Modeling and simulation of thermal chlorine etching of gallium arsenide with application to real-time feedback control

A dynamic model for the simulation of thermal chlorine etching of gallium arsenide is developed. The primary motivation for the development of the simulation is the design and testing of real time adaptive feedback controllers which rely upon in-situ optical measurements of etch depth obtained via spectroscopic ellipsometry. The basis for the model is an empirically derived relationship between etch rate, chlorine pressure, and substrate temperature. The chlorine pressure in the chamber is regulated by a throttle valve which determines the effective pumping rate of a turbo-molecular pump which is used to evacuate chlorine pressure dynamics and a second-order damped harmonic oscillator with zero-order hold valve position command inputs is used to model the dynamics of the throttle valve. An output equation is used to model the fact that ellipsometry based etch depth and chamber pressure can be observed at discrete time intervals. Unmeasurable parameters which appear in the model are identified, and the model is validated using experimental data. An adaptive linear-quadratic Gaussian based controller based on our model which forces etching to precede at a desired rate while estimating the often difficult to measure substrate temperature is designed and then tested using our simulation.     

Nonlinear feedback control of chaotic pendulum in presence of saturation effect

In present paper, a feedback linearization control is applied to control a chaotic pendulum system. Tracking the desired periodic orbits such as period-one, period-two, and period-four orbits is efficiently achieved. Due to the presence of saturation in real world control signals, the stability of controller is investigated in presence of saturation and sufficient stability conditions are obtained. At first feedback linearization control law is designed, then to avoid the singularity condition, a saturating constraint is applied to the control signal. The stability conditions are obtained analytically. These conditions must be investigated for each specific case numerically. Simulation results show the effectiveness and robustness of proposed controller. A major advantage of this method is its shorter chaotic transient time in compare to other methods such as OGY and Pyragas controllers.     

A decentralized volume variations observer for open channels

This paper derives a linear model of open channels enabling to design a decentralized volume variations observer. The proposed observer allows to implement decentralized constant volume controllers under the realistic assumption of non-measurable state. The main advantage of this approach is that each state variable may be reconstructed on the base of only local measurements, thus not vanishing the advantage of decentralization in the controller.Since the fundamental property which must be retained for all possible perturbations of the plant is stability of the feedback system, this paper studies whether a given decentralized controller used in conjunction with the proposed observer is robust when output-multiplicative perturbations occur due to the low-frequency approximations and to the variations with respect to the reference configuration of uniform flow.     

Positive real control for 2-D discrete delayed systems via output feedback controllers

This paper considers the problem of positive real control for two-dimensional (2-D) discrete delayed systems in the Fornasini–Marchesini second local state-space model. Attention is focused on the design of dynamic output feedback controllers, which guarantee that the closed-loop system is asymptotically stable and the closed-loop transfer function is extended strictly positive real. We first present a sufficient condition for extended strictly positive realness of 2-D discrete delayed systems. Based on this, a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality (LMI). When the LMI is feasible, an explicit parametrization of a desired output feedback controller is presented. Finally, we provide a numerical example to demonstrate the application of the proposed method.     

An indirect Lyapunov approach to robust stabilization for a class of linear fractional-order system with positive real uncertainty

The paper is concerned with the problem of the robust stabilization for a class of fractional order linear systems with positive real uncertainty under Riemann–Liouville (RL) derivatives. Firstly, by utilizing the continuous frequency distributed model of the fractional integrator, the fractional order system is expressed as an infinite dimensional integral order system. And via using indirect Lyapunov approach and linear matrix inequality techniques, sufficient condition for robust asymptotic stability of the fractional order systems and design methods of the state feedback controller are presented. Secondly, by using matrixs singular value decomposition technique the static output feedback controller and observer-based controller for asymptotically stabilizing the fractional order systems are derived. Finally, the validity of the proposed methods are demonstrated by numerical examples.     

An LMI approach to positive real control for discrete time-delay systems

This paper focuses on the problem of positive real controlfor discrete time-delay systems. The problem we address is thedesign of a dynamic output feedback controller, which guaranteesthe asymptotic stability of the closed-loop system and achievesthe extended strictly positive realness of a certain closed-looptransfer function. Then, a condition for extended strictly positiverealness for discrete-delay systems is developed. Based on this,a sufficient condition for the existence of the desired controllersis proposed in terms of three linear matrix inequalities (LMIs).When these LMIs are feasible, an explicit parametrization ofthe desired output feedback controller is presented. An illustrativeexample is given to demonstrate the applicability of the proposedapproach.     

