Stabilization and tracking control of underactuated ball and beam system using metaheuristic optimization based TID-F and PIDD²–PI control schemes

• Farhan Zafar,

  Roles Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Writing – original draft

  Affiliation Department of Electrical and Computer Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad (IIUI), Islamabad, Pakistan

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• Suheel Abdullah Malik,

  Roles Conceptualization, Project administration, Supervision, Validation, Writing – review & editing

  Affiliation Department of Electrical and Computer Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad (IIUI), Islamabad, Pakistan

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• Tayyab Ali,

  Roles Data curation, Investigation, Methodology, Resources, Software, Writing – review & editing

  Affiliation Department of Electrical and Computer Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad (IIUI), Islamabad, Pakistan

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• Amil Daraz ,

  Roles Conceptualization, Methodology, Validation, Writing – original draft

  * E-mail: amil.daraz@nbt.edu.cn

  Affiliation School of Information Science and Engineering, NingboTech University, Ningbo, China

  https://orcid.org/0009-0002-3425-4618

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• Abdul Rahman Afzal,

  Roles Conceptualization, Investigation, Resources, Software, Validation, Writing – review & editing

  Affiliation Department of Industrial Engineering, University of Business and Technology (UBT) University, Jeddah, Saudi Arabia

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• Farkhunda Bhatti,

  Roles Data curation, Investigation, Validation, Writing – review & editing

  Affiliation Department of Electronic Engineering, Mehran University of engineering & Technology Jamshoro, Jamshoro, Pakistan

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• Irfan Ahmed Khan

  Roles Data curation, Formal analysis, Resources, Visualization

  Affiliation Department of Electrical Engineering, Faculty of Engineering, Universiti Malaya, Kuala Lumpur, Malaysia

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