Backstepping-Based Exponential Stabilization of Timoshenko Beam with Prescribed Decay Rate

This is an open access article under the CC BY-NC-ND license.In this paper, we present a rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE backstepping. We introduce a transformation to map the Timoshenko beam states into a (2+2) × (2+2) hyperbolic PIDE-ODE system. Then backstepping is applied to obtain a control law guaranteeing closed-loop stability of the origin in the H1 sense. Arbitrarily rapid stabilization can be achieved by adjusting control parameters. Finally, a numerical simulation shows that the proposed controller can rapidly stabilize the Timoshenko beam. This result extends a previous work which considered a slender Timoshenko beam with Kelvin-Voigt damping, allowing destabilizing boundary conditions at the uncontrolled boundary and attaining an arbitrarily rapid convergence rate

Mechatronics of systems with undetermined configurations

This work is submitted for the award of a PhD by published works. It deals with some of the efforts of the author over the last ten years in the field of Mechatronics. Mechatronics is a new area invented by the Japanese in the late 1970's, it consists of a synthesis of computers and electronics to improve mechanical systems. To control any mechanical event three fundamental features must be brought together: the sensors used to observe the process, the control software, including the control algorithm used and thirdly the actuator that provides the stimulus to achieve the end result. Simulation, which plays such an important part in the Mechatronics process, is used in both in continuous and discrete forms. The author has spent some considerable time developing skills in all these areas. The author was certainly the first at Middlesex to appreciate the new developments in Mechatronics and their significance for manufacturing. The author was one of the first mechanical engineers to recognise the significance of the new transputer chip. This was applied to the LQG optimal control of a cinefilm copying process. A 300% improvement in operating speed was achieved, together with tension control. To make more efficient use of robots they have to be made both faster and cheaper. The author found extremely low natural frequencies of vibration, ranging from 3 to 25 Hz. This limits the speed of response of existing robots. The vibration data was some of the earliest available in this field, certainly in the UK. Several schemes have been devised to control the flexible robot and maintain the required precision. Actuator technology is one area where mechatronic systems have been the subject of intense development. At Middlesex we have improved on the Aexator pneumatic muscle actuator, enabling it to be used with a precision of about 2 mm. New control challenges have been undertaken now in the field of machine tool chatter and the prevention of slip. A variety of novel and traditional control algorithms have been investigated in order to find out the best approach to solve this problem

Multiphysics modelling and experimental validation of microelectromechanical resonator dynamics

