The 2nd-Order Smooth Variable Structure Filter (2nd-SVSF) for State Estimation: Theory and Applications

Abstract

Kalman-type filtering methods are mostly designed based on exact knowledge of the system’s model with known parameters. In real applications, there may be considerable amount of uncertainties about the model structure, physical parameters, level of noise, and initial conditions. In order to overcome such difficulties, robust state estimation techniques are recommended. This PhD thesis presents a novel robust state estimation method that is referred to as the 2nd-order smooth variable structure filter (2nd-order SVSF) and satisfies the first and second order sliding conditions. It is an extension to the 1st-order SVSF introduced in 2007. In the 1st-order SVSF chattering is reduced by using a smoothing boundary layer; however, the 2nd-order SVSF alleviates chattering by preserving the second order sliding condition. It reduces the estimation error and its first difference until the existence boundary layer is reached. Then after, it guarantees that the estimation error and its difference remain bounded given bounded noise and modeling uncertainties. As such, the 2nd-order SVSF produces more accurate and smoother state estimates under highly uncertain conditions than the 1st-order version. The main issue with the 2nd-order SVSF is that it is not optimal in the mean square error sense. In order to overcome this issue, the dynamic 2nd-order SVSF is initially presented based on a dynamic sliding mode manifold. This manifold introduces a variable cut-off frequency coefficient that adjusts the filter bandwidth. An optimal derivation of the 2nd-order SVSF is then obtained by minimizing the state error covariance matrix with respect to the cut-off frequency matrix. An experimental setup of an electro-hydrostatic actuator is used to compare the performance of the 2nd-order SVSF and its optimal version with other estimation methods such as the Kalman filter and the 1st-order SVSF. Experiments confirm the superior performance of the 2nd-order SVSF given modeling uncertainties.