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Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm

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Abstract

This paper introduces a new version of the particle swarm optimization (PSO) method. Two basic modifications for the conventional PSO algorithm are proposed to improve the performance of the algorithm. The first modification inserts adaptive accelerator parameters into the original velocity update formula of the PSO which speeds up the convergence rate of the algorithm. The ability of the algorithm in escaping from local optima is improved using the second modification. In this case, some particles of the swarm, which are named the superseding particles, are selected to be mutated with some probability. The proposed modified PSO (MPSO) is simple to be implemented, fast and reliable. To validate the efficiency and applicability of the MPSO, it is applied for designing optimal fractional-order PID (FOPID) controllers for some benchmark transfer functions. Then, the introduced MPSO is applied for tuning the parameters of FOPID controllers for a five bar linkage robot. Sensitivity analysis over the fractional order of the PID controller is also provided. Numerical simulations reveal that the MPSO can optimally tune the parameters of FOPID controllers.

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Authors and Affiliations

  1. Faculty of Electrical and Computer Engineering, Urmia University of Technology, Urmia, Iran

    Mohammad Pourmahmood Aghababa

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  1. Mohammad Pourmahmood Aghababa
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Correspondence to Mohammad Pourmahmood Aghababa.

Additional information

Communicated by V. Loia.

Appendix: Pseudocode for MPSO algorithm

Appendix: Pseudocode for MPSO algorithm

Begin;

  1. 1.

    Set initial values such as swarm size, random particles, random velocity vector, maximum number of iterations, etc;

  2. 2.

    For each particle calculate the objective value;

  3. 3.

    Update the global and local best particles and their corresponding objective values;

  4. 4.

    Find the new positions of each particle using Eqs. (9) and (10);

  5. 5.

    Replace up to \(\gamma \, \% \) of the particles by superseding particles;

  6. 6.

    Check if termination condition is true then stop; otherwise, go to step 2;

End.

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Aghababa, M.P. Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm. Soft Comput 20, 4055–4067 (2016). https://doi.org/10.1007/s00500-015-1741-2

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  • DOI: https://doi.org/10.1007/s00500-015-1741-2

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