Observer design and model augmentation for bias compensation with a truck engine application

Abstract

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.

Model Based Engine Map Adaptation Using EKF

“…Here and henceforth system, measurement, and random walk noise terms are left out to increase readability. Note that this is similar to the formulation used in Höckerdal et al (2008b), the difference is that the bias states have been exchanged for a parameterized function and the function parameters are introduced as new states. If (4c) is inserted into (4a), a standard state space form is obtained which means that any suitable observer design can be applied.…”

“…To develop a model like (4) and use it for estimation and identification entails that some new issues have to be addressed compared to Höckerdal et al (2008b). Of these the main concern in this paper is how to update the function parameters, θ t , in a controlled manner.…”

“…Based on the method developed in Höckerdal et al (2008b), an information preserving observer, i.e. with memory, can be obtained by exchanging the assumption of a bias modeled as a random walk…”

“…However, since the observer designed in Höckerdal et al (2008b) treats the bias as a random walk it is not able to keep track of the changes in bias between operating points over time. That is, as soon as the system changes operating point, all information about the bias in the previous operating point is discarded.…”

“…Basically map adaptation can be viewed as a desire to reduce and store the compensation of an operating point dependent estimation error, and a way to reduce stationary estimation errors in model based observers was developed in Höckerdal et al (2008b). It utilizes an observable default state space model…”