Sliding Mode Control Strategy for Wind Turbine Power Maximization

The efficiency of the wind power conversions systems can be greatly improved using an appropriate control algorithm. In this work, a sliding mode control for variable speed wind turbine that incorporates a doubly fed induction generator is described. The electrical system incorporates a wound rotor induction machine with back-to-back three phase power converter bridges between its rotor and the grid. In the presented design the so-called vector control theory is applied, in order to simplify the electrical equations. The proposed control scheme uses stator flux-oriented vector control for the rotor side converter bridge control and grid voltage vector control for the grid side converter bridge control. The stability analysis of the proposed sliding mode controller under disturbances and parameter uncertainties is provided using the Lyapunov stability theory. Finally simulated results show, on the one hand, that the proposed controller provides high-performance dynamic characteristics, and on the other hand, that this scheme is robust with respect to the uncertainties that usually appear in the real systems.

可压平面混合层稳定性分析及数值模拟

可压平面混合层是包含复杂多时空尺度运动的非定常流体力学部问题，具有深刻的理论意义和广泛的应用背景。针对该问题所涉及内容的多面性，本文的目的是，基于高精度、高分辨率数值算法的构造、发展和数值行为分析，采用线性稳定性分析和直接数值模拟方法。从理论和计算两方面集中研究压缩性效应、粘性效应、初值效应以及燃烧反应放热效应等对可压平面混合层早期稳定性行为和大尺度拟序涡结构非线性演化的影响。以混合层已有研究成果的分析和综述为开端，论文主体共包括四部分：第一部分是可压平面混合层时间/空间模式数值线性稳定性分析。实现了高精度对称紧致差分格式（SCD）对可压粘性扰动线性稳定性边值问题的求解，对导出的线性和非线性离散特征值问题，提出了两个高效局部解法。研究涉及二维/三维扰动波、无粘/粘性扰动波、特征函数和特征值谱、第一/第二模态、超声速快/慢模态、速度比和密度比等。验证了对流Mach数Mc为一个合理的压缩性参数。指出压缩性效应和粘性效应对最不稳定扰动波的波数（频率）和增长率呈相拟的抑制作用，且时间模式稳定性分析结果在许多方面是可信的。从随机和线性扰动场出发，采用高精度五阶迎风紧致和六阶对称紧致混合差分算法（UCD5/SCD6）对可压平面混合层的稳定性特征进行了直接数值模拟，揭示了初始主导线性扰动与一些实际涡结构非线性作用形态间的内在关联，印证了线性稳定性分析方法的合理性和有效性。第二部分是高精度迎风紧致差分格式（UCD）时空全离散数值行为分析。导出了其一维/二维一般色散表达式。研究表明，UCD格式在高波数区具有内在的全离散耗散和色散特性；其数值群速度的快/慢特征可因CFL数不同而改变；在稳定CFL数下简单附加人工粘性可强化UCD格式在高波数区的耗散量；提高时间精度可放宽稳定CFL数限制；UCD格式的二维全离散色散介质中存在三个不同性质的数值波，其全离散稳定性由数值声波主控。第三部分实现了高精度UCD5/SCD6差分算法对空间发展可压平面混合层的直接数值模拟。通过亚谐扰动波的个数和扰动频率的控制，捕捉到了基频涡的饱和、一次和二次对并等现象，显示了大尺度涡结构与入中初始扰动方式之间的内在联系。利用参数Mc观察了压缩性效应对大尺度涡空间演化及其相互作用的影响。第四部分实现了高精度UCD5/SCD6差分算法对非预混扩散火焰化学反应平面混合层的直接数值模拟。研究指出，放热效应可抑制和延迟涡的形成，使基频涡卷拉伸甚至丧失，混合层Reynolds 应力ρu'v'和流向速度波动关联项u'v'下降，以致涡结构与外流动量交换和标量输运减少，脉动输运能力被削弱，从而混合效率、产物生成率和混合层增长率下降，放热主要通过膨胀效应和斜压效应来抑制大尺度涡的演化。

Robust speed control for a variable speed wind turbine

Modern wind turbines are designed in order to work in variable speed opera-tions. To perform this task, these turbines are provided with adjustable speed generators, like the double feed induction generator (DFIG). One of the main advantages of adjustable speed generators is improving the system efficiency compared with _xed speed generators, because turbine speed can be adjusted as a function of wind speed in order to maximize the output power. However, this system requires a suitable speed controller in order to track the optimal reference speed of the wind turbine. In this work, a sliding mode control for variable speed wind turbines is proposed. The proposed design also uses the vector oriented control theory in order to simplify the DFIG dynamical equations. The stability analysis of the proposed controller has been carried out under wind variations and pa-rameter uncertainties using the Lyapunov stability theory. Finally, the simulated results show on the one hand that the proposed controller provides a high-performance dynamic behavior, and on the other hand that this scheme is robust with respect to parameter uncertainties and wind speed variations, which usually appear in real systems.

Sliding mode position control for real-time control of induction motors

A sliding mode position control for high-performance real-time applications of induction motors in developed in this work. The design also incorporates a simple flux estimator in order to avoid the flux sensors. Then, the proposed control scheme presents a low computational cost and therefore can be implemented easily in a real-time applications using a low cost DSP-processor. The stability analysis of the controller under parameter uncertainties and load disturbances in provided using Lyapunov stability theory. Finally, simulated and experimental results show that the proposed controller with the proposed observer provides a good trajectory tracking and that this scheme is robust with respect to plant parameter variations and external load disturbances.

