String System Research Articles

On (Non) Applicability of a Mode-Truncation of a Damped Traveling String

This study investigates a linear homogeneous initial-boundary value problem for a traveling string under linear viscous damping. The string is assumed to be traveling with constant speed, while it is fixed at both ends. Physically, this problem represents the vertical (lateral) vibrations of damped axially moving materials. The axial belt speed is taken to be positive, constant and small in comparison with a wave speed, and the damping is also considered relatively small. A two timescale perturbation method together with the characteristic coordinate’s method will be employed to establish the approximate analytic solutions. The damped amplitude-response of the system will be computed under specific initial conditions. The obtained results are compared with the finite difference numerical technique for justification. It turned out that the introduced damping has a significant effect on the amplitude-response. Additionally, it is proven that the mode-truncation is applicable for the damped axially traveling string system on a timescale of order ε -1

Calculation and analysis of dynamic drag and torque of horizontal well strings

In recent years, shale gas production horizontal well types mainly include conventional horizontal well, highly deviated well and scoop-shape horizontal well. For the sake of construction decision making, it is necessary to study these three types of wells from the aspects of drag and torque characteristic, weight on bit transferring efficiency, key hole sections or links and extreme penetration length. In this paper, these three types of horizontal wells were taken as the study objects. Their drag and torque, load transfer and extended reach drilling were explored based on the dynamic model of full hole drilling string and the simulation calculation of dynamic characteristics of full hole drilling string system. And the results were applied and tested on site in three shale gas wells (a conventional horizontal well, a highly deviated well and a scoop-shape horizontal well) in the Changning area, Sichuan Basin. And the following research results were obtained. First, the contact friction strength of the deeper part of the buildup section in the scoop-shape horizontal well is very high, and it is 1.67 times that of the hold section. The total contact force of buildup section in the scoop-shape horizontal well is 1.62 times that in the highly deviated well. Second, the contact friction strength of the hold section in highly deviated well is not only higher than that of its buildup section, but also higher than any characteristic section in the three well types of the same depth. Third, the operating stress of drilling strings during the drilling of three well types is not high, but during the extended reach drilling in the curved section of the scoop-shape horizontal well, it is necessary to focus on the twist off of drilling string in the hold section. Fourth, the weight on bit transferring efficiency of scoop-shape horizontal well is lower than that of conventional horizontal well and highly deviated well. In conclusion, the research results preliminarily reveal the drag and torque characteristics and active load transferring mechanisms of conventional horizontal well, highly deviated well and scoop-shape horizontal well for shale gas production, and present important hole sections for safety assessment. They can be used as references for efficient and safe construction of shale gas horizontal wells.

Sliding mode boundary control of a vibrating string under time-varying distributed disturbance

This paper is concerned with sliding-mode boundary control (SMBC) of a vibrating string system under parameter variation. The string is excited by time-varying distributed disturbance. Dynamics of the vibrating string are described by two types of differential equations, namely: (a) non-homogenous hyperbolic partial differential equation (PDE) and (b) ordinary differential equations (ODEs). In the proposed scheme, the perturbations of the vibrating string are damped in the presence of system parameter variation. The boundary control law based on the original infinite dimensional model is applied at the free end of the string. Robustness of this scheme is validated through different lengths of the string system. The suggested control system is proven to be exponentially converging to zero by using Lyapunov direct method. Simulation results show that the proposed design is valid for attenuating the vibrations effectively.

Active-Passive Combined Control System in Crane Type for Heave Compensation

For the purpose of researching the displacement control system of heave compensation for offshore drilling platform, a set of crane type active and passive combined heave compensation device are designed on the basis of the similarity principle. As it known that platform heaving will be caused by the wind, sea wave and ocean current when conducting the drilling operations on the offshore drilling platform, which then will disturb the drilling operation. Therefore, the compensation device must be adopted to keep the vertical relative motion between the drill string system and the drilling platform to zero during the operation. Meanwhile, to improve the real-time performance of the heave compensation, the control system is optimized by establishing the simulation model of the active-passive combined crane, and LS-SVM (Least Squares Support Vector Machine) is improved by the artificial immune algorithm to predict the motion trend of offshore platforms. Eventually, in order to acquire the best control scheme, the Proportion Integration Differentiation (PID), fuzzy PID, BP neural network PID control method are utilized to carry out the simulation analysis, and the BP neural network PID control is found to be the optimum. Experiments showed that after using the BP neural network PID control algorithm, the displacement compensation rate of hook for active-passive combined crane device is more than 90%, the performance of the heave compensation is better, and the control is in time.

