Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

Hybrid passive/active inertial actuators to attenuate the structural response of a submerged hull

This paper theoretically investigates the application of tuned vibration absorbers and hybrid passive/active inertial actuators to reduce the vibrational responses of plates and shells. The passive/active actuators are initially applied to a simple plate. A model of a submerged hull consisting of a ring stiffened finite cylinder with bulkheads and external fluid loading is then considered. The fluctuating forces from the propeller result in excitation of the low frequency global hull modes. Inertial actuators and tuned vibration absorbers are located at each end of the hull and in circumferential arrays to reduce the hull structural response at its axial resonances. The control performance of the hybrid passive/active inertial actuator, where the passive component is tuned to a structural resonance, is compared to the attenuation achieved by a fully passive tuned vibration absorber. This work shows the potential of using hybrid passive/active inertial actuators to attenuate the global structural responses of a submerged vessel.

Active control of the accordion modes of a submerged hull

Active vibration control of a submerged hull is presented. A submarine hull can be idealised as a ring stiffened finite cylinder with applied fluid loading. At low frequencies, rotation of the propeller results in discrete tones at the blade passing frequency and its harmonics. The low frequency axial and radial vibration modes of the submerged body can result in a high level of radiated noise. Global hull modes are difficult to attenuate since passive control techniques such as damping materials are not practical due to size and weight constraints. This work investigates active vibration control of a submarine hull for attenuation of the structural and acoustic responses. Based on a feedforward algorithm at tonal frequencies, active vibration suppression of the axial and radial hull displacements are investigated. The effect of the various control arrangements on the structure-borne radiated noise is examined. Numerical simulations of the control performance are presented.

Structural sensitivity of spiral vortex breakdown

Previous numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier-Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the m=-1 azimuthal mode is the most unstable and that the wavemaker regions of the m=-1 mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown. © 2013 Cambridge University Press.

Constructive Nonlinear Control

In this book several streams of nonlinear control theory are merged and di- rected towards a constructive solution of the feedback stabilization problem. Analytic, geometric and asymptotic concepts are assembled as design tools for a wide variety of nonlinear phenomena and structures. Di®erential-geometric concepts reveal important structural properties of nonlinear systems, but al- low no margin for modeling errors. To overcome this de¯ciency, we combine them with analytic concepts of passivity, optimality and Lyapunov stability. In this way geometry serves as a guide for construction of design procedures, while analysis provides robustness tools which geometry lacks.

Active control of high frequency vibration in uncertain structures

The active suppression of structural vibration is normally achieved by either feedforward or feedback control. In the absence of a suitable reference signal feedforward control cannot be employed and feedback control is the only viable approach. Conventional feedback control algorithms (e.g. LQR and LQG) are designed on the basis of a mathematical model of the system and ideally the performance of the system should be robust against uncertainties in this model. The aim of this paper is to numerically investigate the robustness of LQR and LQG algorithms by designing the controller for a nominal system, and then assessing (via Monte Carlo simulation) the effects of uncertainties in the system. The ultimate concern is with the control of high frequency vibrations, where the short wavelength of the structural deformation induces a high sensitivity to imperfection. It is found that standard algorithms such as LQR and LQG are generally unfeasible for this case. This leads to a consideration of design strategies for the robust active control of high frequency vibrations. The system chosen for the numerical simulation concerns two coupled plates, which are randomized by the addition of point masses at random locations.

An analytical study of the low frequency structural responses of a submerged hull

This paper studies the low frequency vibrational behaviour of a submerged hull. The submerged hull is modelled as a finite fluid-loaded cylindrical shell closed at each end by circular plates. The external pressure acting on the hull due to the fluid loading is analytically calculated using an infinite model. Three excitation cases of the hull are considered. In the first model, an axial point force is applied at the centre of one end plate, giving rise to an axisymmetric case in which only the zeroth circumferential shell modes are excited. In the second model, an axial point force is applied at the edge of the end plate. In the third model, a radial point force is applied also at the edge of the end plate. In the second and third load cases, all cylindrical shell circumferential modes are excited. The effects of fluid loading and different excitation locations are studied. A more complex hull model including stiffeners and bulkheads is then examined. A smeared approach is used to analytically model the ring stiffeners. All load cases are again considered and the effects of the various influencing factors on the low frequency responses are described.