Boundary control of a parallel-flow heat exchanger by input–output linearization

A design of the control of the internal fluid temperature at the outlet of a parallel-flow heat exchanger by manipulating the inlet external fluid temperature is proposed. The dynamic model of the heat exchanger is given by two partial differential equations that are used without spatial discretization to design the control law. Based on nonlinear control, a state-feedback law that ensures a desired performance of a measured output defined as the spatial weighted average temperature of the internal fluid is derived. Then, in order to control the outlet internal fluid temperature, a control strategy is proposed where an external controller is introduced to provide the set point of the considered measured output by taking as input the error between the outlet internal fluid temperature and its desired set point. As the designed control law is a state feedback of distributed nature, for practical application, a Kalman filter is used to reconstruct the entire state of the system from the measurements of the outlet fluids temperatures. The closed-loop system is shown to be exponentially stable. The validity of the proposed control design is examined in simulation by considering the tracking and perturbation rejection problems.     

Topology optimization for fluid–thermal interaction problems under constant input power

This paper deals with density-based topology optimization considering fluid and thermal interactions, in which the Navier–Stokes and heat transport equations are coupled. We particularly focus on designing heat exchangers. In the engineering context, heat exchangers are designed while considering a certain amount of input power. Therefore it is important to maximize the performance of a heat exchanger under a constant input power. In this paper we propose a way to control the input power by introducing an extra integral equation. To be more precise, in the fluid analysis, the inlet pressure is determined by solving the extra integral equation together with the Navier–Stokes equation. By doing this we can keep the inlet power constant even when the flow channels are changed in the optimization process. Consequently, the system of equations of the fluid field takes an integrodifferential form. On the other hand, in the heat transport analysis, a single governing equation is defined for simultaneously modeling both the solid and fluid parts. The design variable is a fluid fraction whose distribution represents the topology of the solid and fluid domains. When designing heat exchangers, two different heat conditions are considered in the formulation of the optimization problems, namely temperature-dependent and temperature-independent heat sources. Through the numerical examples for designing flow channels in a heat exchanger, it is shown that distinct topologies can be obtained according to the input power and the heat source conditions.     

Boundary geometric control of a linear Stefan problem

This paper addresses the geometric control of the position of a liquid–solid interface in a melting process of a material known as Stefan problem. The system model is hybrid, i.e. the dynamical behavior of the liquid-phase temperature is modeled by a heat equation while the motion of the moving boundary is described by an ordinary differential equation. The control is applied at one boundary as a heat flux and the second moving boundary represents the liquid–solid interface whose position is the controlled variable. The control objective is to ensure a desired position of the liquid–solid interface. The control law is designed using the concept of characteristic index, from geometric control theory, directly issued from the hybrid model without any reduction of the partial differential equation. It is shown by use of Lyapunov stability test that the control law yields an exponentially stable closed-loop system. The performance of the developed control law is evaluated through simulation by considering zinc melting.     

具有边界扰动的不确定Euler-Bernoulli梁方程输出反馈控制

针对带有边界扰动、内部不确定扰动和外部扰动的Euler-Bernoulli梁方程,为克服传统扰动观测器引入的高增益及未知扰动导数难以准确求解问题,本文将主动干扰抑制控制(ADRC)技术应用到Euler-Bernoulli梁方程这个偏微分方程(PDE)系统上,提出并设计了一种新的在线扰动观测器,可实时估计扰动值.依据估计扰动值,设计了一个边界输出反馈控制器.仿真结果表明,本文所提出的方法可很好地实现对内部不确定扰动和外部扰动的估计,配合输出反馈控制器,可对边界扰动进行有效抑制,进而实现系统的指数稳定.     

Effects of slip on sheet-driven flow and heat transfer of a non-Newtonian fluid past a stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian fluid due to a stretching surface subject to partial slip is considered. The constitutive equation of the non-Newtonian fluid is modeled by that for a third grade fluid. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHFcase) in presence of a uniform heat source or sink. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip, magnetic field, heat source (sink) parameter and the third grade fluid parameters on the velocity, skin friction coefficient and the temperature field. It is interesting to find that slip decreases the momentum boundary layer thickness and increases the thermal boundary layer thickness, whereas the third grade fluid parameter has an opposite effect on the thermal and velocity boundary layers.     

