Now showing 1 - 10 of 11
  • Publication
    A new approach to modal analysis of uniform chain systems
    (Elsevier, 2008-04-08) ;
    A new method is presented to determine the mode shapes and frequencies of uniform systems consisting of chains of masses and springs of arbitrary number with arbitrary boundary conditions. Instead of the classical eigenproblem approach, the system is analysed in terms of circulating waves and associated phase lags. The phasor conditions for the establishment of standing waves determine the vibration modes. The conditions fully specify their shapes and frequencies, and lead to simple, explicit expressions for the components of the modal vectors and the associated natural frequencies. In addition, the form of the phasor diagrams of the modes gives insight into the modal behaviour. The orthogonality of mode shapes also readily emerges. Examples are presented for different boundary conditions. Although not presented, it is possible to extend the approach to non-uniform lumped systems and to forced frequency responses.
    Scopus© Citations 8  1164
  • Publication
    Wave-based control of non-linear flexible mechanical systems
    The need to achieve rapid and accurate position control of a system end-point by an actuator working through a flexible system arises frequently, in cases from space structures to disk drive heads, from medical mechanisms to long-arm manipulators, from cranes to special robots. The system’s actuator must then attempt to reconcile two, potentially conflicting, demands: position control and active vibration damping. Somehow each must be achieved while respecting the other’s requirements. Wave-based control is a powerful solution with many advantages over previous techniques. The central idea is to consider the actuator motion as launching mechanical waves into the flexible system while simultaneously absorbing returning waves. This simple, intuitive idea leads to robust, generic, highly efficient, adaptable controllers, allowing rapid and almost vibrationless re-positioning of the remote load (tip mass). This gives a generic, high-performance solution to this important problem that does not depend on an accurate system model or near-ideal actuator behaviour. At first sight wave-based control assumes superposition and therefore linearity. This paper shows that wave-based control is also robust (or can easily be made robust) to non-linear behaviour associated with non-linear elasticity and with large-deflection effects.
      1447Scopus© Citations 30
  • Publication
    Wave-Based Analysis and Control of Lump-Modeled Flexible Robots
    (IEEE, 2007-04)
    Flexible robots are frequently represented by lumped models. In the mechanics of lumped systems, wave concepts have been avoided, for good reasons, generally. In the control of lumped flexible systems, however, wave concepts prove very fruitful. This paper provides a foundation for the wave-based control application by exploring the validity and nature of wave concepts in lumped robotic systems. A new wave-based model of uniform mass-spring systems is proposed and verified. The model is exact but not unique. Useful simplifications and approximations are also presented. The model leads to control strategies for flexible robotic systems that are simple, powerful, robust, and generic. The wave approach also provides a new analysis tool and conceptual framework for lumped dynamic systems.
      599Scopus© Citations 75
  • Publication
    An alternative TLM method for steady-state convection-diffusion
    (Wiley Blackwell (John Wiley & Sons), 2009-09-03) ;
    Recent papers have introduced a novel and efficient scheme, based on the transmission line modelling (TLM) method, for solving one-dimensional steady-state convection–diffusion problems. This paper introduces an alternative method. It presents results obtained using both techniques, which suggest that the new scheme outlined in this paper is the more accurate and efficient of the two. Copyright © 2009 John Wiley & Sons, Ltd.
      435
  • Publication
    Quantitative MRI analysis of brain volume changes due to controlled cortical impact
    More than 85% of reported brain traumas are classified clinically as “mild” using GCS; qualitative MRI findings are scarce and provide little correspondence to clinical symptoms. Our goal, therefore, was to establish in-vivo sequellae of traumatic brain injury following lower and higher levels of impact to the frontal lobe using quantitative MRI analysis and a mechanical model of penetrating impact injury. To investigate time-based morphological and physiological changes of living tissue requires a surrogate for the human central nervous system. The present model for TBI was a systematically varied and controlled cortical impact on deeply-anaesthetized Sprague Dawley rats designed to mimic different injury severities. Whole-brain MRI scans were performed on each rat prior to either a lower or a higher level of impact and then at hourly intervals for five hours post-impact. Both brain volume and specific anatomical structures were segmented from MR images for inter-subject comparisons post-registration. Animals subjected to lower and higher impact levels exhibited elevated intracranial pressure (ICP) in the low compensatory reserve (i.e., nearly exhausted) and terminal disturbance (i.e., exhausted) ranges, respectively. There was a statistically-significant drop in cerebrospinal fluid of 35% in the lower impacts and 65% in the higher impacts at Hr5 in comparison to the sham control. There was a corresponding increase in corpus callosum volume starting from Hr1 of 60-110% and 30-40% following the lower and higher impact levels, respectively. A statistically significant change in the abnormal tissue from Hr2 to Hr5 was observed for both impact levels, with greater significance for higher impacts. Furthermore, a statistically significant difference between the lower impacts and the sham controls occurred at Hr3. These results are statistically substantiated by a fluctuation in the physical size of the corpus callosum, a decrease in the volume of CSF, and elevated levels of atrophy in the cerebral cortex.
