An Adaptive Algorithm for the Tuning of Two Input Shaping Methods

The paper presents an algorithm for the tuning of two input shaping methods. These methods are designed to prevent the excitation of oscillatory modes in resonant systems. The first input shaping method produces a control signal that is the linear combination of delayed versions of the reference input. The resulting control system is linear time-invariant but infinite-dimensional. Its transfer function has an infinite number of complex zeros, with some of them placed exactly at the locations of the resonant modes of the plant. In contrast, the second input shaping method is based on a pole/zero cancellation of the resonant modes using a finite-dimensional controller. For both input shaping methods, tuning is useful to optimize performance and an algorithm is developed for the automatic adjustment of the controller parameters. Experimental results are presented for a system in which a motor is used to control the position of a flexible arm. The step response of the plant is poorly damped, but is much improved with input shaping. The control performance is found to be comparable for both methods, and the tuning method is found to be simple and effective.