Maps or look-up tables are frequently used in engine control systems, and can be of dimension one or higher. Their use is often to describe stationary phenomena such as sensor characteristics or engine performance parameters like volumetric efficiency. Aging can slowly change the behavior, which can be manifested as a bias, and it can be necessary to adapt the maps. Methods for bias compensation and on-line map adaptation using extended Kalman filters are investigated and discussed. Key properties of the approach are ways of handling component aging, varying measurement quality, as well as operating point dependent model quality. Handling covariance growth on locally unobservable modes, which is an inherent property of the map adaptation problem, is also important and this is solved for the Kalman filter. The method is applicable to off-line calibration ofmaps where the only requirement of the data is that the entire operating region of the system is covered, i.e. no special calibration cycles are required. Two truck engine applications are evaluated, one where a 1-D air mass-ffow sensoradaptation map is estimated, and one where a 2-D volumetric efficiency map is adapted, both during a European transient cycle. An evaluation on experimental data shows that the method estimates a map, describing the sensor error, on a measurement sequence not specially designed for adaptation.

A method for bias compensation in model based estimation utilizing model augmentation is developed. Based on a default model, that suffers from stationary errors, and measurements from the system a low order augmentation is estimated. The method handles models described by differential algebraic equations and the main contributions are necessary and sufficient conditions for the preservation of the observability properties of the default model during the augmentation.

A method for bias compensation and online map adaptation using extended Kalman filters isdeveloped. Key properties of the approach include the methods of handling component aging, varyingmeasurement quality including operating-point-dependent reliability and occasional outliers, andoperating-point-dependent model quality. Theoretical results about local and global observability,specifically adapted to the map adaptation problem, are proven. In addition, a method is presented tohandle covariance growth of locally unobservable modes, which is inherent in the map adaptationproblem. The approach is also applicable to the offline calibration of maps, in which case the onlyrequirement of the data is that the entire operating region of the system is covered, i.e., no specialcalibration cycles are required. The approach is applied to a truck engine in which an air mass-flowsensor adaptation map is estimated during a European transient cycle. It is demonstrated that themethod manages to find a map describing the sensor error in the presence of model errors on ameasurement sequence not specifically designed for adaptation. It is also demonstrated that themethod integrates well with traditional engineering tools, allowing prior knowledge about specificmodel errors to be incorporated and handled.

Control and diagnosis of complex systems demand accurate information of the system state to enable efficient control and to detect system malfunction. Physical sensors are expensive and some quantities are hard or even impossible to measure with physical sensors. This has made model-based estimation an attractive alternative.

Model based observers are sensitive to errors in the model and since the model complexity has to be kept low to enable use in real-time applications, the accuracy of the models becomes limited. Further, modeling is difficult and expensive with large efforts on model parametrization, calibration, and validation, and it is desirable to design robust observers based on existing models. An experimental investigation of an engine application shows that the model have stationary errors while the dynamics of the engine is well described by the model equations. This together with frequent appearance of sensor offsets have led to a demand for systematic ways of handling operating point dependent stationary errors, also called biases, in both models and sensors.

Systematic design methods for reducing bias in model based observers are developed. The methods utilize a default model, described by systems of ordinary differential equations (ODE) or differential algebraic equations (DAE), and measurement data. A low order description of the model deficiencies is estimated from the default model and measurement data, which results in an automatic model augmentation. The idea is then to use the augmented model in observer design, yielding reduced stationary estimation errors compared to an observer based on the default model. Three main results are: a characterization of possible model augmentations from observability perspectives, a characterization of augmentations possible to estimate from measurement data, and a robustness analysis with respect to noise and model uncertainty.

An important step is how the bias is modeled, and two ways of describing the bias are analyzed. The first is a random walk and the second is a parameterization of the bias. The latter can be viewed as an extension of the first and utilizes a parameterized function that describes the bias as a function of the operating point of the system. By utilizing a parameterized function, a memory is introduced that enables separate tracking of aging and operating point dependence. This eliminates the trade-off between noise suppression in the parameter convergence and rapid change of the offset in transients. Direct applications for the parameterized bias are online adaptation and offline calibration of maps commonly used in engine control systems.

