Nonlinear robust observer for structures with configuration-dependent natural frequencies: experimental and theoretical results

Abstract

The theoretical development of advanced controllers and observers has greatly surpassed the experimental work in this field. The current study represents a significant step toward an overall objective of providing experimental validation of these advanced concepts. Therefore, the present work focuses on validating the robust performance of a self-tuning nonlinear observer in accurately estimating the state variables of a structure whose natural frequencies are configuration-dependent. The observer design is based on both the variable structure systems theory and the self-tuning fuzzy logic scheme. Its robustness and self-tuning characteristic allows the use of an imprecise model of the system and eliminates the need for the extensive tuning associated with a fixed rule-based expert fuzzy inference system. The physical system is selected to be a spherical robotic manipulator where only the protruding portion of the third link from the second link is considered to be flexible. The prismatic joint causes the length of the flexible link to vary, which induces significant variations in the natural frequencies of the link. The observer has been implemented to estimate the generalized coordinates of the flexible motion under two different types of excitation. The first one involves disturbances in the initial conditions or the use of initial impulsive forces. While in the second type, the structural deformations are induced by the rigid body motion of the arm during a tracking maneuver. Same numerical values for the observer’s parameters were used in conducting both theoretical and experimental works. The results demonstrate the robustness of the observer in accurately estimating the generalized coordinates of the flexible motion of the third link in spite of significant modeling imprecision and external disturbances.