Vibration Control of an Axially Moving System with Restricted Input

In this study, we consider the global stabilization of an axially moving system under the condition of input saturation nonlinearity and external perturbation. Based on Lyapunov redesign method, observer backstepping, and high‐gain observers, an output feedback control strategy with an auxiliary system is constructed to eliminate the input saturation constraint effect and suppress the string system vibration, and a boundary disturbance observer is exploited to cope with the external disturbance. The stability of the controlled system is analyzed and proven based on Lyapunov stability without simplifying or discretizing the infinite dimensional dynamics. The presented simulation results show the effectiveness of the derived control.

Vibration Control for Two Kinds of Flexible Mechanical Systems With Full State Output Constraints

This paper concentrates on the vibration control problem of a flexible string system and a flexible Euler-Bernoulli beam system for considering full state output constraints, i.e., deflection and speed constraints. For either system, a boundary control law is developed based on a barrier Lyapunov function. By employing the control scheme, the deflection and speed are limited into desirable regions. With the help of a rigorous unique solution proof for the time derivative of the barrier Lyapunov function, the asymptotic stability of the considered system is achieved via LaSalle's Invariance Principle. Finally, numerical simulations are provided to verify the control performances of the proposed controls.

Boundary control for a flexible string system with input saturation constraint

AbstractIn this study, we focus on the boundary control problem for a vibrating string system with saturated input under the condition of external disturbances. Based on the backstepping approach, a boundary vibration control scheme is proposed to globally stabilize the string around the equilibrium position. A smooth hyperbolic tangent function is exploited to restrict the control input, an auxiliary system and a Nussbaum function are adopted to cope with the nonlinear term derived from the input saturation, and a disturbance observer is employed to tackle the boundary disturbance. The developed controller can assure the convergence of the closed‐loop system state to a small neighbourhood of zero. By the appropriate choice of control design parameters, numerical simulation is conducted to show the effectiveness of the derived control.

Closed string symmetries in open string field theory: tachyon vacuum as sine-square deformation

We revisit the identity-based solutions for tachyon condensation in open bosonic string field theory (SFT) from the viewpoint of the sine-square deformation (SSD). The string Hamiltonian derived from the simplest solution includes the sine-square factor, which is the same as that of an open system with SSD in the context of condensed matter physics. We show that the open string system with SSD or its generalization exhibits decoupling of the left and right moving modes and so it behaves like a system with a periodic boundary condition. With a method developed by Ishibashi and Tada, we construct pairs of Virasoro generators in this system, which represent symmetries for a closed string system. Moreover, we find that the modified BRST operator in the open SFT at the identity-based tachyon vacuum decomposes to holomorphic and antiholomorphic parts, and these reflect closed string symmetries in the open SFT. On the basis of SSD and these decomposed operators, we construct holomorphic and antiholomorphic continuous Virasoro algebras at the tachyon vacuum. These results imply that it is possible to formulate a pure closed string theory in terms of the open SFT at the identity-based tachyon vacuum.

Dynamic modeling and vibration control of a three-dimensional flexible string with variable length and spatiotemporally varying parameters subject to input constraints

In this paper, a three-dimensional dynamic model is developed for a flexible string system with variable length as well as spatiotemporally varying parameters. The dynamic system model is described by coupled partial differential equations and ordinary differential equations. On the basis of the established model, a boundary control method is proposed via backstepping technology and Nussbaum functions to eliminate the vibration of the three-dimensional string with input constraints and disturbances. Deformations of the three-dimensional string system can be verified to converge to small neighborhoods of zero under the proposed control. Input constraints can also be guaranteed by applying smooth hyperbolic tangent function. Simulation results present that the vibration suppression of the flexible string can be achieved and input constraints can be ensured with the proposed control scheme.

