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.     

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.     

An application of geometric programming to heat exchanger design

This paper presents a geometric programming model for optimal design of refrigeration heat exchangers. A dual method is used to solve the design problem to obtain the optimum values of the design variables. Analyses are performed to determine the changes in the optimum values of the design variables with respect to the changes in the unit costs of components, material specifications, and tube sizes.     

An application of stochastic geometric programming to heat exchanger design

This article presents an application of stochastic geometric programming to heat exchanger design. The design problem has been formulated based on the geometry and heat transfer characteristics of a horizontal shell-and-tube condenser for industrial refrigeration plants. Solutions of various stochastic geometric programming models indicate a range of estimates of the optimum life cycle cost and the values of the corresponding design parameters such as physical dimensions of the heat exchanger. The method presented here can be applied to other engineering design problems by appropriately modifying the problem formulation.     

列管式热交换器的特征模型控制

列管式热交换器具有时滞和大惯性的特点,其出口温度会受到冷热流体流量和入口温度等的干扰,一般的PID控制系统的超调量大,过渡时间长,动态特性较差;本文通过研究热交换器的过程特性,建立对象特征模型,利用在线辨识构建自适应控制律,实时更新控制器参数,使用西门子SIMATIC PCS7对热交换器对象进行出料口的温度控制。结果表明,用该方法建立的热交换器控制系统能够很好地克服对象存在的各种扰动,缩短了过渡过程时间,具有良好的动态性能。     

Optimal setpoint control of complex heat exchanger systems

This paper presents an approach for calculating the best way of distributing the streams following through a certain class of complex heat exchanger systems in order to achieve maximum heat recovery within the system. A computer code has been developed by which the described method is demonstrated, off-line, for two real cases. This program can be readily integrated into an over-all, on-line computer control system for any complex process consisting of an exchanger system of this class. Using an accurate and detailed heat exchanger model, the exit temperatures of each exchanger are calculated by a simple mathematical procedure based on Gilmour's design method. This procedure has been included in a general model for the complete scheme of the system. The scheme is made up of a series of heat exchanger groups with parallel paths in each group. The optimal distribution of the streams within a group is found by the direct search method of Hooke and Jeeves, modified to include constraints; while the overall optimization of the system is achieved via dynamic programming.     

Stability of a heat exchanger feedback control system using the circle criterion

The standard linearized model of a controlled heat exchanger in the form of a system of two first-order PDEs is interpreted as an abstract semigroup system on an appropriately selected Hilbert state space. We analyse some its basis properties: exponential stability, admissibility of an observation functional and regularity of the system impulse response. Next we give a proof of a version of the circle criterion which bases on the use of the Leray–Schauder fixed point theorem jointly with a uniqueness result. The circle criterion is then implemented to a feedback control system of the heat exchanger with a proportional controller and a non-linear valve in the feedback loop. All considerations are illustrated by a numerical example of the heat exchanger installed in central heating system at the AGH University of Science and Technology, Cracow, Poland, for which we estimate feasible settlements of the proportional controller.     

Feedback linearisation of a heat exchanger

A discrete-time nonlinear heat exchanger model is linearised via the feedback linearisation technique. Explicit necessary and sufficient conditions for feedback linearisation of the heat exchanger model in terms of parameters directly related to heat transfer parameters are derived. Some useful results relating to independence of distributions with respect to input are also derived in the process.     

Artificial neural network control of a heat exchanger in a closed flow air circuit

This paper experimentally investigates the control of a heat exchanger in a closed flow air circuit. The temperature inside the test section of the test facility has been maintained at a set value by variation of air flow rate over the heat exchanger tube surface and the water flow inside the heat exchanger tubes. The neural network based control has been implemented in a Labview platform and compared with the PID control. The performance of the controller has been investigated for multiple changes in set points and under externally imposed disturbance. The neural network based control has higher speed of response and the steady-state error for the neural network control has a smaller average value than that of the PID control. The control action based on the neural network technique shows less oscillation in comparison to that of the PID based control. Dual actuations, i.e. both air flow and water flow control, have better performance than that with single actuation, i.e. either air flow or water flow control. Both the ANN and PID based control are equally robust in the presence of externally imposed disturbance.     

换热器热焓控制系统的研究与实现

若换热器出口物料是汽、液混合相,则温度与热焓之间没有单值关系,应采用热焓控制.根据蒸汽加热器的热量衡算式,分析确定蒸汽加热器出口物料的热焓控制方案,讨论基于GE 90-30 PLC的热焓控制系统的硬件配置、主要组态策略,上位机组态软件选用美国GE Fanuc自动化公司的自动化监控软件CIMPLICITY HMI实现热焓调节器组件的组态设计.系统实用表明,该控制方案可保证能量平衡的精确控制,避免能量损耗,实现换热器整体操作的最优化,提高企业经济效益.     

原油换热网络多变量预测控制

针对原油换热网络输入输出变量多、传统的控制方法控制难度大等问题,本文建立了用于仿真的Simulink辨识模型.利用模型预测控制原理,采用旁路控制的方法,借助预测控制工具箱(MPC toolbox)实现对换热网络Simulink模型的多变量预测控制,实现了输入变量平稳、输出变量控制稳定、控制精确及动态响应时间短等优点.在本机控制的基础上,借助OPC工具箱实现不同PC机问MATLAB与PHD数据库的实时交换,达到实时控制的目的,进而实现了整个换热网络的实时多变量预测控制.     

