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Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems

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Abstract

The structure-control design approach of mechatronic systems requires a different design formulation where the mechanical structure and control system are simultaneously designed. Optimization problems are commonly stated to confront the structure-control design formulation. Nevertheless, these problems are often very complex with a highly nonlinear dependence between the design variables and performance functions. This fact has made the use of evolutionary algorithms, a feasible alternative to solve the highly nonlinear optimization problem; the method to find the best solution is an open issue in the structure-control design approach. Hence, this paper presents a mechanism to exhaustively exploit the solutions in the differential evolution (DE) algorithm in order to find more non-dominated solutions with uniformly distributed Pareto front and better trade-offs in the structure-control design framework. The proposed approach adopts an external population to retain the non-dominated solutions found during the evolutionary process and includes a mechanism to mutate the individuals in their corresponding external population region. As a study case, the structure-control design of a serial-parallel manipulator with its control system is stated as a dynamic optimization problem and is solved by using the proposed approach. A comparative analysis shows that the multi-objective exhaustive exploitation differential evolution obtained a superior performance in the structure-control design framework than a DE algorithm which did not consider the proposal. Hence, the resulting designs provide better trade-offs between the structure-control performance functions.

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Acknowledgements

The author acknowledges support from the COFAA of the Instituto Politécnico Nacional and from SEP-CONACyT, via the project numbers 20160826 and 182298, respectively. Furthermore, I would like to express my appreciation for the help provided in the grammatical expressions by English professor Lawrence Whitehill.

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  1. Postgraduate Department, Instituto Politécnico Nacional, CIDETEC, Mexico City, Mexico

    Miguel G. Villarreal-Cervantes

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  1. Miguel G. Villarreal-Cervantes
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Correspondence to Miguel G. Villarreal-Cervantes.

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Communicated by Mauro Pontani.

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Villarreal-Cervantes, M.G. Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems. J Optim Theory Appl 173, 628–657 (2017). https://doi.org/10.1007/s10957-016-1053-4

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