Estimation and Fault Diagnosis of Lithium-Ion Batteries: A Fractional-Order System Approach

This study investigates estimation and fault diagnosis of fractional-order Lithium-ion battery system. Two simple and common types of observers are designed to address the design of fault diagnosis and estimation for the fractional-order systems. Fractional-order Luenberger observers are employed to generate residuals which are then used to investigate the feasibility of model based fault detection and isolation. Once a fault is detected and isolated, a fractional-order sliding mode observer is constructed to provide an estimate of the isolated fault. The paper presents some theoretical results for designing stable observers and fault estimators. In particular, the notion of stability in the sense of Mittag-Leffler is first introduced to discuss the state estimation error dynamics. Overall, the design of the Luenberger observer as well as the sliding mode observer can accomplish fault detection, fault isolation, and estimation. The effectiveness of the proposed strategy on a three-cell battery string system is demonstrated.

Disturbance Rejection Control for a Vibrating String System

AbstractThis paper is concerned with disturbance rejection control for a vibrating flexible string system in the presence of unknown disturbances. First, the boundary disturbance observer is proposed to deal with the boundary disturbance and the infinite dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. Subsequently, the boundary control and distributed control are developed to suppress the vibration and globally stabilize the string system at its equilibrium position. Under the control proposed, the uniformly bounded stability of the controlled system is testified employing rigorous analysis without resorting to discretization of the partial differential equation dynamics depending on the time and space. Finally, the simulation and comparison results verify the performance of the derived control.

Hysteretic bit/rock interaction model to analyze the torsional dynamics of a drill string

Abstract The present paper proposes a novel hysteretic (non-reversible) bit/rock interaction model for the torsional dynamics of a drill string. Non-reversible means that the torque-on-bit depends not only on the bit speed, but also on the bit acceleration, producing a type of hysteretic cycle. The continuous drill string system is discretized by means of the finite element method and a reduced-order model is constructed using the normal modes of the associated conservative system. The parameters of the proposed hysteretic bit/rock interaction model is fitted with field data. The non-linear torsional vibration and the stability map of the drill string system are analyzed employing the proposed bit/rock interaction model and also a commonly used reversible model (without hysteresis). It turns out that the hysteretic model affects the stability region of the system.

Boundary control design for a vibrating flexible string system with input nonlinearities

In this paper, the main concern lies in developing a vibration control scheme for globally stabilizing the string system under the influence of input nonlinearities and external disturbance. To that end, an antidisturbance boundary control is presented by merging Lyapunov approach and disturbance observer control theory. Besides, the auxiliary system and auxiliary function are introduced to compensate for the input nonlinearities effects. Using the rigorous analysis without simplifying or discretizing the infinite-dimensional dynamics, the designed control laws can be proven to ensure the uniformly bounded stability of the controlled system. In the end, simulation results are presented for control performance verification.

Adaptive Control of a Flexible String System With Input Hysteresis

In this brief, a vibration suppression scheme is investigated for a flexible string system with input hysteresis. The input hysteresis is formulated as a linear desired input and a “disturbance-like” term, whose unknown bound is then estimated by an adaptive law. Without constructing a hysteresis inverse, adaptive boundary control is designed to suppress the vibrations of the flexible string, cope with the uncertainties of system parameters, and tackle the hysteresis nonlinearities. Based on the extended LaSalle’s invariance principle, asymptotic stability of the closed-loop system is also manifested. Simulations are also provided to show the effectiveness of the designed control.

Self-dual connections and the equations of fundamental fields in a Weyl–Cartan space

Spaces with a Weyl-type connection and torsion of a special type induced by the structure of the differentiability conditions in the algebra of complex quaternions are considered. The consistency of these conditions implies the self-duality of curvature. The Maxwell and SL(2, C) Yang-Mills fields associated with the irreducible components of the connection also turn out to be self-dual, so that the corresponding equations are fulfilled on the solutions of the generating system. Using the twistor structure of the latter, its general solution is obtained. The singular locus has a string-like (particle-like) structure and generates the self-consistent algebraic dynamics of the string system.

Vibration dissipation of an axially traveling string with boundary damping

At present, the control of vibration problem of many engineering equipment can be simplified as a study on transverse vibration of axially traveling string system. In this paper, transverse vibration control and energy dissipation of axially traveling string system is investigated by using a boundary viscous damper. By analyzing the nature frequencies of the fixed length and the variable length of the string system, the resonance frequency of the external concentrated force is obtained. The amplitude and the energy reflection ratio of reflected wave to incident wave is investigated respectively by the force equilibrium principle and the energy equation at the boundary. According to amplitude and the energy reflection ratio, the range and the optimal value of damping coefficient are obtained. The effect of vibration dissipation with a viscous damper and an external concentrated force at the left boundary is investigated respectively by the numerical simulation.

