Suppression of two-dimensional vortex-induced vibration with active velocity feedback controller

ABSTRACTHeart rate can be used to define exercise intensity; feedback control systems for treadmills which automatically adjust speed to track arbitrary heart rate target profiles are therefore of interest. The aim of this study was to compare linear (L) and nonlinear (NL) controllers using quantitative performance measures. Sixteen healthy male subjects participated in the experimental L vs. NL comparison. The linear controller was calculated using a direct analytical design that employed an existing approximate plant model. The nonlinear controller had the same linear component, but it was augmented using static plant-nonlinearity compensation. At moderate-to-vigorous intensities, no significant differences were found between the linear and nonlinear controllers in mean RMS tracking error (2.34 vs. 2.25 bpm [L vs. NL], p=0.26) and average control signal power (51.7 vs. m2/s2, p=0.16), but dispersion of the latter was substantially higher for NL (range 45.2 to 56.8 vs. 30.7 to m2/s2, L vs. NL). At low speed, RMS tracking errors were similar, but average control signal power was substantially and significantly higher for NL (28.1 vs. m2/s2 [L vs. NL], p<0.001). The performance outcomes for linear and nonlinear control were not significantly different for moderate-to-vigorous intensities, but NL control was overly sensitive at low running speed. Accurate, stable and robust overall performance was achieved for all 16 subjects with the linear controller. This points to disturbance rejection of very-low-frequency heart rate variability as the overriding challenge for design of heart rate controllers.

An experimental approach to multi-input multi-output nonlinear active vibration control of a clamped sandwich beam

The method of pulling a steel catenary riser (SCR) through a steel tube (termed as a pull tube) is common practice for deepwater riser tie back applications. Vortex-induced vibration (VIV) of such a system is complex. VIV analysis programs, such as Shear7 [1], are suitable only for a single, chain-like structure. The application of such a software tool in VIV design of the SCR-pull tube system requires careful consideration of a number of structural and hydrodynamic factors. This paper presents a methodology for VIV analysis of the combined structural system of the SCR with the pull tube. Firstly, the entire SCR-pull tube system is modeled with the finite element program Flexcom [2]. The modes are then calculated for the entire structure with program Modes [3]. Afterwards, the structural nodes are rearranged for VIV analysis with Shear7. The pull tube is secured on the platform through a number of guides on the truss structure of the hull. The diameter of the pull tube is much larger than that of the SCR, and the pull tube is much stiffer in bending than the SCR is. If the entire structure is analyzed with Shear7, the mode for the pull tube (a mode involving a large motion of the pull tube section), which is very high in order, would be embedded in the analysis. It makes sense to single out the pull tube mode for study as if it is the first mode. A computer program, named as V-Span [4] for subsea span VIV analysis, is used to analyze both in-line and cross-flow VIV of the pull tube. A numerical example is presented to demonstrate this methodology. This is a deepwater SCR, which has a diameter of 9 inches. The water depth is 6,300 ft. The pull tube is 640 feet long and 20 inch in diameter. Both the loop-eddy and background currents are analyzed. The fatigue damage resulted from both in-line and cross-flow VIV is estimated.

This paper proposes, designs, and analyses a novel nonlinear feedback controller that realizes fast, and oscillation free convergence of the synchronization error to the equilibrium point. Oscillation free convergence lowers the failure chances of a closed-loop system due to the reduced chattering phenomenon in the actuator motion, which is a consequence of low energy sm ooth control signal. The proposed controller has a novel structure. This controller does not cancel nonlinear terms of the plant in the closed-loop; this attribute improves the robustness of the loop. The controller consists of linear and nonlinear parts; each part executes a specific task. The linear term in the controller keeps the closed-loop stable, while the nonlinear part of the controller facilitates the fast convergence of the error signal to the vicinity of the origin. Then the linear controller synthesizes a smooth control signal that moves the error signals to zero without oscillations. The nonlinear term of the controller does not contribute to this synthesis. The collaborative combination of linear and nonlinear controllers that drive the synchronization errors to zero is innovative. The paper establishes proof of global stability and convergence behavior by describing a detailed analysis based on the Lyapunov stability theory. Computer simulation results of two numerical examples verify the performance of the proposed controller approach. The paper also provides a comparative study with state-of-the-art controllers.

