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Input predictive shaping for vibration control of flexible systems

This paper presents the foundation of a new class of input shapers, designed using a predictive approach. The method is used to control the transient and residual vibrations in flexible nonlinear systems with time-varying parameters. The motivation is the development of simple algorithms and architectures for controlling the motion in flexible nonlinear systems with minimal modeling effort. The approach trains an artificial neural network to obtain closed-form expressions used for calculating, in real time, the amplitudes and the time locations of the impulses required by a common input — shaping technique. In this work we use this idea to design a command shaper for controlling the motion of the simplest flexible nonlinear system, an overhead crane with a suspended payload. We validate the approach using simulations and experiments. The benefits of such a control system will, in the end, enable using this method for controlling the motion of complex nonlinear systems, resulting in almost zero vibrations.