On output feedback control of singularly perturbed systems

We treat the problem of robustness of output feedback controllers with respect to singular perturbations. Given a singularly perturbed control system whose boundary layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a (possibly dynamical) output feedback controller, we present a sufficient condition which ensures that the system obtained by applying the same controller to the original full order singularly perturbed control system is exponentially stable for sufficiently small values of the perturbation parameter. This condition, which is less restrictive than those previously given in the literature, is shown to be always satisfied when the singular perturbation is due to the presence of fast actuators and/or sensors. Furthermore, we show explicitly that, in the linear time-invariant case, if this condition is not satisfied then there exists an output feedback controller which stabilizes the reduced order system but destabilizes the full order system.     

Boundary feedback stabilization of Boussinesq equations

The aim of this work is to design oblique boundary feedback controller for stabilizing the equilibrium solutions to Boussinesq equations on a bounded and open domain in R~2. Two kinds of such feedback controller are provided, one is the proportional stabilizable feedback control, which is obtained by spectrum decomposition method, while another one is constructed via the Ricatti operator for an infinite time horizon optimal control problem.An example of periodic Boussinesq flow in 2-D channel is also given.     

基于实物期权的风险投资退出决策模型研究

针对传统NPV方法应用于风险投资退出决策的局限,本文利用实物期权理论,将可观测的利润流作为内生变量,建立了风险投资的最优退出决策模型,通过模型求出了不同退出方式条件下的实物期权价值和退出时机的临界值,并用实例进行了说明,有效地解决了风险投资的退出方式的选择问题,使得风险投资的退出决策过程更具操作性和现实性。     

Multiphase transient flow model in wellbore annuli during gas kick in deepwater drilling based on oil-based mud

Transient-state gas and oil-based mud (OBM) two-phase flow in wellbore annuli will occur during gas kick. The phase behavior of influx gas and OBM will make the gas kick during OBM drilling more complicated. There are three possible cases in an annulus: only liquid flow in the entire annulus, gas and liquid two-phase flow in part of the annulus, and gas and liquid two-phase flow in the entire annulus. First, the phase behaviors of gas and OBM in wellbore annuli are studied based on the phase behavior of methane and diesel. A multiphase transient-flow model in annuli during gas kick based on OBM is then established based on gas–liquid two-phase flow theory and on flash theory in annuli. The influences of phase behavior in annuli and annular geometry are taken into account. The local flow parameters are predicted by the hydrodynamic models and the local thermodynamic parameters are predicted by the heat-transfer models in the corresponding flow pattern. The proposed model has a better performance, compared with two other models, against the published experimental data. Finally, the variation of pit gain, well-bottom hole pressure, and gas void fraction are obtained, leading to a better understanding of the occurrence and evolution mechanism of gas kick during deepwater drilling.     

离散交通流模型的反馈线性化与拥堵控制

在自动化高速公路环境下,提出一种改进的宏观离散交通流模型密度控制方法.利用反馈线性化方法,将宏观离散交通流模型转换为一般容易处理的线性系统模型,简化了密度控制器的设计.利用线性系统中具有输入变换的跟踪反馈控制方法,对线性化后的系统模型设计控制律.通过控制该线性系统的状态变量,间接稳定离散交通流模型中的交通流密度,达到对道路交通流拥堵的控制.同时给出设计方法和步骤,仿真实例说明了方法的实用性.     

Coupled lattice Boltzmann method for simulating electrokinetic flows: A localized scheme for the Nernst–Plank model

We present a coupled lattice Boltzmann method (LBM) to solve a set of model equations for electrokinetic flows in micro-/nano-channels. The model consists of the Poisson equation for the electrical potential, the Nernst–Planck equation for the ion concentration, and the Navier–Stokes equation for the flows of the electrolyte solution. In the proposed LBM, the electrochemical migration and the convection of the electrolyte solution contributing to the ion flux are incorporated into the collision operator, which maintains the locality of the algorithm inherent to the original LBM. Furthermore, the Neumann-type boundary condition at the solid/liquid interface is then correctly imposed. In order to validate the present LBM, we consider an electro-osmotic flow in a slit between two charged infinite parallel plates, and the results of LBM computation are compared to the analytical solutions. Good agreement is obtained in the parameter range considered herein, including the case in which the nonlinearity of the Poisson equation due to the large potential variation manifests itself. We also apply the method to a two-dimensional problem of a finite-length microchannel with an entry and an exit. The steady state, as well as the transient behavior, of the electro-osmotic flow induced in the microchannel is investigated. It is shown that, although no external pressure difference is imposed, the presence of the entry and exit results in the occurrence of the local pressure gradient that causes a flow resistance reducing the magnitude of the electro-osmotic flow.     