This paper presents the initial results from VIV (Vortex-Induced Vibration) field testing of a long, flexible, model riser at high mode number. The experiments were designed to better understand the dynamic behavior of a long riser in uniform flow responding at mode numbers from 10 to 25 in cross-flow vibration. The 1.31 inch, (0.0333 m), diameter riser model was made from fiberglass line pipe, manufactured by Fiberspar Corp. Two model configurations with length of 201 feet (61.26m) and 401 feet (122.23m) were towed behind a vessel in a deep lake in upstate New York. Motion was recorded with twenty four evenly spaced internal tri-axial accelerometers. Observed reduced velocity and RMS displacement response levels are reported. Mean drag coefficients and hydrodynamic damping derived from measured data are compared to calculated values from formulas commonly used in engineering design of offshore systems. Introduction The Experiments at Lake Seneca, New York took place in the summer of 2004. They are part of a larger testing program developed by DEEPSTAR (A joint industry technology development project) aimed at improving the ability to model and mitigate VIV. While these particular tests were focused on investigating uniform flow conditions, a second set of tests designed for shear flow conditions was subsequently performed in November 2004 and will be reported on in the future. The initial motivation for this uniform flow VIV field experiment was to improve the understanding of VIV at high mode number. Most model testing has been conducted at low mode numbers (&amp;lt;10). As a consequence, low mode number VIV is quite well understood. There have been numerous tests conducted on very long cables as well, Reference [1]. In such experiments the dynamic behavior can be represented by cables of infinite length. Traveling waves dominate the response and standing wave modal behavior is not observed. Current drilling and production in 1000 to 3000 meters depths has brought on the need to understand VIV behavior at higher mode number, but still short of infinite length behavior. The principal objectives, of the MIT towed pipe experiments were:To gather vortex-induced vibration response data on a densely instrumented circular pipe at high mode number,To investigate mean drag coefficient (CD) at high mode number,To validate or improve drag coefficient prediction formulas,To test the efficacy of helical strakes at high mode numbers,To obtain statistics on the distribution of single-mode vs. multi-mode response of a pipe at high mode number,To determine the relative contribution to damage rate from the in-line and cross-flow VIV,To improve knowledge of damping factors. In this paper, RMS response, reduced velocities, drag coefficients and damping factors are presented. Experiment Description The Lake Seneca test facility was selected as the testing site, because it is a fully equipped field test station moored in calm, deep water. It was ideal for conducting a controlled test on a long circular pipe in uniform flow. This was accomplished by towing a vertical, composite pipe with a suspended bottom weight to produce the desired tension.

This paper deals with the chaotic synchronization of a discrete chaotic system. Based on a stable analysis, improved piece-wise linear feedback and nonlinear feedback control methods were given. Both the methods can achieve chaotic synchronization efficiently with one control input. The range of coupling coefficient is calculated in both the methods. Compared with nonlinear controls, the improved piece-wise linear controls have simpler structures and can be obtained more easily. Finally, the numerical simulation results verified the effectiveness of both the methods.