The modelling of microelectromechanical systems provides a very challenging task in microsystems engineering. This field of research is inherently multiphysics of nature, since different physical phenomena are tightly intertwined at microscale. Typically, up to four different physical domains are usually considered in the analysis of microsystems: mechanical, electrical, thermal and fluidic. For each of these separate domains, well-established modelling and analysis techniques are available. However, one of the main challenges in the field of microsystems engineering is to connect models for the behavior of the device in each of these domains to equivalent lumped or reduced-order models without making unacceptably inaccurate assumptions and simplifications and to couple these domains correctly and efficiently. Such a so-called multiphysics modelling framework is very important for simulation of microdevices, since fast and accurate computational prototyping may greatly shorten the design cycle and thus the time-to-market of new products. This research will focus on a specific class of microsystems: microelectromechanical resonators. MEMS resonators provide a promising alternative for quartz crystals in time reference oscillators, due to their small size and on-chip integrability. However, because of their small size, they have to be driven into nonlinear regimes in order to store enough energy for obtaining an acceptable signal-to-noise ratio in the oscillator. Since these resonators are to be used as a frequency reference in the oscillator circuits, their steady-state (nonlinear) dynamic vibration behaviour is of special interest. A heuristic modelling approach is investigated for two different MEMS resonators, a clamped-clamped beam resonator and a dog-bone resonator. For the clamped-clamped beam resonator, the simulations with the proposed model shows a good agreement with experimental results, but the model is limited in its predictive capabilities. For the dogbone resonator, the proposed heuristic modelling approach does not lead to a match between simulations and experiments. Shortcomings of the heuristic modelling approach serve as a motivation for a first-principles based approach. The main objective of this research is to derive a multiphysics modelling framework for MEMS resonators that is based on first-principles formulations. The framework is intended for fast and accurate simulation of the steady-state nonlinear dynamic behaviour of MEMS resonators. Moreover, the proposed approach is validated by means of experiments. Although the multiphysics modelling framework is proposed for MEMS resonators, it is not restricted to this application field within microsystems engineering. Other fields, such as (resonant) sensors, switches and variable capacitors, allow for a similar modelling approach. In the proposed framework, themechanical, electrical and thermal domains are included. Since the resonators considered are operated in vacuum, the fluidic domain (squeeze film damping) is not included. Starting from a first-principles description, founded on partial differential equations (PDEs), characteristic nonlinear effects from each of the included domains are incorporated. Both flexural and bulk resonators can be considered. Next, Galerkin discretization of the coupled PDEs takes place, to construct reduced-order models while retaining the nonlinear effects. The multiphysics model consists of the combined reduced-order models from the different domains. Designated numerical tools are used to solve for the steady-state nonlinear dynamic behaviour of the combined model. The proposed semi-analytical (i.e. analytical-numerical) multiphysics modeling framework is illustrated for a full case study of an electrostatically actuated single-crystal silicon clamped-clamped beam MEMS resonator. By means of the modelling framework, multiphysics models of varying complexity have been derived for this resonator, including effects like electrostatic actuation, fringing fields, shear deformation, rotary inertia, thermoelastic damping and nonlinear material behaviour. The first-principles based approach allows for addressing the relevance of individual effects in a straightforward way, such that the models can be used as a (pre-)design tool for dynamic response analysis. The method can be considered complementary to conventional finite element simulations. The multiphysics model for the clamped-clamped beam resonator is validated by means of experiments. A good match between the simulations and experiments is obtained, thereby giving confidence in the proposed modelling framework. Finally, next to themodelling approach for MEMS resonators, a technique for using these nonlinear resonators in an oscillator circuit setting is presented. This approach, called phase feedback, allows for operation of the resonator in its nonlinear regime. The closedloop technique enables control of both the frequency of oscillation and the output power of the signal. Additionally, optimal operation points for oscillator circuits incorporating a nonlinear resonator can be defined

From plain visualisation to vibration sensing: using a camera to control the flexibilities in the ITER remote handling equipment

