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

为了估计强非线性、强噪声的动态系统，提出了一种切换模式增强扩展卡尔曼滤波算法。SEEK算法基于对观测矩阵的最优选择，以保证估计误差协方差矩阵的收敛性最大化。用二阶线性系统概述了基本概念，并成功地通过数值演示进行了验证。然后应用SEEK滤波算法对叠加高斯白噪声的洛伦兹系统进行估计。传统的扩展卡尔曼滤波绝对不能得到精确的状态估计，而SEEK滤波器对混沌系统的状态估计得到了很好的估计。提出了一种选择最优采样模式的优化算法，并将其应用于具有切换参数的洛伦兹系统的估计。我们认为这个演示是令人信服的证据，证明SEEK滤波器作为状态变量的准确估计器的能力，即使对于强非线性系统，如洛伦兹系统的这种特殊实现也是如此。在离散涡模拟中，SEEK算法也被用于识别流动中伴随微结构扩散的大结构演化。即使在高噪声环境下，SEEK滤波器也能实现准确的估计。在将SEEK算法应用于离散涡旋模拟时，发现只有雅可比矩阵的对角元占主导地位。这个证据对于减少大型代码估计中的计算时间应该是非常有用的。然后，从卡尔曼滤波技术在控制实践中的适用性角度，比较了传统PID、LQG和h -∞控制的控制性能，假设控制对象具有典型的传递函数，这在粉末过程中是很常见的。

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.