Model reduction and control of reactor–heat exchanger networks

This paper focuses on the dynamics and control of process networks consisting of a reactor connected with an external heat exchanger through a large material recycle stream that acts as an energy carrier. Using singular perturbation arguments, we show that such networks exhibit a dynamic behavior featuring two time scales: a fast one, in which the energy balance variables evolve, and a slow time scale that captures the evolution of the terms in the material balance equations. We present a procedure for deriving reduced-order, non-stiff models for the fast and slow dynamics, and a framework for rational control system design that accounts for the time scale separation exhibited by the system dynamics. The theoretical developments are illustrated with an example and numerical simulation results.     

考虑换热器详细设计的换热网络综合的研究进展

随着对工业生产成本控制要求的不断提高,换热网络优化的深入研究已经引起了越来越多研究人员的重视。在换热网络综合过程中考虑换热器的详细设计是换热网络综合细化深入研究的一个重要方面,可以降低换热网络的年度总费用,并且提高换热网络综合结果的实际可行性。本文通过文献中的算例结果分析,考虑换热器详细设计的换热网络综合的总费用明显低于不考虑换热器详细设计的总费用,阐述了换热网络综合中考虑换热器详细设计的必要性,强调了换热器的详细设计对换热网络综合的影响。文献中考虑换热器详细设计进行换热网络综合时主要采用了夹点分析法和数学规划法,夹点分析法综合换热网络虽然使包含换热器设计的换热网络结构变得简化易于求解,但是无法保证结果是最优解,而数学规划法综合换热网络能有效的考虑换热器详细设计对换热网络综合的影响,但是考虑换热器详细设计也大大增加了模型的复杂性,本文对此进行了对比和评述,同时认为深入研究换热网络细化设计研究并利用快速而高效的算法搜索全局最优解是未来研究方向。     

换热网络的分析

通过对换热网络的研究发现,当物流有分流时,换热网络分析的数学模型为非线性规划问题。本文给出换热网络分析的非线性规划模型,同时优化各路分流的流量及换热单元进出口温度。经模型转化,用复合形法与线性规划法的双层组合求解,成功地解决了换热网络分析中非线性规划的求解问题。经实例考核计算证明,本文所建立的数学模型是正确可靠的,使用的双层组合法与其它方法相比,方法简单实用,结果准确,可在工程研究、设计中应用,分析后所得的最佳参数可大大提高换热网络的热回收量,节能效益十分显著。     

输出约束条件下一类热传导方程的边界控制

约束问题普遍存在于物理系统中,如何解决分布参数系统的约束问题还没有有效的方法.本文以一类非齐次的热传导方程作为研究对象,设计了一种新型的边界控制方法来稳定系统状态并解决热传导方程的约束问题.为此首先简要地介绍了由偏微分方程和常微分方程共同描述的热传导方程.然后,在未知的分布式外界扰动的影响下,设计一种新型的基于障碍-积分型李雅普诺夫函数的边界控制方法.此方法是基于原始的分布参数系统模型,没有任何的模型简化,因此有效地避免了溢出不稳定问题.本文采用李雅普诺夫方法证明系统稳定性并保证系统的边界输出约束在一定的范围内.最后采用有限差分法进行仿真验证,仿真结果进一步证明了所提出的边界控制方法的有效性.     

Stability analysis of a degenerate hyperbolic system modelling a heat exchanger

Mathematical modelling of a heat exchanger in a carbon dioxide heat pump, an evaporator, is considered. A reduced model, called the the zero Mach-number limit, is derived from the Euler equations of compressible liquid flow through elimination of time scales associated with sound waves. The well-posedness of the resulting partial differential-algebraic equation (PDAE) is investigated by analysis of a frozen coefficient linearisation as well as by numerical experiments.     

Comparison and application of DDC algorithms for a heat exchanger

In recent years, several algorithms for Direct Digital Control (DDC) have been proposed in literature. Although some of these, such as PID or cascade controllers, are very commonly used in industrial applications, the more recent ones like optimal state feedback controllers using an observer or parameter adaptive controllers have rarely been applied to a real plant. The primary difficulty behind this application has been perhaps the lack of testing such algorithms on a pilot plant. Moreover, there has been no serious attempt to make a comparative study of the merits of such algorithms for an existing plant under actual operating conditions. In this paper, seven DDC algorithms are applied to the temperature control of a heat exchanger. These algorithms are: PID, cascade, compensation (pole assignment), deadbeat, half-proportional, adaptive and optimal state feedback controller using an observer. The system performance and sensitivity with respect to changes of the plant parameters, disturbances and set point variations are investigated for the heat exchanger using these algorithms. The results indicate that the more sophisticated algorithms, e.g. optimal state feedback, compensation and adaptive controllers, requiring more computer time and memory, yield relatively less improvement when applied to a low-order plant than do the simple algorithms such as PID or cascade. It was deduced that the PID controller with anti-windup is the most suitable one.     

Design and fabrication of a cross flow micro heat exchanger

A cross flow micro heat exchanger was designed to maximize heat transfer from a liquid (water-glycol) to a gas (air) for a given frontal area while holding pressure drop across the heat exchanger of each fluid to values characteristic of conventional scale heat exchangers. The predicted performance for these plastic, ceramic, and aluminum micro heat exchangers are compared with each other and to current innovative car radiators. The cross flow micro heat exchanger can transfer more heat/volume or mass than existing heat exchangers within the context of the design constraints specified. This can be important in a wide range of applications (automotive, home heating, and aerospace). The heat exchanger was fabricated by aligning and then bonding together two identical plastic parts that had been molded using the LIGA process. After the heat exchanger was assembled, liquid was pumped through the heat exchanger, and minimal leakage was observed