Recursive Estimation of Displacement and Velocity in a Cantilever Beam Using a Measured Set of Distributed Strain Data

A new form of recursive algorithm to estimate the transverse and angular displacement and/or velocity at any location along the length of a one-dimensional cantilever beam using the strain/strain-rate data measured from a set of sensors distributed along the length of the beam is presented. This is based on the linear spline functions used to approximate the strain distribution in the beam. One of the main applications of this algorithm is in controlling the vibrations in a flexible cantilever beam. To demonstrate its use in such a problem, a linear quadratic regulator (LQR) algorithm is considered and the recursive algorithm stated earlier is used for the state estimation which can be used in conjunction with the state feedback controller. Experimental results for both static and dynamic cases are furnished to validate the proposed estimation algorithm. In the case of static loading, strain gauges are used to measure the strain, while piezoelectric sensors are used in the dynamic case. Results showing the performance of the control algorithm that utilizes the recursive algorithm developed are presented.