# Constrained Control of Nonlinear Engineering Systems in The Presence of The Delay

### Aberdeen UniversitySchool of Engineering

Applications accepted all year round Self-Funded PhD Students Only

The real world is inherently nonlinear, and particularly in mechanical systems this nonlinearity arises 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]. Such nonlinearities frequently cause undesirable behaviour in engineering structures, for example instabilities, limit cycles, coexistence of desired and undesired attractors or even chaos. In recent decades advances in nonlinear dynamics have developed a great potential, enabling a deeper understanding and analysis of complex systems.

Once the possible system responses are known, it is often desirable to maintain a specific behaviour avoiding the unwanted ones by apply adequate control methods through actuators. Actuators, such as electrical motors, hydraulic or pneumatic valves, do not typically have instantaneous responses and their dynamics usually involve one or two limitations: (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 cannot be ignored as they would make the control systems unsuccessful, inefficient and occasionally unstable.

Candidates should have (or expect to achieve) the UK honours degree at 2.1 or above (or equivalent) in Mechanical/Electrical/Applied Mathematics/Physics or closely related discipline. It is essential that the applicant has a Good understanding of “linear system dynamics and control” and basic knowledge of “nonlinear systems” along with proficiency in simulating system dynamics using MATLAB or Python and the Ability to design and simulate some of well-known Nonlinear and Chaos Control methods such as sliding mode, Time-delayed Feedback etc.

Knowledge of:
Engineering Mathematics especially ODEs.
Dynamics (Lumped mass modelling and analysis)
Programming in MATLAB or Python to solve ODEs and piece-wise linear systems.

APPLICATION PROCEDURE:

• 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

Informal inquiries can be made to Dr V Vaziri (), with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ()

It is possible to undertake this project by distance learning. Interested parties should contact Dr Vaziri to discuss this.

## Funding Notes

This project is advertised in relation to the research areas of the discipline of Theoretical and Applied Mechanics. The successful applicant will be expected to provide the funding for Tuition fees, living expenses and maintenance. Additional research costs of £1,000 per annum may be required to modify small-scale experimental rigs. Details of the cost of study can be found by visiting View Website. THERE IS NO FUNDING ATTACHED TO THIS PROJECT

## References

[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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