Advancing Fractional-order control for engineering applications

   School of Engineering

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  Dr S S Aphale, Dr Vahid Vaziri  Applications accepted all year round  Self-Funded PhD Students Only

About the Project

Fractional Calculus is an exciting area with the potential to make key inroads into the wider area of system modelling and control. It lies at the cusp between linear and nonlinear system theory [1]. As a result, several recent applications of Fractional Calculus have been reported to improve the modelling and control of a wide range of systems. Fractional Calculus can be potentially applied to simplify the modelling of nonlinear phenomena, such as hysteresis and creep. Additionally, the almost infinite freedom fractional-order controllers provide, hitherto unexploited, can provide significant performance benefits to a wide range of systems. This thesis will focus on expanding the boundaries of application for Fractional Calculus. Our recent work has identified several research gaps as well as avenues to push knowledge boundaries [2, 3]. After an initial review of the state-of-the-art and aligning the research focus on individual student/s’s interests, this research can focus on system modelling (mechanical / electrical engineering, applied physics, bioengineering etc) or system control (new control theory / focussed control designs for applications such as precision positioning systems, drill-strings, robots etc), development, implementation, optimization, and validation.

Successful candidates will join the interdisciplinary Artificial Intelligence, Robotics and Mechatronic Systems Group (ARMS) at the School of Engineering, University of Aberdeen and will have access to area experts as well as a well-furnished laboratory for all their experimental studies, should they choose to explore that direction. They will also be involved (as opportunities arise) in short-term live industry projects as paid research assistants, allowing them to broaden their industry-relevant skillset. A limited number of paid teaching assistantship positions can also be availed (subject to budget restrictions and course requirements). Students will have the opportunity to collaborate with one or more of the authors of [1].

Selection will be made on the basis of academic merit. The successful candidate should have, or expect to obtain, a UK Honours degree at 2.1 or above (or equivalent) in Electrical / Mechanical / Mechatronics Engineering, Applied Physics / Mathematics along with evidence of adequate competence in the underlying concepts.

Familiarity with any two of the following subject areas is required:

i.                    Mathematical modelling of systems

ii.                  System kinematics and dynamics

iii.                Linear Algebra and Matrix Theory

iv.                Linear Control Systems

v.                  Nonlinear Control Systems

vi.                Nonlinear dynamics

vii.               Differential Calculus

Candidates must be competent with MATLAB and SIMULINK and / or similar mathematical software.


Formal applications can be completed online:

• Apply for Degree of Doctor of Philosophy in Engineering

• State name of the lead supervisor as the Name of Proposed Supervisor

• State ‘Self-funded’ as Intended Source of Funding

• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)

• Detailed CV, Personal Statement/Motivation Letter and Intended source of funding

Informal inquiries can be made to Dr S Aphale ([Email Address Removed]) with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ([Email Address Removed])

Engineering (12) Mathematics (25)

Funding Notes

This PhD project has no funding attached and is therefore available to students (UK/International) who are able to seek their own funding or sponsorship. Supervisors will not be able to respond to requests to source funding. Details of the cost of study can be found by visiting


[1] C. A. Monje, YQ Chen, B. M. Vinagre, D. Xue and V. Feliu, Fractional-order systems and controls: fundamentals and applications, Springer, 2010.
[2] L. Li, Z. Chen, S. S. Aphale and LM Zhu, Fractional Repetitive Control of Nanopositioning Stages for High-Speed Scanning Using Low-Pass FIR Variable Fractional Delay Filter, IEEE/ASME Transactions on Mechatronics, vol. 25, no. 2, pp. 547 – 557, 2020
[3] A. San-Millan, V. Feliu-Batlle and S. S. Aphale, Fractional order implementation of Integral Resonant Control – A nanopositioning application, ISA Transactions, vol. 82, pp. 223-231, 2018

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