Nonlinear excitation control of a synchronous generator with implicit terminal voltage regulation

As an important component transporting resources such as oil and mineral ores mixture from the seabed to the surface in ocean engineering, vortex-induced vibration (VIV) of flexible risers can be encountered when the risers are subjected to the external environmental conditions. As VIV can lead to structural fatigue for the riser system, which threatens to the facility safety during deepsea resource exploitation, it is of great significance to investigate VIV mechanism and dynamics. Therefore, VIV dynamics of a flexible fluid-conveying riser undergoing external shear current is studied based on the combination of the Euler-Bernoulli beam theory and the semi-empirical hydrodynamic model. The finite element method and Newmark-β method are adopted to discretize and solve the governing equation. The model is firstly validated by comparing with the experimental data in order to examine the accuracy of the present model. Subsequently, cross-flow (CF) VIV response of the fluid-conveying riser is mainly examined and analyzed while various internal flow velocity and fluid density are considered and changed. The results show that when the flexible riser is subjected to both internal flow and shear current, there appears multi-frequency response for CF VIV. And the CF vibrating frequency and the CF root mean square (RMS) displacement are evidently influenced by the internal flow velocity and fluid density. With the increase of the internal flow velocity and fluid density, the CF vibrating frequency decreases while the RMS displacement shows an increasing trend in CF direction. Furthermore, in addition to the variation of the CF vibrating frequency and RMS displacement, the change of internal flow densities can cause notable mode and frequency transitions.

This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions. A recently introduced non-quadratic Lyapunov function, the convex hull quadratic function, is used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least /spl Lscr//sub 2/ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Optimization problems with BMI constraints are formulated and solved effectively by combining the path-following algorithm and the direct iterative algorithm. The design results are guaranteed to be at least as good as the existing results obtained from LMI conditions. In most examples, significant improvements on system performances have been achieved, which demonstrate the advantages of using nonlinear feedback control over linear feedback control for linear differential inclusions. It is also observed through numerical computation that nonlinear control strategies may help to reduce control effort substantially.

As the search for oil and gas takes place on increasing water depths, the traditional production systems based on fixed or floating platforms becomes increasingly costly. A good alternative to the traditional production systems are subsea to shore solutions, where pipelines transport the product to a land terminal for processing. One of the main challenges of documenting pipeline integrity in subsea to shore solutions is related to fatigue induced by vortex induced vibrations (VIV). Rough and uneven seabed introduce free spans that can be short or long, have small or large clearance and can have a large variety of boundary conditions at the shoulders. Hence, there is a need for methods that can give reliable estimate for fatigue damage under all realistic conditions. This paper investigates the measured VIV for a free spanning pipeline model. The model has L/D ratios from 72 to 350 and includes both single and multi-spans. It is exposed to uniform current and is free to vibrate in both cross-flow (CF) and in-line (IL) direction. Bending strains are measured in CF and IL direction at ten locations along the pipe. The observed cross-sectional trajectories are analyzed, with particular focus on the complex interaction between CF and IL VIV, and the significance of higher order response components. The purpose of this investigation is to understand the behaviour of the free spanning pipelines with respect to response amplitudes, frequency and modal composition, and also to identify characteristic cross section trajectories for further investigation. This work is a continuation of the earlier published results by Nielsen et al. [1] and Soreide et al. [2].

To avoid or mitigate global warming, several ocean carbon capture and storage concepts have been proposed. One of the recent approaches is to dispose carbon dioxide via a fixed vertical cantilevered pipe onto the seabed in deep waters. Due to a high aspect ratio and flexibility of such long pipe conveying fluid with fixed-free end conditions and external hydrodynamic loading caused by currents, the pipe may experience large-amplitude 3-D vibrations leading to structural failure. Hence, it is essential to understand and investigate the pipe nonlinear dynamic behaviors subject to combined flow-induced vibration (FIV) and vortex-induced vibration (VIV). In this study, the 3-D nonlinear equations of a cantilevered pipe discharging fluid in the sea are analyzed using a Galerkin-based multi modal approach combined with a finite difference Houbolt’s integration scheme. Particular attention is paid to the combined effects of FIV and VIV on the dynamic response of the cantilevered pipe in water. To model the fluctuating lift and drag forces associated with VIV, the two dimensional wake oscillators distributed along the pipe are adopted. Numerical simulations in the FIV case of a pipe discharging fluid in the air are first validated with experimental results in the literature to justify the mathematical models and numerical approaches. Modal convergence analysis is also performed. Results in the combined FIV and VIV cases are then highlighted in order to show the effects of cross-flow and in-line VIV when compared with the pure FIV case. The effects of geometric nonlinearities, the coupling/interaction of multi modes and the space-time modifications of pipe responses and trajectories are highlighted. It is hoped that the numerical observations and findings obtained from this study could be verified by experimental studies which are presently lacking in the literature.