The methods are evaluated on measurement data from heavy duty diesel engines. A first order model augmentation is found for an ODE of an engine with EGR and VGT. By modeling the bias as a random walk, the estimation error is reduced by 50 % for a certification cycle. By instead letting a parameterized function describe the bias, better estimation accuracy and increased robustness is achieved. For an engine with intake manifold throttle, EGR, and VGT and a corresponding stiff ODE, experiments show that it is computationally beneficial to approximate the fast dynamics with instantaneous relations, transforming the ODE into a DAE. A main advantage is the possibility to use more than 10 times longer step lengths for the DAE based observer, without loss of estimation accuracy. By augmenting the DAE, an observer that achieves a 55 % reduction of the estimation error during a certification cycle is designed.

A method for online map adaptation is developed. The method utilizes the EKF as a parameter estimator and handles parameter aging, operating point dependent model and measurement quality. Map adaptation, by construction, gives marginally stable models with locally unobservable modes, that are handled. The method is also suitable for offline calibration of maps where the only requirement of the data is that the entire operating region of the system is covered. The method is applied to a truck engine where an air mass-flow sensor adaptation map is estimated based on data from a diesel engine during an ETC. It is shown that an adaptation map can be found in a measurement sequence not specially designed for adaptation.

A systematic design method for reducing bias in observers is developed. The method utilizes an observable default model of the system together with measurement data from the real system and estimates a model augmentation. The augmented model is then used to design an observer which reduces the estimation bias compared to an observer based on the default model. Three main results are a characterization of possible augmentations from observability perspectives, a parameterization of the augmentations from the method, and a robustness analysis of the proposed augmentation estimation method. The method is applied to a truck engine where the resulting augmented observer reduces the estimation bias by 50% in a European transient cycle.

With stricter emission legislations and customer demands on low fuel consumption, good control strategies are necessary. This may involve control of variables that are hard, or even impossible, to measure with real physical sensors. By applying estimators or observers, these variables can be made available. The quality of a real sensor is determined by e.g. accuracy, drift and aging, but assessing the quality of an estimator is a more subtle task. An estimator is the result of a design work and hence, connected to factors like application, model, control error and robustness.

The air mass-flow in a diesel engine is a very important quantity that has a direct impact on many control and diagnosis functions. The quality of the air mass-flow sensor in a diesel engine is analyzed with respect to day-to-day variations, aging, and differences in engine configurations. The investigation highlights the necessity of continuous monitoring and adaption of the air mass-flow. One way to do this is to use an estimator. Nine estimators are designed for estimation of the air mass-flow with the aim of assessing different quality measures. In the study of the estimators and quality measures it is evident that model accuracy is important and that special care has to be taken, regarding what quality measure to use, when the estimator performance is evaluated.

Control and diagnosis of complex systems demand accurate knowledge of certain quantities to be able to control the system efficiently and also to detect small errors. Physical sensors are expensive and some quantities are hard or even impossible to measure with physical sensors. This has made model-based estimation an attractive alternative.

Model-based estimators are sensitive to errors in the model and since the model complexity needs to be kept low, the accuracy of the models becomes limited. Further, modeling is hard and time consuming and it is desirable to design robust estimators based on existing models. An experimental investigation shows that the model deficiencies in engine applications often are stationary errors while the dynamics of the engine is well described by the model equations. This together with fairly frequent appearance of sensor offsets have led to a demand for systematic ways of handling stationary errors, also called bias, in both models and sensors.

In the thesis systematic design methods for reducing bias in estimators are developed. The methods utilize a default model and measurement data. In the first method, a low order description of the model deficiencies is estimated from the default model and measurement data, resulting in an automatic model augmentation. The idea is then to use the augmented model for estimator design, yielding reduced stationary estimation errors compared to an estimator based on the default model. Three main results are: a characterization of possible model augmentations from observability perspectives, an analysis of what augmentations that are possible to estimate from measurement data, and a robustness analysis with respect to noise and model uncertainty.

An important step is how the bias is modeled, and two ways of describing the bias are introduced. The first is a random walk and the second is a parameterization of the bias. The latter can be viewed as an extension of the first and utilizes a parameterized function that describes the bias as a function of the operating point of the system. The parameters, rather than the bias, are now modeled as random walks, which eliminates the trade-off between noise suppression in the parameter convergence and rapid change of the offset in transients. This is achieved by storing information about the bias in different operating points. A direct application for the parameterized bias is the adaptation algorithms that are commonly used in engine control systems.

The methods are applied to measurement data from a heavy duty diesel engine. A first order model augmentation is found for a third order model and by modeling the bias as a random walk, an estimation error reduction of 50 % is achieved for a European transient cycle. By instead letting a parameterized function describe the bias, simulation results indicate similar, or better, improvements and increased robustness.