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  Novel constrained control schemes for nonlinear systems

   School of Engineering

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

About the Project

The real world is inherently nonlinear. Particularly in mechanical systems, these nonlinearities arise from one or more of the following reasons: geometry of the system, materials applied interactions between parts of the system and nonlinear elements such as nonlinear stiffness damping and friction [1]. Moreover, such nonlinearities frequently cause undesirable behaviour in engineering structures, for example, instabilities, limit cycles, the coexistence of desired and undesired attractors or even chaos. Nevertheless, recent advances in nonlinear dynamics have developed a great potential, enabling a deeper understanding and analysis of complex systems.

Well-performing control schemes are usually employed to ensure the system maintains desired behaviour and steers away undesirable dynamics. These schemes are required synergistic interconnection of actuators and sensors. Actuators, such as electrical motors, hydraulic or pneumatic valves, do not typically have instantaneous responses, and their dynamics usually exhibit (i) delay and (ii) maximum/minimum value (constrained control effort) [2-3]. It was shown in [4] that the effect of simultaneous existence of both limitations could not be ignored as they would make the control unsuccessful, inefficient, and occasionally drive the controlled system to instability. Despite several linear, nonlinear and chaos control methods introduced theoretically in the last few decades, significant work is needed to develop control schemes that accommodate delays and/or actuator constraints. Therefore this project aims at advancing control schemes for time-delayed nonlinear systems with actuator constraints. As a result, the key objectives of this project are:

•        Nonlinear dynamics analysis and parametric study of selected systems in open-loop.

•        Development of new, high-performance control scheme[s] to minimise / eliminate performance limitations due to delay and control effort constraints.

•        Numerical investigation and experimental validation on the efficiency of the designed control scheme[s].

Successful candidates will join the interdisciplinary Centre for Applied Dynamic Research (CADR) & 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.

Selection will be made on academic merit. The successful candidate should have (or expect to achieve) a minimum of a UK Honours degree at 2.1 or above (or equivalent) in Electrical / Mechanical / Mechatronics Engineering, Applied Physics / Mathematics can apply. Candidates with a solid 2-1 degree in these disciplines will also be considered if they are able to show 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 V Vaziri ([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] Slotine, J.J.E. and Li, W., 1991. Applied nonlinear control (Vol. 199, No. 1). Englewood Cliffs, NJ: Prentice hall.
[2] Liu, Y., Wiercigroch, M., Ing, J. and Pavlovskaia, E., 2013. Intermittent control of coexisting attractors. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1993), p.20120428.
[3] Vaziri, V., Kapitaniak, M. and Wiercigroch, M., 2018. Suppression of drill-string stick–slip vibration by sliding mode control: Numerical and experimental studies. European Journal of Applied Mathematics, 29(5), pp.805-825.
[4] Vaziri, V., Oladunjoye, I., Kapitaniak, M., Aphale, S.S. & Wiercigroch, M., A Parametric Analysis of a Sliding-Mode Controller Designed to Alleviate Drill-String Stick-Slip Vibrations, Meccanica, Accepted, March 2019.

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