Collision detection of controlled flexible structures with random disturbance

This paper presents a method of collision detection using a Kalman filter for controlled flexible structures modeled by an Euler-Bernoulli type partial differential equation subject to distributed random disturbance. Applying the modal expansion method, the finite-dimensional model corresponding to the mathematical model is obtained. The Kalman filter as a state estimator is constructed for the finite-dimensional system consisting of the modal representation models. The controller for suppressing the vibration of the structure is designed via the LQG control theory. The collision detection is achieved by testing a scalar statistic consisting of the innovation process of the Kalman filter.