Time-Delayed Acceleration Feedback Control of a Single-Link Flexible Manipulator Using Kalman Filter

The design problem of a discrete controller with time delay and acceleration feedback for a single-link flexible manipulator system is addressed in this paper. The dynamical model of a single-link flexible manipulator system is presented by the adoption of the finite element method and Lagrange's equation. Based on the random-walk process and the discrete reduction method, an augmented discretized delay-free state derivate space equation containing the random noise is established. An acceleration-based Kalman filtering method is developed in order to estimate the system state and external excitation necessary for the controller design. In light of the estimated augmented states, a hybrid controller that combines a feedback control algorithm and a feedforward control algorithm is designed according to optimal control theory and Moore-Penrose theory. Numerical simulation results show that the proposed controller can damp out the vibration response of the flexible manipulator system effectively upon external excitations. Moreover, it is further revealed that the control performance of the presented method can be improved by adding the time delay appropriately.