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

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  • Miguel G. Villarreal-Cervantes

    (Instituto Politécnico Nacional, CIDETEC)

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.

Suggested Citation

  • Miguel G. Villarreal-Cervantes, 2017. "Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 628-657, May.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:2:d:10.1007_s10957-016-1053-4
    DOI: 10.1007/s10957-016-1053-4
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    References listed on IDEAS

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    1. Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
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    Cited by:

    1. Josué Nathán Martínez-Castelán & Miguel Gabriel Villarreal-Cervantes, 2021. "Integrated Structure-Control Design of a Bipedal Robot Based on Passive Dynamic Walking," Mathematics, MDPI, vol. 9(13), pages 1-26, June.

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