基于内流动力学的海洋输油柔性立管鲁棒边界控制

海洋输油柔性立管的振动是引起立管疲劳破坏的主要原因,对其研究边界控制是消除振动疲劳、减少断裂的有效方法.本文引入内流动力学,完善了立管原始无穷维分布参数模型,更好地表达了柔性立管的动力学响应.为抑制柔性立管在内外流激励下的振动奠下基础,本文用Lyapunov直接法对柔性立管系统的稳定性和状态一致有界性进行了证明,设计了边界控制器调节柔性立管的振动,其中控制器使用了符号函数来消除不确定性环境扰动对振动控制效果的影响,提高了系统的鲁棒性.仿真实验表明本文所设计的控制算法有效地减少了柔性立管的振动偏移量.     

ODE–热方程级联系统的事件触发控制

本文针对常微分方程(ODE)耦合偏微分方程(PDE)建模的分布式参数多智能体系统进行研究, 针对一致性同步问题, 提出了事件触发的网络化ODE–热方程级联系统多智能体一致性边界交互协议. 本文考虑的热方程左边界为Neumann边界条件, 并且与ODE系统耦合, 右边界为绝热边界条件. 假设网络化多智能体系统的连接方式为全联通有向拓扑图, 给出ODE–热方程级联系统的多智能体的一致性控制协议. 另外针对现有数字式控制器, 设计了事件触发的一致性控制协议, 并利用李雅普诺夫函数验证了在事件触发条件下ODE–热方程级联系统的稳定性. 最后给出了由5个ODE–热方程级联的多智能体系统的仿真结果, 验证了事件触发控制器的有效性.     

Nonlinear observer-based Lyapunov boundary control of distributed heat transfer mechanisms for membrane distillation plant

This paper presents a nonlinear observer-based Lyapunov control for a membrane distillation (MD) process. The control considers the inlet temperatures of the feed and the permeate solutions as inputs, transforming it to boundary control process, and seeks to maintain the temperature difference along the membrane boundaries around a sufficient level to promote water production. MD process is modeled with advection diffusion equation model in two dimensions, where the diffusion and convection heat transfer mechanisms are best described. Model analysis, effective order reduction and parameters physical interpretation, are provided. Moreover, a nonlinear observer has been designed to provide the control with estimates of the temperature evolution at each time instant. In addition, physical constraints are imposed on the control to have an acceptable range of feasible inputs, and consequently, better energy consumption. Numerical simulations for the complete process with real membrane parameter values are provided, in addition to detailed explanations for the role of the controller and the observer.     

Vibration control of the flexible manipulator with input constraints and external disturbances based on Nussbaum function

In this paper, a boundary control scheme based on the partial differential equation (PDE) model is proposed for the vibration control problem of the flexible manipulator with input constraints and external disturbances. Based on the backstepping method, two boundary controllers are designed to stabilize the position loop subsystem and the attitude loop subsystem, respectively, and auxiliary systems based on the smooth hyperbolic tangent function and Nussbaum function are designed in the controllers to deal with the input saturation and external disturbances. The Nussbaum function can overcome the difficulties in controller design and stability analysis caused by the derivatives of smooth hyperbolic tangent functions. The well-posedness of the closed-loop system is proven by employing the semigroup theory, and the uniformly bounded stability is proved by Lyapunov direct method. Finally, the performance of the proposed control laws is verified by numerical simulations.     

Stabilization of an unstable tubular reactor by nonlinear passive output feedback control

The multiple–input multiple–output (MIMO) output feedback (OF) control problem of an exothermic multi-jacket tubular open-loop unstable reactor is addressed. Over its axial length, the reactor has several equally sized cooling jackets. The controller must adjust the jacket temperatures on the basis of per jacket temperature measurements so that the closed-loop system is robustly stable. The problem is solved within a constructive framework, by combining notions and tools from chemical reactor engineering and partial differential equations (PDEs) control systems theory. The result is a MIMO nonlinear OF dynamic control design with (i) a decentralized MIMO passive state feedback (SF) controller implemented with a pointwise observer (PWO), (ii) closed-loop stability conditions in terms of sensor set and control gains, and (iii) efficient late lumping-based on-line implementation. The design is put in perspective with industrial PI and inventory control, and applied to a representative example through numerical simulation with favorable comparison against adaptive controllers.     

