Switching ZVDk input shaper for flexible closed-loop system with saturation

Input shapers have been used to suppress residual vibration of flexible systems. The shaped reference, which is the output from the input shaper, avoids exciting the vibratory modes of the flexible closed-loop systems, resulting in zero residual vibration. Nevertheless, in practice, actuator saturation normally exists. The saturation changes the shaped control effort, intended for residual vibration suppression. As a result, the performance of the input shaper is degraded. This paper presents a technique to avoid violating the saturation by choosing the right input shaper for every reference step size. Using the rigid plant model, the control effort is computed for the shaped reference. Hence, given a saturation level of the control effort, the right input shaper that does not produce the shaped reference that violates the saturation level can be selected. The step size of the baseline reference can be varied, leading to switching among input shapers. The ZVD
^k
input shaper was used. The proposed technique applied favorably both in simulation and in experiment.