INPUT SHAPING FOR RESIDUAL VIBRATION REDUCTION

Abstract

In this thesis, a method to shape the input such that the residual vibration of a flexible system can be reduced is presented. The problem is formulated as an optimization problem to minimize the time taken for a rest-to-rest motion. The system model of a generalised system, the system model of a crane system and the system model of a flexible beam system are first developed. Based on the model for the generalized system, the requirement for zero residual vibration is then written as• constraints for the optimization. Other constraints such as system constraints arising from the rigid-body motion and physical considerations are derived for arbitrary and step inputs. As a comparison, a system without input shaping for rest-to-rest motion is first considered. Simulations and experiments show that such a system will usually result in some residual vibration. In addition, it is shown that residual vibration reduction cannot always be achieved by simply slowing down the system. In the proposed method, the problem is re-cast as a time optimization problem with rigid-body motion constraints and residual vibration reduction constraints. Other physical constraints such as limits on the maximum acceleration and velocity can be added. A solution can then be found using standard optimization technique. It is shown that the solution, in the form of step sequences can significantly reduce the residual vibration while causing the rigid body to perform a desired motion. The shaped input method developed here is straightforward and does not require measurements of the system's states. Hence it is direct and easier to implement on actual systems. Although the structure of the control is open loop, it is shown that such shaped input can possess some robustness to variations in the system's parameters such as natural frequencies and damping ratios. Simulations and experiments show that the proposed method is easy to design and effective in implementations.