Flow stabilisation by Dirichlet boundary control

Re–attachment of separated flow is investigated for the model problem of a backward facing step at moderate Reynolds number (up to 400), where the length of the detachment zone is reduced by blowing in (or sucking out) fluid through a nozzle below the step. Both optimal feed forward control as well as a simple feedback control are considered, with surprisingly good results obtained by a very simple (non–optimal) linear feedback controller. Numerical results are shown. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The galerkin method and feedback control of linear distributed parameter systems

In the development of feedback control theory for distributed parameter systems (DPS), i.e., systems described by partial differential equations, it is important to maintain the finite dimensionality of the controller even though the DPS is infinite dimensional. Since this dimension is directly related to the available on-line computer capacity, it must be finite (and not very large) in order to make the controller implementable from an engineering standpoint. In previous work, it has been our intention to investigate what can be accomplished by finite-dimensional control of infinite-dimensional systems; in particular, we have concentrated on controller design and closed-loop stability. The starting point for all of this is some means for producing a finite-dimensional approximation—a reduced-order model—of the actual DPS. When the “modes” of the DPS are known, the natural candidate for model reduction is projection onto the modal subspace spanned by a finite number of critical modes. Unfortunately, in real engineering systems, these modes are never known exactly and some other reasonable approximation must be used. In this paper, the model reduction is based on the well-known Galerkin procedure. We generate the Galerkin reduced-order model and develop a finite-dimensional controller from it; then we analyze the stability of this controller in closed loop with the actual DPS. Our results indicate conditions under which model reduction based on consistent Galerkin approximations will lead to stable finite-dimensional control.     

Normal Feedback Stabilization of Periodic Flows in a Two-Dimensional Channel

We consider a two-dimensional incompressible channel flow with periodic condition along one axis. We stabilize the linearized system by a boundary feedback controller with vertical velocity observation, which acts on the normal component of the velocity only. The stability is achieved without any a priori condition on the viscosity coefficient, that is, on the Reynolds number.     

A systematic comparison of buildingEXODUS predictions with experimental data from the Stapelfeldt trials and the Milburn House evacuation

In this paper, the buildingEXODUS evacuation model is described and discussed and attempts at qualitative and quantitative model validation are presented. The data sets used for validation are the Stapelfeldt and Milburn House evacuation data. As part of the validation exercise, the sensitivity of the buildingEXODUS predictions to a range of variables is examined, including occupant drive, occupant location, exit flow capacity, exit size, occupant response times and geometry definition. An important consideration that has been highlighted by this work is that any validation exercise must be scrutinised to identify both the results generated and the considerations and assumptions on which they are based. During the course of the validation exercise, both data sets were found to be less than ideal for the purpose of validating complex evacuation models. However, the buildingEXODUS evacuation model was found to be able to produce reasonable qualitative and quantitative agreement with the experimental data.     

合成射流激励器射流矢量控制的物理因素

对不同出口构型合成射流激励器进行射流矢量控制进行了数值研究,并对决定合成射流激励器射流矢量控制的物理因素进行了分析和归纳．低压区位置和面积及其压强梯度、合成射流动量分量、合成射流对主流的卷吸率是直接控制主射流矢量力和矢量角的物理因素．合成射流的3个特征参数直接影响和控制低压区的面积及其压强梯度,合成射流激励器出口台阶和出口斜喷角都对低压区位置、面积和合成射流对主流的卷吸率有影响和调节作用,合成射流激励器出口斜喷角还直接控制合成射流动量分量．基于对合成射流激励器射流矢量控制物理因素的分析,确定了控制物理因素的源变量,建立了由控制能力函数和调节功能函数组成的合成射流矢量控制初步模型,初步模型能够对源变量引起的合成射流激励器射流矢量控制效率不同作出解释,并进一步指出了进行射流矢量控制的最佳激励器是充分利用调节功能函数．     

Controlling chaotic Chua''s circuit based on piecewise quadratic Lyapunov functions method

In this paper, we present a linear feedback controller design method for controlling chaotic Chua's circuit based on piecewise quadratic Lyapunov functions. Firstly, we get the piecewise linear differential inclusions (pwLDIs) model of tracking error dynamics, then we design a linear state feedback controller to stabilize it based on the piecewise quadratic Laypunov functions. Finally, we give some numerical simulations to demonstrate the effectiveness of our theoretical results.     

Delay-dependent robust control for uncertain discrete-time singular systems with time-delays

The robust memoryless state feedback H_∞ control problem for uncertain time-delay discrete-time singular systems is discussed. Under a series of equivalent transformation, the equivalence of this problem and the robust state feedback H_∞ control problem for standard state-space uncertain time-delay discrete-time systems is presented. In terms of matrix inequality, the delay-dependent sufficient condition for the solution of this problem is given, the design method of the memoryless state feedback controller and the controller are also given.