Thermonuclear fusion is expected to play a key role in the energy market during the second half of this century, reaching 20% of the electricity generation by 2100. For many years, fusion scientists and engineers have been developing the various technologies required to build nuclear power stations allowing a sustained fusion reaction. To the maximum possible extent, maintenance operations in fusion reactors are performed manually by qualified workers in full accordance with the "as low as reasonably achievable" (ALARA) principle. However, the option of hands-on maintenance becomes impractical, difficult or simply impossible in many circumstances, such as high biological dose rates. In this case, maintenance tasks will be performed with remote handling (RH) techniques. The International Thermonuclear Experimental Reactor ITER, to be commissioned in southern France around 2025, will be the first fusion experiment producing more power from fusion than energy necessary to heat the plasma. Its main objective is “to demonstrate the scientific and technological feasibility of fusion power for peaceful purposes”. However ITER represents an unequalled challenge in terms of RH system design, since it will be much more demanding and complex than any other remote maintenance system previously designed. The introduction of man-in-the-loop capabilities in the robotic systems designed for ITER maintenance would provide useful assistance during inspection, i.e. by providing the operator the ability and flexibility to locate and examine unplanned targets, or during handling operations, i.e. by making peg-in-hole tasks easier. Unfortunately, most transmission technologies able to withstand the very specific and extreme environmental conditions existing inside a fusion reactor are based on gears, screws, cables and chains, which make the whole system very flexible and subject to vibrations. This effect is further increased as structural parts of the maintenance equipment are generally lightweight and slender structures due to the size and the arduous accessibility to the reactor. Several methodologies aiming at avoiding or limiting the effects of vibrations on RH system performance have been investigated over the past decade. These methods often rely on the use of vibration sensors such as accelerometers. However, reviewing market shows that there is no commercial off-the-shelf (COTS) accelerometer that meets the very specific requirements for vibration sensing in the ITER in-vessel RH equipment (resilience to high total integrated dose, high sensitivity). The customisation and qualification of existing products or investigation of new concepts might be considered. However, these options would inevitably involve high development costs. While an extensive amount of work has been published on the modelling and control of flexible manipulators in the 1980s and 1990s, the possibility to use vision devices to stabilise an oscillating robotic arm has only been considered very recently and this promising solution has not been discussed at length. In parallel, recent developments on machine vision systems in nuclear environment have been very encouraging. Although they do not deal directly with vibration sensing, they open up new prospects in the use of radiation tolerant cameras. This thesis aims to demonstrate that vibration control of remote maintenance equipment operating in harsh environments such as ITER can be achieved without considering any extra sensor besides the embarked rad-hardened cameras that will inevitably be used to provide real-time visual feedback to the operators. In other words it is proposed to consider the radiation-tolerant vision devices as full sensors providing quantitative data that can be processed by the control scheme and not only as plain video feedback providing qualitative information. The work conducted within the present thesis has confirmed that methods based on the tracking of visual features from an unknown environment are effective candidates for the real-time control of vibrations. Oscillations induced at the end effector are estimated by exploiting a simple physical model of the manipulator. Using a camera mounted in an eye-in-hand configuration, this model is adjusted using direct measurement of the tip oscillations with respect to the static environment. The primary contribution of this thesis consists of implementing a markerless tracker to determine the velocity of a tip-mounted camera in an untrimmed environment in order to stabilise an oscillating long-reach robotic arm. In particular, this method implies modifying an existing online interaction matrix estimator to make it self-adjustable and deriving a multimode dynamic model of a flexible rotating beam. An innovative vision-based method using sinusoidal regression to sense low-frequency oscillations is also proposed and tested. Finally, the problem of online estimation of the image capture delay for visual servoing applications with high dynamics is addressed and an original approach based on the concept of cross-correlation is presented and experimentally validated

Fluid flow induced by travelling waves in beam-like structures: modelling, simulation and experimental validation

The configuration of a beam submerged in liquid can offer many advantages in engineering applications by providing an ability to generate alternative propulsion systems. These are achieved via travelling waves that propagate through the beam and, interacting with the surrounding fluid, generate thrust. Numerous concepts and implementations have been proposed differing in general arrangements that lead to different structural and fluid characteristics. Understanding the characteristics and limitations of travelling waves on the beam can provide advantages toward more effective and efficient actuations. The aim of this thesis is to provide insight into the mechanisms that allow structural travelling waves induced through electromagnetic actuation to interact with the surrounding fluid. This study would contribute to the development of controllable devices capable of self-propulsion. In this thesis, the dynamic behaviours of a cantilever beam submerged in a fluid is approximated by simplifying fluid effects with hydrodynamic forces. Accordingly, the Galerkin-based model for fluid structure interaction can be derived and solved with a linear approximation method. This technique allows to investigate the vibration patterns of the beam under hydrodynamic loads that can be used to provide an assessment into factors affecting modal parameters and influencing the generation of travelling waves. Advanced experimental techniques using Laser Doppler Anemometry (LDA) in conjunction with numerical simulation of fluid-structure interaction (FSI) models are used to provide a thorough and systematic characterisation of the fluid-structure interactions that constitute the fundamental of the correlation between structural travelling waves and thrust generated by a beam submerged in a viscous fluid. The discussion is expanded to consider the potential use of an additional mechanical element in attempting to improve features that promote travelling waves and large beam displacements without necessarily inducing high input power in a contactless actuation system