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Structural Nonlinear Dynamics and Diagnosis pp 145–165Cite as

On Optimal Control of a Nonlinear Robotic Mechanism Using the Saturation Phenomenon

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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 168))

Abstract

In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified for a wide range of parameters. Controlling of the chaotic behaviour of the system were implemented using two control techniques, the nonlinear saturation control (NSC) and the optimal linear feedback control (OLFC). The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The NSC is based in the second order differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The OLFC involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.

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Authors and Affiliations

  1. Technological Center of Alegrete, UNIPAMPA—Federal University of Pampa, Alegrete, RS, Brazil

    Jorge Luis Palacios Felix

  2. Mechanical Aeronautics Division, ITA—Aeronautics Technological Institute—São José dos Campos, SP, Brazil

    José Manoel Balthazar

  3. Faculty of Mechanical Engineering, UNESP—São Paulo State University, Bauru, SP, Brazil

    José Manoel Balthazar

  4. Department of Mathematics, UTFPR—Federal Technological University of Paraná, Ponta Grossa, Brazil

    Ângelo Marcelo Tusset & Vinícius Piccirillo

  5. Department of Control and Automation Engineering, UNESP—São Paulo State University, Sorocaba, Brazil

    Atila Madureira Bueno

  6. CECS—Center of Engineering, Modelling and Applied Social Science, UFABC—Federal University of ABC, Santo André, Brazil

    Reyolando Manoel Lopes Rebello da Fonseca Brasil

Authors
  1. Jorge Luis Palacios Felix
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  2. José Manoel Balthazar
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  3. Ângelo Marcelo Tusset
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  4. Vinícius Piccirillo
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  5. Atila Madureira Bueno
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  6. Reyolando Manoel Lopes Rebello da Fonseca Brasil
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Corresponding author

Correspondence to José Manoel Balthazar .

Editor information

Editors and Affiliations

  1. Laboratory of Mechanics, Hassan II-Casablanca University, Casablanca, Morocco

    Mohamed Belhaq

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Felix, J.L.P., Balthazar, J.M., Tusset, Â.M., Piccirillo, V., Bueno, A.M., da Fonseca Brasil, R.M.L.R. (2015). On Optimal Control of a Nonlinear Robotic Mechanism Using the Saturation Phenomenon. In: Belhaq, M. (eds) Structural Nonlinear Dynamics and Diagnosis. Springer Proceedings in Physics, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-319-19851-4_8

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