A Si/Glass Bulk-Micromachined Cryogenic Heat Exchanger for High Heat Loads: Fabrication, Test, and Application Results

This paper reports on a micromachined Si/glass stack recuperative heat exchanger with in situ temperature sensors. Numerous high-conductivity silicon plates with integrated platinum resistance temperature detectors (Pt RTDs) are stacked, alternating with low-conductivity Pyrex spacers. The device has a $1 times 1hbox{-cm}^{2}$ footprint and a length of up to 3.5 cm. It is intended for use in Joule–Thomson (J–T) coolers and can sustain pressure exceeding 1 MPa. Tests at cold-end inlet temperatures of 237 K–252 K show that the heat exchanger effectiveness is 0.9 with 0.039-g/s helium mass flow rate. The integrated Pt RTDs present a linear response of 0.26%–0.30%/K over an operational range of 205 K–296 K but remain usable at lower temperatures. In self-cooling tests with ethane as the working fluid, a J–T system with the heat exchanger drops 76.1 K below the inlet temperature, achieving 218.7 K for a pressure of 835.8 kPa. The system reaches 200 K in transient state; further cooling is limited by impurities that freeze within the flow stream. In J–T self-cooling tests with an external heat load, the system reaches 239 K while providing 1 W of cooling. In all cases, there is an additional parasitic heat load estimated at 300–500 mW.$ hfill$[2009-0093]      

Distributed control of nonlinear diffusion systems by input–output linearization

This paper addresses the distributed control by input–output linearization of a nonlinear diffusion equation that describes a particular but important class of distributed parameter systems. Both manipulated and controlled variables are assumed to be distributed in space. The control law is designed using the concept of characteristic index from geometric control by using directly the PDE model without any approximation or reduction. The main idea consists in the control design in assuming an equivalent linear diffusion equation obtained by use of the Cole–Hopf transformation. This framework helps to demonstrate the closed‐loop stability using some concepts from the powerful semigroup theory. The performance of the proposed controller is successfully tested, through simulation, by considering a nonlinear heat conduction problem concerning the control of the temperature of a steel plate modeled by a nonlinear heat equation with Dirichlet boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Repetitive control of tubular heat exchangers

Effective operation of heat exchangers involves optimum control of the fluid outlet temperature. Several ideas have been proposed in the literature to cope with intrinsic resonance dynamics aimed at widening the bandwidth of the closed-loop system to achieve fast, well-damped responses in controlling the outlet fluid temperature by means of the steam temperature. This is also the main purpose of this article, in which the use of a repetitive control scheme is proposed to take resonance dynamics into account when residence time is variable, as in this case the control variable is the fluid flow rate and not the steam temperature. The scheme is based on a model of the tubular heat exchanger dynamics in which the explicit terms of resonance are cancelled out by the controller. Simulation results are provided both for a typical tubular heat exchanger and for a special sort of heat exchanger, the distributed collector field of a solar power plant.     

空间应用流体回路旁路控制算法仿真研究

针对复杂流体回路流量控制问题,设计了一种适应多种工况的改进型模糊PID控制器。应用集总参数法,使用液阻系数和热交换分别推导了空间应用流体回路流量和温度变化模型,同时建立了回路中离心泵、步进电动阀、液液热交换器等重要组件的数学模型。以此仿真模型为基础,基于模糊控制理论设计了一种结合阀门状态信号的改进型自整定模糊PID控制器,解决下游负载变化对主路影响的问题。文中对包括改进型模糊PID在内的4种控制算法效果进行了对比。仿真结果表明,改进型自整定控制方法控制效果最好,具有良好的非线性适应性,相比传统PID减少了实验柜阀门关闭前后50%超调量和75%响应时间。     

Self-tuning and stable adaptive control of a batch polymerization reactor

Two adaptive control techniques are evaluated by application to a realistic mathematical model of a suspension polyvinyl chloride (PVC) reactor. Both techniques, the self-tuning regulator and a globally stable adaptive control algorithm, prove to be very robust and give excellent control of the temperature or the rate of conversion in the PVC reactor by manipulating the heat removal rate from the reactor jacket. Satisfactory regulation and setpoint changes in the temperature and the conversion rate are obtained in each case even in the presence of measurement noise and highly nonlinear reactor dynamics. The performance of the two adaptive techniques is compared with the performance of a classical, PID controller. The adaptive controllers are shown to always outperform the PID controller.     

