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In this study, a modified fractional-order proportional–integral–derivative (PID) controller is proposed for controlling a class of nonlinear robotic manipulator. The proposed control structure is designed by cascading a nonlinear function of state and error with linear fractionalorder PID controller. The introduction of nonlinearity provides the self-tuning control capability, whereas inclusion of fractional-order operator increases the flexibility by providing extra degrees of freedom to the controller. Nonlinear PID, fractional-order PID and conventional PID controllers are also designed for comparative analysis. The parameters of all the designed controllers are optimized using multi-objective modified black hole optimization algorithm. Further, robustness of the proposed controller is examined by performing intensive simulation studies in the system. Finally, the extensive studies and hardware-in-theloop simulation for experimental validation clearly suggest that the proposed controller performs significantly better and is more robust as compared to conventional PID, FOPID and NPID controllers for all the case studies.

RETRACTED ARTICLE: Optimal non-integer PID controller for a class of nonlinear systems: multi-objective modified black hole optimization algorithm