Simulering av simulinkmodeller med Extended Kalman Filter

Sammanfattning: Simulations of simulink models using Kalman filters are often very time-consuming. This problem depends mainly on the fact that the Kalman correction has to be performed at each sample instance through the whole simulation. The goal for this thesis work is to reduce that time-consumption for the filtering part (the integration partis treated in a complementary report) of a simulation. Furthermore a Matlab routine to perform parameter tuning and finally a graphical user interface is developed. The filtering part of the simulation in this thesis is based on an Extended Kalman Filter (EKF). The time optimization of this filter considers searching for the possibility to replace the today’s existing Matlab functions that is used to perform the filtering calculations. Examples of such functions are routines for linearization and integration. To decrease the time-consumption, we have also developed a routine to make it possible to convert a simulink model to a state-space description. This conversion makes it possible to avoid a lot of time-consuming calls to the simulink model. In this case it is the built-in functions in Matlab that causes the large time-consumption. The main time-consuming parts in the filter are the built-in routines for linearization (linmod) and the numerical method that is used to calculate the prediction error (riccatiequation). By creating new routines to solve these problems, the total time-consumption for the filtering part is reduced by approximately a factor of eighteen. As a final step the time optimized Kalman filter and the time optimized integration (treated in a complementary report) are brought together in a time efficient routine for simulation. This final routine for simulation may further be used to perform a time efficient simulation, but also to form a routine, which can be used to estimate unknown parameters in a simulink model. Using the time optimized parts of the simulation routine will make it possible to reduce the execution time for a filtering simulation by approximately a factor of ten. Three kinds of models are used to confirm that the different element of the Kalman filter and the new developed routines work properly. These models consist of one fermentation system that describes a biological process, and two different tank systems that describe the level and the torrent of water in several water tanks.