In the industry, Multi-objectives

Biogeography-based optimization (BBO) is one of the recently developed population-based algorithms which has shown impressive performance over evolutionary algorithms. BBO is based on the study of geographical distribution of biological organisms over space and time. In this paper, non-dominated sorting BBO (NSBBO) is proposed to tune proportionalderivative control system for the six degree arm manipulator PUMA 560. The BBO algorithm is based on mathematical models of biogeography, which describe the migration of species between habitats. To tune six PD controller of a PUMA 560 arm manipulator, we need to minimize simultaneously six position errors so there exists a multi-objective optimization problem. The NSBBO algorithm searches for the controller gains, so that integral absolute error in joint space is minimized. Results obtained show the effectiveness of the algorithm to optimize the controlling parameters and minimizing the error.

Background: In control system design there are often a number of design objectives to be considered. The objectives are sometimes connecting and no design exists which can be considered best with respect to all objectives. Hence, there is an inevitable tradeoff between design objectives, for example, between and output performance objective and stability robustness. These considerations have led to the study of multi objective optimization methods for control systems. Methods: In this study a multi-objective Non-dominated Sorting Genetic Algorithms NSGA-II is used to tuning of Proportional Derivative (PD) controller of a six freedom arm manipulator PUMA560. The NSGAII algorithm searches for the controller PD gains so that the six Integral Absolute Errors (IAE) in joint space are minimized. Results: Simulation numerical results of multivariable PD control and convergence of the NSGA-II are presented and discussed. Conclusion: The proposed optimization method based on NSGA-II is capable of generating adequate gains for PUMA560 system with minimum errors.

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