Arbitrary Disturbances Research Articles

Robust Stability of positive continuous time systems

In this note a simple formula for the real stability radius of uncertain positive linear continuous time systems is established and it is shown that the real stability radius coincides with the complex one. Arbitrary disturbance norms induced by monotonic vector norms (e.g. p—norms ) are considered. The distance of intervals of positive systems from instability is also determined

EXISTENCE AND REGULARITY OF SOLUTIONS AND THE STABILITY OF THE REST STATE FOR FLUIDS WITH SHEAR DEPENDENT VISCOSITY

In this paper we clarify and discuss some subtle features concerning the non-Newtonian fluid models which were considered by Málek, Nečas and Růžička.19 We establish new results regarding the stability of the rest state of mechanically isolated flows of such non-Newtonian fluids for arbitrary initial disturbances. We also discuss some results concerning the existence and regularity of solutions for small data. These results are based on a new method, giving convergence almost everywhere of approximations of gradients from boundedness of fraction of the L2-norm of the second and first derivatives, developed by Nečas to study existence of solutions (global in time) to a class of partial differential equations.

The damping of flexural and acoustic waves by a bias-flow perforated elastic plate

An analysis is made of the damping of sound and structural vibrations by vorticity production in the apertures of a bias flow, perforated elastic plate. Unsteady motion causes vorticity to be generated at the aperture edges; the vorticity and its energy are swept away by the bias flow and result in a net loss of acoustic and vibrational energy. In this paper we investigate the interaction of an arbitrary fluid-structure disturbance with a small circular aperture in the presence of a high Reynolds number, low Mach number bias flow. By considering the limit in which the aperture is small compared to the length scale of the impinging disturbance, it is shown that the effect of the interaction can be represented by a concentrated source in the plate bending wave equation consisting of a delta function and two of its axisymmetric derivatives. A generalized bending wave equation is then formulated for a plate perforated with an homogeneous distribution of small, bias flow circular apertures. This equation is used to predict the attenuation of sound and resonant bending waves by vorticity production. Acoustic damping is found to be significant provided the fluid loading is sufficiently small for the plate to be regarded as rigid (e.g. for an aluminium plate in air when the frequency is not too small). On the other hand, a bending wave is effectively damped only when the fluid loading is large enough for the wave to produce a substantial pressure drop across the plate; when this occurs the predicted attenuations are comparable with those usually achieved by the application of elastomeric damping materials. Numerical predictions are presented for steel and aluminium plates in air and water.

A parametric nonlinear Schrödinger equation and stability criterion

Stability investigation is carried out for a parametric nonlinear Schrödinger equation containing the first order spatial and the first order temporal derivatives of a complex conjugate type. It is derived formally from an arbitrary system in which a scalar dependent variable u satisfies an equation of the form ( L + α) u = N. L is a linear operator involving the temporal and spatial differential operators, α is a periodic function of time and N represents all the nonlinear terms. A useful analysis of dispersive perturbations for a periodic temporal solution is developed. A stability criterion for arbitrary linear disturbance is obtained.

Adaptive Tracking with Disturbance Attenuation for a Class of Nonlinear Systems

For a class of single-input, single-output uncertain nonlinear systems, affected both by unknown constant parameters and time-varying bounded disturbances, we present an adaptive state feedback control algorithm which guarantees arbitrary disturbance attenuation when disturbances are present. When no disturbance is acting on the system, asymptotic tracking with arbitrary transient performance is obtained. The result generalizes those given in [3] when there are no disturbances and improve those given in [7] when there are unknown parameters with known bounds and the reference output to be tracked is time-varying.

Control of Nonlinear Differential-Algebraic-Equation Systems with Disturbances

We address the control of a class of nonlinear, multivariable, high-index differential-algebraic-equation systems with external disturbances. Initially, an algorithmic procedure is developed to derive an equivalent state-space realization of the constrained system, valid for arbitrary disturbances. Then, on the basis of the derived state-space realization, a feedforward/feedback controller is developed to completely eliminate the effects of the measurable disturbances and induce a well-characterized input/output behavior in the constrained system. The application of the proposed control methodology is illustrated on a high-purity absorption column.

