Spillover-free control of flexible beams using piezoelectric sensors and actuators (S3.5-ELE-Selivanov)

The need for precise control of flexible structures is more critical than ever. Whether it’s reducing the weight of next-generation aircraft, ensuring the stability of towering skyscrapers, or improving the energy efficiency of mechanical systems, advanced control methods are at the heart of these challenges. Effective control mitigates vibrations, boosts performance, enhances energy efficiency, ensures safety, enables adaptability, and cuts maintenance costs.

This PhD project aims to develop innovative control strategies for flexible structures modelled by partial differential equations (PDEs). Our goal is to design finite-dimensional controllers that are not only straightforward to implement but also robust against real-world imperfections, including system disturbances, measurement noise, and communication delays. The challenge lies in ensuring the desired behaviour of an infinite-dimensional system with limited computing, sensing, and actuating resources. To tackle these theoretical and practical challenges, we will employ advanced techniques such as modal decomposition, Lyapunov-based analysis, linear matrix inequalities, and H-infinity methods.

Why This Research Matters

• Aerospace Engineering: Advancing control methods for lightweight aircraft wings can significantly reduce overall aircraft weight, contributing to the development of more sustainable and efficient aviation technologies.
• Civil Engineering: Improving traditional tuned mass dampers with piezoelectric actuators can enhance the stability of skyscrapers, thereby increasing safety and occupant comfort in high-rise buildings.
• Mechanical Engineering: Designing adaptable and energy-efficient systems that minimise vibrations will not only extend the operational lifespan of critical components but also enhance the overall performance and reliability of mechanical systems.

Project Objectives

1. System identification. We will start by constructing a physical model of a flexible beam, using the Euler-Bernoulli beam equation and incorporating various friction models. You will conduct experiments with a physical rig to identify essential system parameters, friction characteristics, and actuator/sensor models. This process will not only lay the groundwork for developing and refining new control strategies but also help you develop a deep understanding of the model’s accuracy and behaviour.
2. Observer design. Using the identified model, you will develop a finite-dimensional state observer incorporating piezoelectric sensors. This will involve applying modal decomposition and H-infinity filter design methods to create an effective observer. The performance of the observer will be evaluated through both numerical simulations and experimental validation.
3. Control system design. A key challenge of this project is to develop a robust output-feedback controller. We will use modal decomposition and H-infinity control theory, complemented by Lyapunov-based analysis, to co-design the controller and observer. The goal is to ensure that the developed methodology is practical and accessible, leading to controllers that are both implementable and reliable for practising engineers.
4. Validation and Refinement. The theoretical insights gained will be validated through comprehensive numerical simulations and physical experiments on the flexible beam. These tests will not only refine your control strategies but also provide valuable feedback for further theoretical advancements.

This project provides a unique opportunity to advance your expertise in system identification and control system design. You will tackle a problem that is not only highly relevant to industry but also rich in both theoretical and practical challenges. By combining rigorous analysis with hands-on experimentation, you will be well-positioned to make a substantial impact in the field of engineering.

If you’re enthusiastic about developing innovative control strategies for flexible structures, we encourage you to apply. For further details or if you have any questions, please reach out to the project supervisor below.

Further Reading

1. A. Selivanov and E. Fridman, “Improved residual mode separation for finite-dimensional control of PDEs: application to the Euler-Bernoulli beam“, arXiv:2308.05551, 2023.
2. A. Selivanov, P. Wang, and E. Fridman, “Guaranteed Cost Boundary Control of the Semilinear Heat Equation”, IEEE Control System Letters, vol. 8, pp. 898–903, 2024.
3. A. Selivanov and E. Fridman, “Finite-Dimensional Boundary Control of a Wave Equation With Viscous Friction and Boundary Measurements”, IEEE Transactions on Automatic Control, 2024.

Candidate Requirements

Strong mathematical background in calculus, linear algebra, and ODEs is essential. Experience in control theory is desirable but not mandatory – a mathematically literate candidate can quickly fill possible gaps. Most importantly, we are looking for candidates passionate about maths and fundamental research in general.

Learning Environment

The University of Sheffield is a Russell Group university. It is located in the centre of the UK, right next to the Peak District National Park. The standard duration of a PhD in the UK is 3.5 years. To learn more about student life in Sheffield, visit https://www.sheffield.ac.uk/sheffield-guide.

Application Process

Informal enquiries are encouraged and should be addressed to Dr Anton Selivanov below.

Applicants are required to hold either an undergraduate honours degree (2:1 or 1st) or MSc (merit or distinction) in mathematics or engineering. If the degree is not from an English-speaking country, the applicant needs an overall IELTS grade of 6.5 with a minimum of 6.0 in each component (or equivalent).

Please refer to the EPSRC DLA webpage for detailed information about the EPSRC DLA and how to apply.. On the DLA application, make sure that you enter the code from the project title. Do not apply for the standard School PhD.

The award will fund the full (UK or Overseas) tuition fee and UKRI stipend (currently £19,237 per annum) for 3.5 years, as well as a research grant of £4,500 to support costs associated with the project.