model. In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs.</p><p>It is sometimes undesirable that small nonlinearities in a system influence the linear approximation of it. In some cases, this influence can be reduced if a small nonlinearity is included in the model. In this thesis, an identification method with this option is presented for nonlinear autoregressive systems with external inputs. Using this method, models with a parametric linear part and a nonparametric Lipschitz continuous nonlinear part can be estimated by solving a convex optimization problem.</p> / <p>Linjära tidsinvarianta approximationer av olinjära system har många användningsområden och kan tas fram på flera sätt. Om man har mätningar av in- och utsignalerna från ett olinjärt system kan man till exempel använda systemidentifiering och prediktionsfelsmetoden för att skatta en linjär modell utan att ta hänsyn till att systemet egentligen är olinjärt. Ett av huvudmålen med den här avhandlingen är att beskriva egenskaper för sådana approximativa modeller.</p><p>Framförallt studeras linjära tidsinvarianta modeller som är optimala approximationer i meningen att de minimerar ett kriterium baserat på medelkvadratfelet. Brusmodeller kan inkluderas i dessa modelltyper och både fallet med och utan brusmodell studeras här. Modeller som är optimala i medelkvadratfelsmening visar sig kunna uppvisa ett antal intressanta, men ibland oönskade, egenskaper. Bland annat visas det att en optimal linjär modell kan vara mycket känslig för små olinjäriteter. Denna känslighet är inte önskvärd i de flesta tillämpningar och innebär att en linjär approximation av ett nästan linjärt system kan vara oanvändbar för till exempel robust reglerdesign. Vidare visas det att en del valideringsmetoder som är framtagna för linjära system inte alltid kan användas för validering av linjära approximationer av olinjära system.</p><p>Man kan dock göra de optimala linjära modellerna mer användbara genom att välja lämpliga insignaler. Bland annat visas det att minfasfiltrerat vitt brus i många avseenden är ett bra val av insignal. Klassen av separabla signaler detaljstuderas också. Denna klass innehåller till exempel alla gaussiska signaler och just dessa signaler visar sig vara speciellt användbara för att ta fram approximationer av generaliserade wiener-hammerstein-system. Dessutom visas det att en viss typ av slumpmässiga multisinussignaler är separabel. Några teoretiska resultat om nästan linjära system presenteras också.</p><p>De flesta metoder för robust reglerdesign kan bara användas om storleken på modellfelet är känd för alla tänkbara insignaler. Detta är emellertid ofta inte realistiskt när ett olinjärt system approximeras med en linjär modell. I denna avhandling beskrivs därför ett alternativt sätt att göra en robust reglerdesign baserat på en tidsdiskret modell och en modellfelsmodell som bara är giltig för begränsade insignaler.</p><p>Ibland skulle det vara önskvärt om en linjär modell av ett system inte påverkades av förekomsten av små olinjäriteter i systemet. Denna oönskade påverkan kan i vissa fall reduceras om en liten olinjär term tas med i modellen. En identifieringsmetod för olinjära autoregressiva system med externa insignaler där denna möjlighet finns beskrivs här. Med hjälp av denna metod kan modeller som består av en parametrisk linjär del och en ickeparametrisk lipschitzkontinuerlig olinjär del skattas genom att man löser ett konvext optimeringsproblem.</p>

<p>Mean Value Engine Modeling (MVEM) is used to make engine control development less expensive. With more and more cars equipped with turbocharged engines good turbo MVEM models are needed. A turbocharger consists of two major parts: turbine and compressor. Whereas the turbine is relatively durable, there exist phenomenons on the compressor that can destroy the turbocharger. One of these is surge.</p><p>Several compressor models are developed in this thesis. Methods to determine the compressor model parameters are proposed and discussed both for the stable operating range as well as for the surge region of a compressor map. For the stationary region methods to automatically parameterize the compressor model are developed. For the unstable surge region methods to get good agreement for desired surge properties are discussed. The parameter sensitivity of the different surge properties is also discussed. A validation of the compressor model shows that it gives good agreement to data, both for the stationary region as well as the surge region.</p><p>Different open loop and closed loop controllers as well as different performance variables are developed and discussed. A benchmark is developed, based on a measured vehicle acceleration, and the control approaches are compared using this benchmark. The best controller is found to be a open loop controller based on throttle and surge valve mass flow.</p>