    Scopus© Citations 20  666
  • Publication
    Wave-like modelling of cascaded, lumped, flexible systems with an arbitrarily moving boundary
    (Elsevier, 2011-06-20)
    This paper considers cascaded, lumped, flexible systems, which may be short and non-uniform, which are driven by an arbitrarily moving boundary. Such systems exhibit vaguely wavelike behaviour yet defy classical wave analysis. The paper proposes novel ways to analyse and model such systems in terms of waves. It presents two new wave models for non-uniform systems, one series and one shunt, defining their component wave transfer functions, and thereby providing a way to define, identify and measure component waves. Features of the models are compared. The series and shunt configurations are mutually consistent and can be combined into a single composite wave model. The models are exact, but elements within them remain arbitrary to some degree, implying slight differences in the wave decomposition of the system. Some good model choices are proposed and explored. Wave speed and wave impedance are briefly considered, as are ways to measure component waves. Implications are discussed.
    Scopus© Citations 14  1969
  • Publication
    Wave-based control of under-actuated flexible structures with strong external disturbing forces
    (Taylor and Francis, 2015-03-18) ;
    Wave-based control of under-actuated, flexible systems has many advantages over other methods. It considers actuator motion as launching a mechanical wave into the flexible system which it absorbs on its return to the actuator. The launching and absorbing proceed simultaneously. This simple, intuitive idea leads to robust, generic, highly efficient, precise, adaptable controllers, allowing rapid and almost vibrationless re-positioning of the system, using only sensors collocated at the actuator-system interface. It has been very successfully applied to simple systems such as mass-spring strings, systems of Euler-Bernoulli beams, planar mass-spring arrays, and flexible three-dimensional space structures undergoing slewing motion. In common with most other approaches, this work also assumed that, during a change of position, the forces from the environment were negligible in comparison with internal forces and torques. This assumption is not always valid. Strong external forces considerably complicate the flexible control problem, especially when unknown, unexpected or unmodelled. The current work extends the wave-based strategy to systems experiencing significant external disturbing forces, whether enduring or transient. The work also provides further robustness to sensor errors. The strategy has the controller learn about the disturbances and compensate for them, yet without needing new sensors, measurements or models beyond those of standard wave-based control.
    Scopus© Citations 7  368
  • Publication
    Wave-Echo Control of Lumped Flexible Systems
    (Elsevier, 2006-12-22)
    An elegant, generic solution is presented to the problem of point-to-point control by a single actuator of a remote load through an intermediate flexible system, modelled by a system of lumped masses and springs. It is based on new ways of looking at the problem that respect and exploit the underlying dynamics. Under wide-ranging conditions the strategy allows rapid, almost-vibrationless, precise position control of the load, independently of the order of the system, without the need for a detailed system model or ideal actuator. During the start-up, the system itself reveals to the controller how to terminate the motion, so that the real system also acts as the model for the controller. The scheme is very robust to modelling, actuator and sensor errors. The strategy is presented, with some of the motivating ideas reviewed.
    Scopus© Citations 34  625
  • Publication
    Gantry crane control of a double-pendulum, distributed-mass load, using mechanical wave concepts
    (Copernicus GmbH, 2013-07-01) ;
    The overhead trolley of a gantry crane can be moved in two directions in the plane. The trolley is attempting to control the motion of a suspended, rigid-body, distributed mass load, supported by a hook, modelled as a lumped mass, in turn connected to the trolley by a light flexible cable. This flexible system has six degrees of freedom, four variables describing the flexible, hanging load dynamics and two (directly controlled) input variables for the trolley position. The equations of motion are developed and the crane model is verified. Then a form of wave-based control (WBC) is applied to determine what trolley motion should be used to achieve a reference motion of the load, with minimum swing during complex manoeuvres. Despite the trolley's limited control authority over the complex, flexible 3-D dynamics, WBC enables the trolley to achieve very good motion control of the load, in a simple, robust and rapid way, using little sensor information, with all measurements taken at or close to the trolley.
    Scopus© Citations 31  834
  • Publication
    Experimental modal analysis of violin and similar thin plates by added point masses
    Novel methods are proposed to measure the modal properties of thin plates, such as free violin plates (prior to assembly), simply and inexpensively, by measuring certain changes when a small mass is added to the resonating plate. Iso-amplitude contours and mode shapes can easily be plotted. Modal mass, stiffness and damping can also be inferred. Underlying theory is developed, and experimental and numerical modelling methods of validation are briefly outlined.
      796