Adaptive variable structure control law for a variable speed wind turbine

Presentado en el 13th WSEAS International Conference on Automatic Control, Modelling and Simulation, ACMOS'11

Sliding mode control law for a variable speedwind turbine

Modern wind turbines are designed in order to work in variable speed operations. To perform this task, wind turbines are provided with adjustable speed generators, like the double feed induction generator. One of the main advantage of adjustable speed generators is improving the system efficiency compared to fixed speed generators, because turbine speed can be adjusted as a function of wind speed in order to maximize the output power. However this system requires a suitable speed controller in order to track the optimal reference speed of the wind turbine. In this work, a sliding mode control for variable speed wind turbines is proposed. An integral sliding surface is used, because the integral term avoids the use of the acceleration signal, which reduces the high frequency components in the sliding variable. The proposed design also uses the vector oriented control theory in order to simplify the generator dynamical equations. The stability analysis of the proposed controller has been carried out under wind variations and parameter uncertainties by using the Lyapunov stability theory. Finally simulated results show, on the one hand that the proposed controller provides a high-performance dynamic behavior, and on the other hand that this scheme is robust with respect to parameter uncertainties and wind speed variations, that usually appear in real systems.

An adaptive sliding mode control law for the power maximization of the wind turbine system

POWERENG 2011

Sliding mode control strategy for variable speed wind turbines

EFTA 2009

The Convective Instabilities in a Liquid-Vapor System with a Non-equilibrium Evaporation Interface

Rayleigh-Marangoni-B,nard instability in a system consisting of a horizontal liquid layer and its own vapor has been investigated. The two layers are separated by a deformable evaporation interface. A linear stability analysis is carried out to study the convective instability during evaporation. In previous works, the interface is assumed to be under equilibrium state. In contrast with previous works, we give up the equilibrium assumption and use Hertz-Knudsen's relation to describe the phase change under non-equilibrium state. The influence of Marangoni effect, gravitational effect, degree of non-equilibrium and the dynamics of the vapor on the instability are discussed.

Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

Some modified bifurcation problems with application to imperfection sensitivity in buckling

The branching theory of solutions of certain nonlinear elliptic partial differential equations is developed, when the nonlinear term is perturbed from unforced to forced. We find families of branching points and the associated nonisolated solutions which emanate from a bifurcation point of the unforced problem. Nontrivial solution branches are constructed which contain the nonisolated solutions, and the branching is exhibited. An iteration procedure is used to establish the existence of these solutions, and a formal perturbation theory is shown to give asymptotically valid results. The stability of the solutions is examined and certain solution branches are shown to consist of minimal positive solutions. Other solution branches which do not contain branching points are also found in a neighborhood of the bifurcation point.

The qualitative features of branching points and their associated nonisolated solutions are used to obtain useful information about buckling of columns and arches. Global stability characteristics for the buckled equilibrium states of imperfect columns and arches are discussed. Asymptotic expansions for the imperfection sensitive buckling load of a column on a nonlinearly elastic foundation are found and rigorously justified.

Nonexistence of looping trajectories in hydromagnetic waves of finite amplitude. Breaking of waves in a cold collision-free plasma in a magnetic field. On stabilities of periodic waves in a cold collision-free plasma in a magnetic field.

This dissertation consists of three parts. In Part I, it is shown that looping trajectories cannot exist in finite amplitude stationary hydromagnetic waves propagating across a magnetic field in a quasi-neutral cold collision-free plasma. In Part II, time-dependent solutions in series expansion are presented for the magnetic piston problem, which describes waves propagating into a quasi-neutral cold collision-free plasma, ensuing from magnetic disturbances on the boundary of the plasma. The expansion is equivalent to Picard's successive approximations. It is then shown that orbit crossings of plasma particles occur on the boundary for strong disturbances and inside the plasma for weak disturbances. In Part III, the existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Then stability analysis is made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation the cutoff frequency is equal to one-fourth of the electron's gyrofrequency. For transverse propagation the cutoff frequency is so high that waves of all frequencies are stable.

Coupled effects of mechanics, geometry, and chemistry on bio-membrane behavior

Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.

We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.

We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane.

光纤光栅传感器干涉型解调仪的稳定性分析和改进

提出了一种利用两种不同温度系数的光纤光栅对来对解调仪的不稳定性进行改进的方法，并进行了理论分析，研究了影响该解调仪稳定性的几个因素。将所研制的传感器布设在东海大桥上，组成传感网络，并用改进后的光纤光栅解调系统对传感器的信号进行解调。在大桥竣工测试时，该传感解调系统表现出较好的性能。

Understanding Micro- and Macro-Mechanics of Soil Liquefaction: A Necessary Step for Field-Scale Assessment

Liquefaction is a devastating instability associated with saturated, loose, and cohesionless soils. It poses a significant risk to distributed infrastructure systems that are vital for the security, economy, safety, health, and welfare of societies. In order to make our cities resilient to the effects of liquefaction, it is important to be able to identify areas that are most susceptible. Some of the prevalent methodologies employed to identify susceptible areas include conventional slope stability analysis and the use of so-called liquefaction charts. However, these methodologies have some limitations, which motivate our research objectives. In this dissertation, we investigate the mechanics of origin of liquefaction in a laboratory test using grain-scale simulations, which helps (i) understand why certain soils liquefy under certain conditions, and (ii) identify a necessary precursor for onset of flow liquefaction. Furthermore, we investigate the mechanics of liquefaction charts using a continuum plasticity model; this can help in modeling the surface hazards of liquefaction following an earthquake. Finally, we also investigate the microscopic definition of soil shear wave velocity, a soil property that is used as an index to quantify liquefaction resistance of soil. We show that anisotropy in fabric, or grain arrangement can be correlated with anisotropy in shear wave velocity. This has the potential to quantify the effects of sample disturbance when a soil specimen is extracted from the field. In conclusion, by developing a more fundamental understanding of soil liquefaction, this dissertation takes necessary steps for a more physical assessment of liquefaction susceptibility at the field-scale.