Online State Estimation of Fine Powder Processes by the Adaptive Extended Kalman Filter

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The switching mode enhanced extended Kalman(SEEK) filter algorithm has been developed to estimate strongly nonlinear and noisy dynamical systems. The SEEK algorithm is based on optimally selecting the observation matrix so as to ensure the convergence of the estimation error covariance matrix is maximized. The basic concept has been outlined using a second order linear system and successfully verified by numerical demonstrations. Then the SEEK filter algorithm has been applied to estimate the Lorenz system with superimposed Gaussian white noise. The SEEK filter has returned good estimates of this chaotic system though the conventional extended Kalman filter absolutely failed to obtain accurate state estimates. The optimization algorithm for selecting the optimal sampling mode has been developed and applied to estimate the Lorenz system with a switched parameter. We regard this demonstration as convincing evidence of the power of the SEEK filter as an accurate estimator of the state variables even for strongly nonlinear systems such as this particular relization of the Lorenz system. The SEEK algorithm has also been applied to identify evolving large structure in flows accompanied with micro-structure diffusion in a discrete vortex simulation. The SEEK filter achieved accurate estimation even in a high level noisy environment. Then only diagonal elements of the Jacobian matrix have been found to be dominant in applying the SEEK algorithm to the discrete vortex simulation. This evidence should be quite useful to reduce the calculation time in a large code estimation. Then, from the viewpoint of applicability of Kalman filtering technology to control practices, therefore, control performances have been compared among the cases of conventional PID, LQG and H-infinity controls, supposing a typical transfer function of the control object,which is certainly common to powder processes.