A new designed fixed output response method to generate a general closed-form waveform command shaper for controlling SDOF time-independent or time-dependent dynamic systems

In this work, a novel Designed Fixed Output Response (DFOR) method that can generate simple and compact forms of waveform command shaper parameters using a simple mathematical formulation is proposed. The approach is based on transforming the actual SDOF dynamic system, either time-independent or time-dependent, into a simpler time-independent SDOF dynamic system. This approach enables the selection of a desirable operational natural frequency, irrespective of the actual natural frequency of the system. This, in turn, enables appropriate control of the actual system through an existing standard command shaper. Furthermore, the newly designed waveform command shaper forces the actual SDOF dynamic system, whether time-independent or time-dependent, to follow the fixed output response of the transformed SDOF dynamic system. The efficiency of the proposed DFOR method and the performance and robustness of the generated new waveform command shaper, with its closed form parameters, was validated numerically and tested experimentally on both time-independent and time-dependent overhead crane systems. The results show the simplicity and accuracy of the proposed approach.