Estimation with low measurement frequency
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The invention of the computer has triggered a technological revolution in many parts ofsociety. For the process industry, computers have led to improvement in both productionrates, safety and profits. One way this has happened is through the use of online estimators.In the process industry, such estimators are typically used for decision support systems oras soft sensors for advanced process control. The Kalman filter has been one of the morepopular estimators since its introduction in 1960. Since then, many versions of the Kalmanfilter have been developed in order to deal with systems with different characteristics. Fornonlinear systems where all measurements are not available on every time step, the MultirateExtended Kalman filter can typically be applied. It is not straight forward to decidehow the Kalman filter should be tuned for the best possible performance when differentmeasurements arrive at different rates.This thesis has two main objectives. The first is to look at the possibility of determiningany criteria for how the noise parameters of the Multi-rate Extended Kalman filter shouldbe tuned to achieve the best possible estimates when the measurement frequencies vary.The second objective is to evaluate if it is reasonable to perform all the different infrequentmeasurements simultaneously or if they should be spread out, for cases where it is possibleto decide the measurement frequencies.To be able to test these objectives, a model of the the aluminium electrolysis processhas been developed. The aluminium electrolysis process is used as an example process becauseit is common to use multiple infrequent process measurements like the temperatureand height of the electrolysis bath, the metal height and the aluminium fluoride concentrationin the monitoring of aluminium electrolysis cells. Early in the thesis, an introductionto the aluminium electrolysis process and the theory behind the Discrete, Extended andMulti-rate Extended Kalman filters is given. This lies to foundation for the model developmentand testing of the Kalman filter properties.In order to investigate the objectives of the thesis, the developed model has been usedboth as a simulated process with one set of parameters, and as a model using a slightly differentset of parameters. The difference in parameters is used to simulate modelling errors,as it will create a process-model mismatch. The Kalman filter has then been used to correctfor this mismatch by estimating on the changed parameters. The obtained results seem toindicate that there is no significant difference in estimator performance between using jointmeasurements or shifting the time at which measurements are performed. With regard toKalman filter tuning for varying measurement frequencies, non of the results suggest thatthe optimal tuning is significantly altered by a change in measurement frequency.