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Model Error Compensation in ODE and DAE Estimators: with Automotive Engine Applications
Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2011. , 30 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1366
National Category
Computer and Information Science Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-67117ISBN: 978-91-7393-209-7OAI: oai:DiVA.org:liu-67117DiVA: diva2:411495
Public defence
2011-05-27, Visionen, Hus B, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2011-04-20 Created: 2011-03-30 Last updated: 2011-04-20Bibliographically approved
List of papers
1. Observer design and model augmentation for bias compensation with a truck engine application
Open this publication in new window or tab >>Observer design and model augmentation for bias compensation with a truck engine application
2009 (English)In: Control Engineering Practice, ISSN 0967-0661, Vol. 17, no 3, 408-417 p.Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
Bias compensation, EKF, Non-linear, Observer
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-17160 (URN)10.1016/j.conengprac.2008.09.004 (DOI)
Note
Original Publication:Erik Höckerdal, Erik Frisk and Lars Eriksson, Observer design and model augmentation for bias compensation with a truck engine application, 2009, CONTROL ENGINEERING PRACTICE, (17), 3, 408-417.http://dx.doi.org/10.1016/j.conengprac.2008.09.004Copyright: Elsevier Science B.V., Amsterdam.http://www.elsevier.com/Available from: 2009-03-19 Created: 2009-03-07 Last updated: 2011-04-20Bibliographically approved
2. EKF-Based Adaptation of Look-Up Tables with an Air Mass-Flow Sensor Application
Open this publication in new window or tab >>EKF-Based Adaptation of Look-Up Tables with an Air Mass-Flow Sensor Application
2011 (English)In: Control Engineering Practice, ISSN 0967-0661, Vol. 19, no 5, 442-453 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2011
Keyword
Bias compensation, EKF, Parameter estimation, Map adaptation
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-67591 (URN)10.1016/j.conengprac.2011.01.006 (DOI)000290744300003 ()
Available from: 2011-04-18 Created: 2011-04-18 Last updated: 2011-06-08
3. Off- and On-Line Identification of Maps Applied to the Gas Path in Diesel Engines
Open this publication in new window or tab >>Off- and On-Line Identification of Maps Applied to the Gas Path in Diesel Engines
2012 (English)In: Lecture notes in control and information sciences, ISSN 0170-8643, Vol. 418, 241-256 p.Article in journal (Refereed) Published
Abstract [en]

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.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-67595 (URN)10.1007/978-1-4471-2221-0_14 (DOI)000306990500014 ()
Conference
Workshop on Identification for Automotive Systems, Johannes Kepler University Linz, Austria, July 15th - 16th
Available from: 2011-04-18 Created: 2011-04-18 Last updated: 2014-11-03Bibliographically approved
4. DAE and ODE Based EKF:s and their Real-Time Performance Evaluated on a Diesel Engine
Open this publication in new window or tab >>DAE and ODE Based EKF:s and their Real-Time Performance Evaluated on a Diesel Engine
(English)Manuscript (preprint) (Other academic)
Abstract [en]

When estimating states in engine control systems there are limitations on the computational capabilities.This becomes especially apparent when designingobservers for stiff systems since the implementation requires small step lengths. One way to reduce the computational burden, is to reduce the model stiffness by approximating the fast dynamics with instantaneous relations, transformingan ODE model into a DAE model.

Performance and sample frequency limitations for extended Kalman filters based on both the original ODE model and the reduced DAE model for a diesel engine is analyzed and compared. The effect of using backward Euler instead of forward Euler when discretizing the continuous time model is analyzed.

The ideas are evaluated using measurement data from a diesel engine.The engine is equipped with throttle, EGR, and VGT and the stiff model dynamics arise as a consequence of the throttle between two control volumes in the air intake system. It is shown that even though the ODE, for each time-update, is less computationally demanding than the resulting DAE, an EKF based on the DAE model achieves better estimation performance than one based on the ODE with less computational effort. The main gain with the DAE based EKF is that it allows increased step lengths without degrading the estimation performance compared to the ODE based EKF.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-67596 (URN)
Available from: 2011-04-18 Created: 2011-04-18 Last updated: 2011-04-20
5. Bias Reduction in DAE Estimators by Model Augmentation: Observability Analysis and Experimental Evaluation
Open this publication in new window or tab >>Bias Reduction in DAE Estimators by Model Augmentation: Observability Analysis and Experimental Evaluation
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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 characterization of possible augmentations found through the estimation, showing the benefits of adding extra sensors during the design, is included. This enables reduction of estimation errors also in states not used for feedback, which is not possible with for example PI-observers. Beside the estimated augmentation the method handles user provided augmentations, found through e.g. physical knowledge of the system.

The method is evaluated on a nonlinear engine model where its ability to incorporate information from additional sensors during the augmentation estimationis clearly illustrated. By applying the method the mean relative estimation error for the exhaust manifold pressure is reduced by 55 %.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-67597 (URN)10.1109/CDC.2011.6160697 (DOI)
Available from: 2011-04-18 Created: 2011-04-18 Last updated: 2014-10-10Bibliographically approved

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