A robust PI-controller for infinite-dimensional systems

In this paper, we deal with single-input single-output systems of the form on a separable Hilbert space H, where the operator A is the generator of an exponentially stable C0-semigroup on H, b ϵ H, C is a A -admissible linear operator and w is an arbitrary constant disturbance vector in H. We propose a low-gain PI-controller which stabilizes and regulates the system such that, for a given reference constant yr, y(t) tends to yr independently of w as t → + ∞ . Our result generalizes the previous one of Pohjolainen (1982) in that the semigroup is not necessarily holomorphic. A numerical example will be given to illustrate the application of the theory.

Dynamics of charged and conducting drops via the hybrid finite-boundary element method

A numerical study on the dynamic behaviour of a charged and conducting drop, with net electrical charge Q , is presented here, that is valid for arbitrary initial disturbances. It employs the integral form of Laplace's equation for the calculation of the velocity and electrostatic potentials, which only requires discretization and solution on the surface of the drop. Thus a hybrid method results with the integral equations solved via the boundary element technique, while the Galerkin finite element formulation is used for the kinematic and dynamic condition at the interface as well as for the net charge conservation equation. Recently, the authors followed this approach in their study on the free nonlinear oscillations of inviscid drops, and they were able to optimize time and space discretization as well as the treatment of the integral equation with excellent results.

A Transfer-Function Formulation For Nonuniformly Distributed Parameter Systems

This paper studies a transfer-function formulation for general one-dimensional, nonuniformly distributed systems, subject to arbitrary boundary conditions and external disturbances. In the development, the governing equations of the nonuniform system are cast into a state-space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state-space equation. Two approximate methods, the step-function approximation and truncated Taylor series, are proposed to evaluate the fundamental matrix. With the transfer-function formulation, various dynamics and control problems for the nonuniformly distributed system can be conveniently addressed. The transfer-function analysis also is applied to constrained/combined nonuniformly distibuted systems. The method developed is illustrated on two nonuniform beams.

Stationary and dynamic simulation of multipass shell and tube heat exchangers with the dispersion model for both fluids

The dispersion model is applied to the description of the effects of shell and tubeside flow maldistribution. By means of this model, an efficient and versatile method of predicting transient response of multipass shell and tube heat exchangers is developed. The method allows for effect of maldistribution on transient process, influence of heat capacities of fluids and solid components, arbitrary inlet temperature variations and step disturbances of flow rates. General forms of initial conditions and two different flow arrangements are considered. A general form of the solution for steady-state and dynamic simulation is derived. Temperature profiles are determined with numerical inversion of the Laplace transform. Some examples are calculated and the effect of maldistribution is discussed.

Propagation of transient waves in a random medium

A theoretical analysis of the propagation of transient scalar waves in a one‐dimensional random medium is presented. The index of refraction of the medium is assumed to deviate only slightly from unity, which allows the analysis to be carried out with the aid of a perturbation method. The specific approach adopted here combines a renormalization technique with a travel‐time‐corrected averaging procedure called asynchronous ensemble averaging. A general expression, valid for an arbitrary initial disturbance, is obtained for the variance of the wave. From that result, an expression for the variance is derived for the special case in which the initial disturbance has the form of a ramp function with arbitrary slope. These results show that the variance of the wave is directly proportional to the variance of the refractive index of the medium, but is only weakly dependent on the propagation path length. It is also found that, as the slope of the ramp function decreases, the wave variance decreases as well. The presentation concludes with some observations on the relevance of these results to the problem of sonic‐boom propagation in the atmosphere. [Research supported by NASA.]

