Real-Time Estimation of Time-Varying Bending Modes Using Fiber Bragg Grating Sensor Arrays

Abstract

An important challenge in launch vehicle simulation and control is created by the time-varying mass and inertia of the vehicle, as well as the consequent changes in modal frequencies and modal shapes of the structure as propellant is exhausted. Estimating modal information from a limited number of onboard sensors is inadequate for attitude control of a launch vehicle in real time, and the use of additional conventional sensors is unwarranted because of the mass penalty and complexity. This limitation has forced mission planners to base vehicle control schemes on pre-calculated modal information from finite element models. Recent advances in fiber Bragg grating (FBG) sensor technology enable locating a large number of sensing elements along a rocket's structure with a negligible mass penalty. This opens the path for real-time modal estimation and control. This paper presents a novel approach for the real-time estimation of mode shapes on a variable mass structure using FBG sensor arrays. The method is validated by comparing estimated modal shapes to both numerical predictions and experimental results from a vertical cantilever beam in which a step change in mass of the beam is introduced. The results show that the first three mode shapes of the beam can be estimated in real time using strain measurements from a FBG sensor array sampled at 1 kHz. Sensitivity and estimation error based on the number of FBG sensors used is also presented.