A Novel Rank-order-centroid Based Reduction of Self-balanced-bicycle-robot Controller Using Grey-wolf Optimizer

In this contribution, order reduction of self-balanced-bicycle-robot (SBBR) controller is proposed by incorporating rank-order-centroid (ROC) based method utilizing grey-wolf-optimizer. The higher-order (HO) SBBR controller system is approximated by minimizing the errors between time-moments (TMs) and Markov-parameters (MPs) of HO SBBR system and desired approximated-model. The minimization of errors are accomplished by framing the weighted objective function utilizing TMs and MPs. The weights are associated with the weighted objective function. These weights are determined by systematic procedure of ROC based method. The main orientation of this proposal is to ascertain the associated weights in a systematic manner exploiting ROC method by providing the appropriate importance to effect-on-steady-state response and effect-on-transient response for SBBR controller based robotic application. The minimization of weighted objective function is done for the determination of unknown coefficients of approximant with the help of grey-wolf-optimizer. The optimization is done by employing matching of first TMs of the HO system and approximated-model ensuring the steady-state-matching. In this approximation, the stability of desired approximant is also ensured with the help of Hurwitz stability criterion. The obtained approximant is compared with already available controller models for SBBR in the literature. The step and impulse along with error and Bode responses are plotted to show the efficacy and productiveness of proposed method. The time-domain-analysis and performance-error-criterion-analysis are also provided in the support of proposed methodology.