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

开关模式增强型扩展卡尔曼滤波器（SEEK）算法已被开发用于估计强非线性和噪声动态系统。SEEK算法基于最优选择观测矩阵，以保证估计误差协方差阵的收敛性最大化。的基本概念已概述使用二阶线性系统，并成功地验证了数值演示。在此基础上，应用SEEK滤波算法对叠加高斯白色噪声的Lorenz系统进行了估计。SEEK滤波器返回了很好的估计，这个混沌系统，虽然传统的扩展卡尔曼滤波器绝对不能获得准确的状态估计。提出了选择最佳采样模式的优化算法，并应用于参数切换的Lorenz系统的估计。我们认为这个演示作为令人信服的证据的电源的SEEK过滤器作为一个准确的估计的状态变量，即使是强非线性系统，如这种特殊的实现的洛伦兹系统。SEEK算法也已被应用于识别演变的大结构在流动中伴随着微结构扩散的离散涡模拟。SEEK滤波器即使在高水平噪声环境中也实现了准确的估计。然后，雅可比矩阵的对角元素已被发现是占主导地位的SEEK算法应用于离散涡模拟。这一证据对于减少大型代码估算中的计算时间非常有用。然后，从卡尔曼滤波技术在控制实践中的适用性的观点出发，假设控制对象具有典型的传递函数，这对于粉末过程是常见的，因此，在常规PID、LQG和H ∞控制的情况下，比较了控制性能。

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.