Dynamics of shell‐and‐tube heat exchangers to arbitrary temperature and step flow variations

AbstractA versatile and efficient method is developed for predicting dynamic performances of parallel and counterflow heat exchangers subject to arbitrary temperature variations and step flow disturbances, including the effect of flow maldistribution and the influence of heat capacities of both fluids, shell wall and tube bank as well as nonzero initial temperatures. Two algorithms of numerical inversion of the Laplace transform are introduced to determine the final temperature profiles in the realtime domain and some examples are calculated with nonuniform initial conditions. The accuracy of the proposed method is demonstrated with the calculated results at new steady states. Experiments are carried out on a labor‐sized heat exchanger to further examine the feasibility of this method and the comparison between calculated and measured temperature profiles is illustrated and discussed.

Stability of the interface in co-extrusion flow of two viscoelastic fluids through a pipe

The linear stability of co-extrusion flow of two upper convected Maxwell fluids through a pipe at low Reynolds numbers is studied for arbitrary wavelength disturbances. The fluids interface can become unstable due to various mechanisms. It is shown that elasticity of the fluids can stabilize the capillary instability and a linearly stable interface can be achieved by appropriate choice of controlling parameters.

Convection in a fluid layer with asymmetric boundary conditions

Steady convection rolls in a horizontal fluid layer heated from below are described numerically with a Galerkin method. A rigid lower and stress-free upper boundary are assumed, while the temperature is fixed at both boundaries. The stability of the steady solutions with respect to arbitrary three-dimensional infinitesimal disturbances is analyzed and the stability boundaries in the Rayleigh number–wave-number plane are determined for selected Prandtl numbers. It is found that results of the analysis correspond more closely to the case of two rigid boundaries than to the case of two stress-free boundaries. The domains of stability in the case of asymmetric boundaries are larger at high Prandtl numbers than in the case of two rigid boundaries, but smaller for low Prandtl numbers. Some of the asymmetric properties of convection rolls are discussed.

Preferred pattern of convection in a porous layer with a spatially non-uniform boundary temperature

The problem of finite-amplitude thermal convection in a porous layer between two horizontal walls with different mean temperatures is considered when spatially non-uniform temperature with amplitude L* is prescribed at the lower wall. The nonlinear problem of three-dimensional convection for values of the Rayleigh number close to the classical critical value is solved by using a perturbation technique. Two cases are considered: the wavelength γ(b)n of the nth mode of the modulation is equal to or not equal to the critical wavelength γc for the onset of classical convection. The preferred mode of convection is determined by a stability analysis in which arbitrary infinitesimal disturbances are superimposed on the steady solutions. The most surprising results for the case γ(b)n = γc for all n are that regular or non-regular solutions in the form of multi-modal pattern convection can become preferred in some range of L*, provided the wave vectors of such pattern are contained in the set of wave vectors representing the spatially non-uniform boundary temperature. There can be critical value(s) L*c of L* below which the preferred flow pattern is different from the one for L* > L*c. The most surprising result for the case γ(b)n ≠ γc and γ(b)n ≡ γ(b) for all n is that some three-dimensional solution in the form of multi-modal convection can be preferred, even if the boundary modulation is one-dimensional, provided that the wavelength of the modulation is not too small. Here γ(b) is a constant independent of n.

Design of Control Algorithm for Operation of Irrigation Canals

Using a linearized finite-difference model of open-channel flow, the canal operation problem was formulated as an optimal-control problem, and an algorithm for gate opening in the presence of arbitrary external disturbances (changes in flow rates) was derived. An observer was designed to estimate the values for depths of flow and flow rates at the intermediate nodes based upon measured values of depth at two points in the pool. Control algorithms were derived for both a constant-level control and a constant-volume control. For the purpose of evaluation, the equations of the controller and the observer, derived with the linearized model, were included as modules in a nonlinear open-channel flow model. In an example problem with an external disturbance of 20% of the initial flow rate in the pool, the performance of the control algorithm and the observer in maintaining a constant level at the downstream end of the pool was found to be acceptable.