Investigation of PDC bit failure base on stick-slip vibration analysis of drilling string system plus drill bit

The undesired stick-slip vibration is the main source of PDC bit failure, such as tooth fracture and tooth loss. So, the study of PDC bit failure base on stick-slip vibration analysis is crucial to prolonging the service life of PDC bit and improving ROP (rate of penetration). For this purpose, a piecewise-smooth torsional model with 4-DOF (degree of freedom) of drilling string system plus PDC bit is proposed to simulate non-impact drilling. In this model, both the friction and cutting behaviors of PDC bit are innovatively introduced. The results reveal that PDC bit is easier to fail than other drilling tools due to the severer stick-slip vibration. Moreover, reducing WOB (weight on bit) and improving driving torque can effectively mitigate the stick-slip vibration of PDC bit. Therefore, PDC bit failure can be alleviated by optimizing drilling parameters. In addition, a new 4-DOF torsional model is established to simulate torsional impact drilling and the effect of torsional impact on PDC bit's stick-slip vibration is analyzed by use of an engineering example. It can be concluded that torsional impact can mitigate stick-slip vibration, prolonging the service life of PDC bit and improving drilling efficiency, which is consistent with the field experiment results.

Adaptive neural network control of a flexible string system with non-symmetric dead-zone and output constraint

Abstract This study is concerned with adaptive neural network control for a vibrating flexible string system under the influence of non-symmetric input dead-zone, output constraint and system uncertainties. First, the backstepping method is incorporated into the context of boundary control scheme and the barrier Lyapunov function is exploited to ensure the output constraints are never transgressed. Subsequently, an adaptive neural network control is developed to globally stabilize the string system and compensate for the effect of the input dead-zone. Besides, the online updating laws are introduced to compensate for the uncertainties of the system and the σ-modification is adopted to adjust the robustness of the system. Under the proposed control, the bounded stability of the closed-loop system is proven based on Lyapunov functions without simplifying or discretizing the infinite-dimensional dynamics. Finally, simulation results are presented for control performance verification.

Separation of traveling and standing waves in a finite dispersive string with partial or continuous viscoelastic foundation

The free and forced vibrations of a linear string with a local spring-damper on a partial elastic foundation, as well as a linear string on a viscoelastic foundation conceptualized as a continuous distribution of springs and dampers, are studied in this paper. Exact, analytical results are obtained for the free and forced response to a harmonic excitation applied at one end of the string. Relations between mode complexity and energy confinement with the dispersion in the string system are examined for the steady-state forced vibration, and numerical methods are applied to simulate the transient evolution of energy propagation. Eigenvalue loci veering and normal mode localization are observed for weakly coupled subsystems, when the foundation stiffness is sufficiently large, for both the spatially symmetric and asymmetric systems. The forced vibration results show that nonproportional damping-induced mode complexity, for which there are co-existing regions of purely traveling waves and standing waves, is attainable for the dispersive string system. However, this wave transition phenomenon depends strongly on the location of the attached discrete spring-damper relative to the foundation and whether the excitation frequency Ω is above or below the cutoff frequency ωc. When Ω<ωc, the wave transition cannot be attained for a string on an elastic foundation, but is possible if the string is on a viscoelastic foundation. Although this study is primarily formulated for a harmonic boundary excitation at one end of the string, generalization of the mode complexity can be deduced for the steady-state forced response of the string-foundation system to synchronous end excitations and is confirmed numerically. This work represents a novel study to understand the wave transitions in a dispersive structural system and lays the groundwork for potentially effective passive vibration control strategies.

Neural network based boundary control of a vibrating string system with input deadzone

Abstract In this paper, a boundary control scheme is developed for a vibrating flexible string system subject to input deadzone and external disturbance. First, a basic boundary control scheme is proposed to suppress the string’s vibration based on the backstepping method. Subsequently, a radial basis function neural network (RBFNN) is utilized to handle the effect of the input deadzone and a disturbance observer is exploited to track the external disturbance. Under the proposed control, the uniformly ultimately bounded stability of the closed loop system is achieved through rigorous Lyapunov analysis without any discretization or simplification of the dynamics in the time and space. Finally, simulation results are demonstrated for control performance verification.