Extended Kalman Filter Observer Research Articles

ON-LINE ESTIMATION AND DETECTION OF ABNORMAL SUBSTRATE CONCENTRATIONS IN WWTPS USING A SOFTWARE SENSOR: A BENCHMARK STUDY

In this paper, a new approach for on-line monitoring and detection of abnormal readily biodegradable substrate (S S) and slowly biodegradable substrate (X S) concentrations, for example due to input of toxic loads from the sewer, or due to influent substrate shock load, is proposed. Considering that measurements of S S and X S concentrations are not available in real wastewater treatment plants, the S S | X S software sensor can activate an alarm with a response time of about 60 and 90 minutes, respectively, based on the dissolved oxygen measurement. The software sensor implementation is based on an extended Kalman filter observer and disturbances are modelled using fast Fourier transform and spectrum analyses. Three case studies are described. The first one illustrates the fast and accurate convergence of the extended Kalman filter algorithm, which is achieved in less than 2 hours. Furthermore, the difficulties of estimating X S when off-line analysis is not available are depicted, and the S S | X S software sensor performances when no measurements of S S and X S are available are illustrated. Estimation problems related to the death-regeneration concept of the activated sludge model no.1 and possible application of the software sensor in wastewater monitoring are discussed.

Monitoring of a CO oxidation reactor through a grey model-based EKF observer

Often, in real applications it is difficult to dispose of a simple, yet, representative kinetic model because of the complexity of the reactions taking place. To overcome this limitation a hybrid modelling approach is proposed for the identification of the dynamic behaviour of chemical reactors. In particular, the tools of neural network modelling have been exploited to represent the kinetic reaction data. The “neural reaction rate model” is integrated within a first principles model that constitutes the basis of a nonlinear observer extended Kalman filter (EKF) for an heterogeneous gas–solid reactor where the catalytic oxidation of carbon monoxide takes place. The outlined procedure shows that artificial neural networks (ANN) can be effectively used to formulate lumped reaction rates because of their capability in capturing the essential characteristics of the functional relationship among the state variables.

Estimation of speed and armature temperature in a brushed DC drive using the extended Kalman filter

Closed-loop speed control of a DC drive requires a rotor-speed feedback signal which can be obtained using a speed measuring device. However this device adds to the cost of the drive and the number of electrical connections to the motor. The paper describes a method of speed estimation using armature voltage and current measurements that eliminates the speed measuring device. By including thermal effects in the estimation process the effect of temperature variations on the speed estimte are minimised and an estimate of average armature temperature is produced. An extended Kalman filter observer for real-time estimation of speed and armature temperature is formulated using electrical, mechanical and thermal models of the motor. The observer is implemented using a TMS 320C30 digital signal processor system. A range of experimental results demonstrating the observer's steady-state and transient performance is presented for the particular case of a 3 kW machine with constant field current supplied from a phase-controlled rectifier, although the estimation method is applicable to DC drives of any power rating and configuration.