Nonlinear Dynamics and Control

Irene de Cesare, Mark Blyth, and Lucia Marucci (Bristol), Krasimira Tsaneva-Atanasova (Exeter)

Mathematical modelling is currently the most popular approach to infer the key dynamical features underpinning the behaviour of biological systems. The major caveat with this approach is that mathematical modelling of biological systems is generally extremely challenging due to the wide range of complex, intrinsically nonlinear, phenomena that interact on different time and spatial scales to govern their behaviour. As such, dynamic features considered as being responsible for a system’s behaviour often critically depend on modelling assumptions and parameters.

This project explores the use of advanced, control-based experimental testing techniques to study the dynamic behaviour of natural and synthetic biochemical systems and to directly map out from the experiment their key nonlinear dynamic characteristics, including bifurcations and multi-stability regions. Irene’s PhD project further develops the control methods required to apply those techniques to living mammalian stem cells while Mark’s PhD project further develops the method’s algorithms to apply them to living neurons.

Oliver Frolovs, David Barton, and Simon Neild (Bristol)

Rotating machines are subject to a wide variety of nonlinear forces coming, for instance, from friction between its components, large-amplitude vibrations, and interactions (impact, rubbing) between its static and rotating parts. This project experimentally investigates the complex (nonlinear) dynamics resulting from impacts between the rotor and stator. The objective is to develop models that can predict the circumstances for which the rotor becomes unstable and starts to exhibit forward and backward whirl motions.

Ludovic Renson

Conventional testing methods used to characterise the dynamics behaviour of nonlinear systems have many limitations which significantly affect the repeatability of the tests and the quality and overall usefulness of the collected experimental data. In this project, supported by a Fellowship from the Royal Academy of Engineering, I develop new, control-based testing methodologies that overcome the limitations of existing experimental testing approaches. My work in this area includes the development of new continuation algorithms, system identification, surrogate modelling, and control design. All the methods developed are experimentally demonstrated on a range of nonlinear mechanical structures.

Arabella Reece, Advaith Sastry

Hardware-in-the-loop (HIL) is an increasingly popular testing approach where the tested specimen (for instance, a landing gear) interacts with a numerical model of the rest of the system (the aircraft) via sensors and actuators. The fundamental idea of this approach is to test the specimen in conditions that are as close as possible to the conditions experienced in the assembled system. In their projects, Arabella and Advaith investigate the performance of HIL tests in the presence of nonlinearity.

Ka Yung, Aditya Tambe; Alexandre Mauroy (Namur)

In his project, Ka investigates the use of the Koopman operator and model predictive control to modify the dynamic behaviour of nonlinear mechanical structures. Aditya’s project investigates the use of the Koopman operator theory to identify nonlinear vibration modes from experimental data.

Amir Bagheri

Numerical continuation is a popular method to investigate the dynamics of nonlinear systems. At its core, continuation solves a zero problem to find the established response of the system, and then traces out the evolution of this response as parameters such as excitation amplitude, frequency, stiffness, or damping coefficients are varied. While continuation is general and systematic, its application to complex systems such as those met in industry is generally not possible due to excessive computational cost. Amir’s project looks at the development of new model reduction techniques that will make continuation applicable to large-scale systems. A particular facet of Amir’s work is to look at parameter-dependent reduced order models.

Syed Ahamed and Loic Salles

Aeronautic structures are increasingly lighter and more flexible, and hence nonlinear. Syed’s project looks at the modelling of a highly flexible structures featuring geometric nonlinearities. The modelling approach taken starts with a physics-based model to describe the linear equations of the system. This baseline model is then augmented using data-driven (machine learnt) models to capture the elastic coupling between the in-plane and out-of-plane vibrations introduced by the geometric nonlinearities, and to capture the aerodynamic damping introduced by the structure’s flapping motion. 

Kyoung Y. Lee and David Barton (Bristol)

Self-excited oscillations can be found in a wide range of engineering systems and often lead to unwanted vibration conditions that are potentially disastrous. The development of mathematical models that can capture such behaviours is challenging as self-excited oscillations often arise from complex interactions and energy transfers between different physical media such as fluid and structure. The objective of this project is to use a physics-based model that captures the fundamental phenomenological aspects of self-excited oscillations and augment it with a data-driven (i.e., machine-learnt) model to enhance its accuracy. This “hybrid” model is tested on several systems featuring self-excited oscillations, including an aerofoil undergoing limit cycle oscillations.

Shreya Basu; Martin Garrad, Helmut Hauser (Bristol); Lucas Wilkins, Beth Mortimer, Fritz Vollrath (Oxford)

Experimental observations suggest that a spider web is more than a simple trap and serves as a sophisticated signal processing device that helps the spider locate and categorise events in the web based on vibration patterns. Taking a mechanical perspective, this project investigates the fundamental principles underpinning the exploitation of structures as signal processing devices. Those principles are then exploited to design new sensors.