Nonlinear feedback auxiliary signals for system interrogation and damage detection

Abstract

Recently, a sensitivity-enhancement technique for system interrogation using linear controllers and eigenstructure assignment has been extended from linear to nonlinear systems. Nonlinearities have been accounted for by forming (higher dimensional) augmented systems that are designed for each trajectory of the nonlinear system, and are characterized by a specific forcing which ensures that the augmented systems follow that trajectory (when projected onto the original lower dimensional space). The use of system augmentation has several benefits beyond its ability to handle nonlinearities. For example, sensitivity can be increased compared with existing linear techniques through nonlinear feedback auxiliary signals (NFASs) because the constraint that the system is stable during its interrogation has to be applied only to the linearized closed-loop system, while the augmented linear system does not have that constraint. In this work, NFASs are designed for interrogating linear systems. System augmentation is used in a linear system because a nonlinear controller is employed to enhance sensitivity. In addition to the increased sensitivity, fewer controller actuator points and sensors are required compared with existing linear techniques due to the efficient use of added (augmented) equations. To demonstrate the approach, damage detection is considered as an application. Numerical simulations for linear mass–spring and mass–spring–damper systems are used to validate the approach and discuss the effects of noise.