The so-called "New Space era" has seen a disruptive change in the business models and manufacturing technologies of launch vehicle companies. However, limited consideration has been given to the benefits that innovation in control theory can bring; not only in terms of increasing the limits of performance but also reducing mission preparation or "missionisation" efforts. Moreover, there is a gap between the current state-of-practice that still relies on linear controls and other modern control techniques that could bring relevant improvements in launcher attitude control; this is the case for nonlinear control algorithms, especially those based on Nonlinear Dynamic Inversion (NDI). NDI is a technique that basically 'cancels' the nonlinearities of a class of nonlinear systems, allowing for a single linear control law to be applied without the need for gain-scheduling across different operational points. Incremental NDI (INDI) is a variation of NDI that generates incremental commands and employs acceleration feedback to reduce model dependency, making it easier to design, and results in being more robust in closed-loop. While INDI has been applied successfully to several aerospace applications, its applicability to launch vehicles has not yet been adequately investigated. The objective of this paper is therefore to introduce and raise awareness of the INDI method among the launcher guidance, navigation, and control (GNC) community, showcasing its implementation on a representative launch ascent application scenario which highlights INDI's strengths and challenges. We present a new, practical approach for stability analysis of INDI for attitude control, and compare INDI with scheduled PD controllers with-and without angular acceleration estimates. Results show that, while INDI controllers are generally more sensitive to sensor noise and actuator delay than linear controllers, their potential benefits outweigh these limitations in terms of robustness and performance.

Linear control of nonlinear processes: recent developments and future directions

This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques. The first scenario addresses the noise itself. The low-frequency noise, traveling as plane waves in a duct, is usually assumed to be broadband random or periodic tonal noise. Linear techniques applied to actively control this noise have been shown to be successful. However, in many practical applications, the noise often arises from dynamical systems, which cause the noise to be nonlinear and deterministic or stochastic, colored, and non-Gaussian. Linear techniques cannot fully exploit the coherence in the noise and, therefore, perform suboptimally. The other scenario is that the actuator in an ANC system has been shown to be nonminimum phase. One of the tasks of the controller, in ANC systems, is to model the inverse of the actuator. Obviously, a linear controller is not able to perform that task. To combat the problems, as mentioned above, a nonlinear controller has been implemented in the ANC system. It is shown in this paper that the nonlinear controller consists of two parts: a linear system identification part and a nonlinear prediction part. The standard filtered-x algorithms cannot be used with a nonlinear controller, and therefore, the control scheme was reconfigured. Computer simulations have been carried out and confirm the theoretical derivations for the combined nonlinear and linear controller.

Experiments have been carried out on models of rigid circular cylinders fitted with three different types of permeable meshes to investigate their effectiveness in the suppression of vortex-induced vibrations (VIV). Measurements of amplitude of vibration and drag force are presented for models with low mass and damping which are free to respond in the cross-flow direction. Results for two meshes made of ropes and cylindrical tubes are compared with the VIV response of a bare cylinder and that of a known suppressor called the “ventilated trousers” (VT). All three meshes achieved an average 50% reduction of the peak response when compared with that of the bare cylinder. The sparse mesh configuration presented a similar behaviour to the VT, while the dense mesh produced considerable VIV response for an indefinitely long range of reduced velocity. All the three meshes have increased drag when compared with that of the bare cylinder. Reynolds number ranged from 5,000 to 25,000 and reduced velocity was varied between 2 and 15.