Learning input shaping technique for non-LTI systems

It is well known that a conventional input shaping technique is not very effective in suppressing residual vibrations for non-LTI systems, such as substantially nonlinear or time-varying systems. In an effort to increase the effectiveness for such systems, this paper presents a learning input shaping technique (LIST), which iteratively updates the parameters of the IST from the previous trials. Simulations are presented for 4 different cases: 1) when the natural frequency or damping of a system does not estimated well; 2) when a system has time varying vibration; 3) when a system has nonlinear flexibility; and 4) when a closed loop system includes the saturation limit in the loop. The experiments are made by using a 6-DOF industrial robot to evaluate the method. Results of both the simulations and experiments show that the residual vibrations become considerably smaller as iteration goes on, thereby demonstrating the effectiveness of the LIST.