Modeling and boundary control of a flexible marine riser coupled with internal fluid dynamics

In this paper, vibration reduction of a flexible marine riser with time-varying internal fluid is studied by using boundary control method and Lyapunov’s direct method. To achieve more accurate and practical riser’s dynamic behavior, the model of marine riser with time-varying internal fluid is modeled by a distributed parameter system (DPS) with partial differential equations (PDEs) and ordinary differential equations (ODEs) involving functions of space and time. The dynamic responses of riser are completely different if the time-varying internal fluid is considered. Boundary control is designed at the top boundary of the riser based on original infinite dimensionality PDEs model and Lyapunov’s direct method to reduce the riser’s vibrations. The uniform boundedness and closed-loop stability are proved based on the proposed boundary control. Simulation results verify the effectiveness of the proposed boundary control.     

Sliding Mode Control for Flexible-link Manipulators Based on Adaptive Neural Networks

This paper mainly focuses on designing a sliding mode boundary controller for a single flexible-link manipulator based on adaptive radial basis function (RBF) neural network. The flexible manipulator in this paper is considered to be an Euler-Bernoulli beam. We first obtain a partial differential equation (PDE) model of single-link flexible manipulator by using Hamiltons approach. To improve the control robustness, the system uncertainties including modeling uncertainties and external disturbances are compensated by an adaptive neural approximator. Then, a sliding mode control method is designed to drive the joint to a desired position and rapidly suppress vibration on the beam. The stability of the closed-loop system is validated by using Lyapunov’s method based on infinite dimensional model, avoiding problems such as control spillovers caused by traditional finite dimensional truncated models. This novel controller only requires measuring the boundary information, which facilitates implementation in engineering practice. Favorable performance of the closed-loop system is demonstrated by numerical simulations.     

基于模型预测控制的数据中心节能调度算法

如今日益增长的数据中心能耗,特别是冷却系统能耗已日益受到重视,降低系统能耗能够减少数据中心碳排放.提出了一种基于模型预测控制（model prediction control,简称MPC）的节能调度策略,该策略可以有效地减小数据中心冷却能耗.该方法采用动态电压频率调节技术来调整计算节点频率,从而减少节点间的热循环;所有节点的峰值温度可被保持在温度阈值下,在任务的执行中稳态误差较小.该方法可以通过动态频率调节来抑制由于负载类型变化造成的模型不确定性带来的内部扰动,分析结果表明,基于模型预测的温控算法系统开销较小,具有良好的可扩展性.基于该算法设计的控制器能够有效地降低输入温度,提高数据中心能耗效率.通过在实际数据中心内运行的模拟网上书店,该方法与安全最小热传递算法和传统反馈温控算法这两种经典方法相比,无论是在正常条件下还是在扰动存在的情况下都能取得较好的温度抑制效果,系统性能如吞吐率也达到最大.在相同的负载条件下,该方法能够获得最小的输入峰值温度和最小的冷却能耗.     

Distributed feedback design for systems governed by the wave equation

This article deals with the geometric control of a one-dimensional non-autonomous linear wave equation. The idea consists in reducing the wave equation to a set of first-order linear hyperbolic equations. Then, based on geometric control concepts, a distributed control law that enforces the exponential stability and output tracking in the closed-loop system is designed. The presented control approach is applied to obtain a distributed control law that brings a stretched uniform string, modelled by a wave equation with Dirichlet boundary conditions, to rest in infinite time by considering the displacement of the middle point of the string as the controlled output. The controller performances have been evaluated in simulation by considering both tracking and disturbance rejection problems. The robustness of the controller has also been studied when the string tension is subjected to sudden variations.     

柔性卫星系统的振动自适应边界控制

针对受外部干扰和具有结构参数不确定性的柔性卫星系统,为了抑制其振动和避免控制溢出问题,采用Hamilton变分原理和Euler-Bernoulli梁理论建立了结构无穷维偏微分方程模型,随后基于该无穷维模型设计了带有干扰自适应律的自适应边界控制对柔性卫星振动进行主动控制,并证明了闭环柔性卫星控制系统解的存在性、唯一性和收敛性.最后,仿真结果验证了所设计的自适应边界控制算法的有效性.