Design of MIMO compensators for systems with unmeasurable disturbances: The polynomial approach

Presented is the frequency domain design of linear time-invariant (reduced-order) compensators for systems subject to unmeasurable arbitrary disturbances of a given class such that the controlled variables asymptotically become equal to pre-assigned tracking signals of a given class, independent of the disturbances occurring in the system. The frequency domain results are shown to be equivalent to those from known time domain approaches. It is further suggested to modify the above results in order to obtain an improved reference behaviour and to use a compensator structure which allows a systematic reset windup prevention.

Instabilities in astrophysical jets. II - Numerical simulations of slab jets

view Abstract Citations (26) References (42) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Instabilities in Astrophysical Jets. II. Numerical Simulations of Slab Jets Zhao, Jun-Hui ; Burns, Jack O. ; Norman, Michael L. ; Sulkanen, Martin E. Abstract In this paper, we describe numerical simulations of an unstable supersonic slab-symmetric jet. The instabilities within the jet are characterized by growing internal body waves and their coupled surface waves that are also predicted in linear perturbation theory. The characteristic theory of fluid dynamics is used to help interpret the wave morphologies. We demonstrate that these waves can be excited by imposing an arbitrary disturbance. From our numerical simulations, we find that the sound waves propagating against the flow slow down as they propagate outward, and they grow in amplitude. These waves eventually disrupt the jet at a certain length. This disruption length is related to the jet Mach number and the perturbation intensity. Thus, the Mach number of a jet observed with a radio telescope can be estimated by measuring the disruption length and estimating the perturbation intensity. The jet Mach numbers in radio tailed sources determined in this way agree quite well with estimates from ram pressure bending arguments. The wiggles and flares observed in many extragalactic jets, especially in tailed radio sources, appear to be intimately related to instabilities and the jet disruption process. Publication: The Astrophysical Journal Pub Date: March 1992 DOI: 10.1086/171062 Bibcode: 1992ApJ...387...83Z Keywords: Computational Astrophysics; Galactic Clusters; Shock Wave Interaction; Supersonic Jet Flow; Mach Number; Perturbation Theory; Radio Telescopes; Shock Wave Propagation; Surface Waves; Very Large Array (Vla); Astrophysics; GALAXIES: JETS; HYDRODYNAMICS; INSTABILITIES; METHODS: NUMERICAL; SHOCK WAVES full text sources ADS | data products SIMBAD (3) NED (1) Related Materials (1) Part 1: 1992ApJ...387...69Z

Nonlinear stability of baroclinic flows over topography

Abstract A new nonlinear stability criterion is derived for baroclinic flows over topography in spherical geometry. The stability of a wide class of exact three-dimensional nonlinear steady state solutions subject to arbitrary disturbances is established. The resonance condition, at the highest total wavenumber, for the steady state solutions and the stability criteria for baroclinic flow in the absence of topography provide the boundaries of the regions of stability in the presence of topography. The analogous results for flow on periodic or infinite beta planes incorporating non-orthogonal function large scale flows are also discussed.

Twist vortices and their instabilities in the Taylor–Couette system

The problem of three-dimensional flows arising from the twist instability of Taylor vortices is investigated numerically in the narrow gap limit of the Taylor–Couette system with nearly corotating cylinders. There are two types of twist vortices: those that do not deform the in– and outflow boundaries of the Taylor vortices and those that do. The latter type are called wavy twist vortices and correspond to class II of Nagata (1986). The stability of the twist vortices with respect to arbitrary infinitesimal disturbances is analysed with the result that the twist solutions are unstable within a large part of the parameter space with respect to Eckhaus and skewed-varicose-type instabilities. An analytical model is described which fits the numerical results on the transition from axisymmetric vortices to unstable twist solutions. The theoretical findings are compared with experimental observations.