Modeling and Control of a Cooling System with compact plate heat exchangers

Project focus

  • Modeling of the heat transfer of a compact plate heat exchanger
  • Physical based model reduction
  • Nonlinear control design based on power considerations


In the operation of machine tools it is necessary to compensate the introduced heat in order to reduce the deformation of the machine and thus minimize the manufacturing tolerances. Usually, the manufacturers of the machine tools demand a temperature tracking control of the supply fluid with the ambient temperature. Therefore, often fluid-fluid cooling systems are used, which consist of two fluid circuits as shown in Fig. 1. The primary circuit (I) is connected to the machine tool and the secondary circuit (II) to a coolant supply. Compact plate heat exchangers are often used as thermal coupling of both circuits. Their advantages are a small overall size, high overall heat transfer coefficients and low production costs.

Schematics of a fluid-fluid cooling system.

The control problem is concerned with the tracking control of the supply temperature of the machine tool by changing the fluid velocity of the secondary circuit with a proportional valve. The temperature of the coolant supply cannot be changed and may vary within a small but unknown range. Neglecting the heat transfer with the environment, the control problem reduces to a tracking control of the outlet temperature of circuit I of the heat exchanger.

The mathematical model of a heat exchanger is a distributed-parameter system because of the convective heat transfer. In addition, from the thermal boundary layers of the fluids, the overall heat transfer coefficient shows a strong nonlinear dependency from the fluid velocities. In this context, the precise identification of the functional relation between the overall heat transfer coefficient and the fluid velocities turns out to be a laborious task.

Compact plate heat exchanger in countercurrent flow arrangement.

Due to the specific design and the typical operating conditions, the mathematical model of the plate heat exchanger can be reduced to only two ordinary nonlinear differential equations. Based on the total power balance a nonlinear control law, which is independent of the overall heat transfer coefficient can be designed.

The proposed control strategies have already been successfully implemented on an industrial control system.

  • A. Michel, Modellbasierte Regelung von industriellen Wärmeübertragern, A. Kugi and K. Schlacher, Eds., Aachen: Shaker Verlag, 2015, vol. 24.
    Title = {Modellbasierte Regelung von industriellen W\"arme\"ubertragern},
    Author = {Michel, Alexander},
    Editor = {A. Kugi and K. Schlacher},
    Publisher = {Shaker Verlag},
    Year = {2015},
    Address = {Aachen},
    Series = {Modellierung und Regelung komplexer dynamischer Systeme},
    Volume = {24},
    ISBN = {978-3-8440-3659-6},
    Organization = {Institute f{\"u}r Automatisierungs- und Regelungstechnik (TU Wien) und Regelungstechnik und Prozessautomatisierung (JKU Linz)},
  • A. Michel and A. Kugi, Model based control of compact heat exchangers independent of the heat transfer behavior, Journal of Process Control, vol. 24, p. 286–298, 2014.
    [BibTex] [Download]
    Title = {Model based control of compact heat exchangers independent of the heat transfer behavior},
    Author = {Michel, Alexander and Kugi, Andreas},
    Journal = {Journal of Process Control},
    Pages = {286--298},
    Volume = {24},
    Year = {2014},
    Doi = {10.1016/j.jprocont.2014.02.003},
  • A. Michel and A. Kugi, Accurate low-order dynamic model of a compact plate heat exchanger, International Journal of Heat and Mass Transfer, vol. 61, iss. 33, pp. 323-331, 2013.
    [BibTex] [Download]
    Title = {Accurate low-order dynamic model of a compact plate heat exchanger},
    Author = {Michel, A. and Kugi, A.},
    Journal = {International Journal of Heat and Mass Transfer},
    Pages = {323-331},
    Volume = {61},
    Year = {2013},
    Number = {33},
    Doi = {10.1016/j.ijheatmasstransfer.2013.01.072},
  • A. Michel, W. Kemmetmüller, and A. Kugi, Modellierung und Regelung eines Plattenwämetauschers, in Tagungsband GMA-Fachausschuss 1.40 “Theoretische Verfahren der Regelungstechnik”, Anif/Salzburg, Austria, 2010, p. 81–99.
    author = {A. Michel and W. Kemmetm{\"u}ller and A. Kugi},
    title = {{M}odellierung und {R}egelung eines {P}lattenw{\"a}metauschers},
    booktitle = {Tagungsband GMA-Fachausschuss 1.40 "Theoretische Verfahren der Regelungstechnik"},
    year = {2010},
    month = {9},
    pages = {81--99},
    address = {Anif/Salzburg, Austria},


  • Control strategies for heat exchangers
  • Process automation
  • Automation of machine tools


Univ.-Prof. Dr.techn. Andreas Kugi


2010 - 2014