The General Toeplitz/Observability Smooth Variable Structure Filter

Abstract

Fault detection can be used to improve the reliability and safety of industrial system. An important component of fault detection is filtering for parameter and state estimation. The challenge is to create a filter that is robust and stable in light of modeling uncertainties and parametric changes due to fault conditions.The Smooth Variable Structure Filter (SVSF) is a recently defined predictor corrector filter based on the Sliding Mode Control concepts. The SVSF defines a hyperplane and then applies a discontinuous corrective action that forces the estimate to go back and forth cross that plane. The discontinuous action results in chattering. To overcome chattering, the SVSF uses a saturated function with an associated fixed-width smoothing boundary layer. The SVSF is useful in applications that require robustness due to modeling uncertainties. In this thesis, the SVSF concepts are explored and further investigated. The chattering signals are used to establish a monitoring and reconstructing algorithm that can be used to detect and extract changes and added uncertainties in the system. However, its ability to determine the source of the added uncertainty is limited to cases involving abrupt step changes. There are limitations to the SVSF due to the use of the Luenberger method in terms of sensitivity to noise and modeling errors. A novel strategy using the Toeplitz and the Observability matrices is proposed to overcome the SVSF's limitations. This strategy is generalized to high order systems with multiple measurements using new proposed the General System Toeplitz and the General Observability matrices. This strategy is linked to the SVSF and improves its performance in terms of robustness and accuracy. A novel parameter estimation technique referred to as the Iterative BiSection/ Shooting Method (IBSS) is derived and is linked to the SVSF to estimate model parameters and states for systems in which only the model structure is known. The benefits of the proposed estimation methods are demonstrated by using example studies involving an electro-hydrostatic actuator proposed in (Habibi, 2007) and a three-degree of freedom mass-spring-damper system.