Oscillation damping of nonlinear control systems based on the phase trajectory length concept: An experimental case study on a cable-driven parallel robot

In this paper, via shortening the phase trajectory length concept, a systematic approach for oscillation damping of nonlinear systems is introduced and the proposed procedure is applied in order to control an under-actuated cable-driven parallel robot both in simulation and experiment. In this regard, at first, the phase trajectory length concept in the state space of a multi-input multi-output nonlinear system is defined and then its lower and upper bounds are computed. Then, the concept of oscillation number index is defined and sufficient conditions for designing an anti-oscillation control system are presented. Moreover, the effect of including the time as a weight in the computation of the phase trajectory length in order to enforce the system response speed beside the oscillation damping is investigated. Finally, based on the governing equations of the robot under study, utilizing the genetic algorithm, the computed torque controller gains are explored in order to minimize the oscillation number index to alleviate the oscillation of the system. In this regard, the performance of the aforementioned index for alleviating the oscillation of the robot is compared with the integral absolute error index, experimentally. Moreover, the Fourier analysis of the obtained results is presented.