Case Study III: Control of a Double-Pipe Heat Exchanger
 
Author
  Carla Martín-Villalba
  Departamento de Informática y Automática, UNED
  Juan del Rosal 16, 28040 Madrid, Spain
 << Back to Sysquake-Dymosim Interface
 
The heat exchanger model is based on the physical model described in (Cutlip and Shacham 99}, and it has been developed using JARA Modelica library.
 
A gaseous mixture of carbon dioxide and sulfur dioxide (in the tube) is cooled by water (in the shell).The temperature dependence with the spatial coordinate has been modeled by dividing
the flow paths of the water and the gas, and the pipe wall in control volumes. This approach allows for local variations in physical properties and heat transfer coefficients. The diagram of the JARA model is shown in Figure 1a (it has been represented using Dymola).
 
The goal of this virtual-lab is to illustrate the application to the heat exchanger of some linearization and control techniques. Three different Modelica models has been composed for that purpose:
the open loop system (see Figure 1a), the system controlled using a PID (see Figure 1b) and the system controlled using a compensator (see Figure 1c).
 
Figure 1: Diagram of the heat-exchanger Modelica model: a) open-loop plant; b) plant controlled using a PID; and c) plant controlled using a compensator.
 
Theses three models, composed using the JARA library and components from the standard Modelica library, have been translated automatically by Dymola into three executable files.
In addition, a Sysquake application has been programmed. It implements the virtual-lab view and controls the execution of the Dymola executable files. The features of this Sysquake application, that constitutes the virtual-lab core, include:
1. The application to the heat-exchanger model of several identification techniques.
2. The design of control strategies (using the linear models previously obtained by applying the identification techniques).
The challenge is to control the gas exit temperature by manipulating the water flow.
 
The virtual-lab supports the automatic calculation of the plant linearized model. This calculation is performed as follows (see Figure 2):
1. The change in the value of the gas exit temperature, in response to a step in the water flow, is calculated simulating the heat exchanger model
2. A transfer function (abbreviated: TF) is fitted to this response.
 
Figure 2: View of the double-pipe heat-exchanger virtual-lab: plant linearization.
 
In this identification procedure, the virtual-lab user is allowed to:
1. Change the parameter values and the input variable values of the heat exchanger model, the simulation communication interval and the total simulation time.
2. Choose among different identification methods, including "first order TF with delay", "second order TF with delay" and "non-parametric identification".
3. Modify the obtained TF.
4. Analyze the obtained TF by means of Bode and zero-pole diagrams, and robustness margins.
5. Start the simulation run.
6. Export the calculated TF to another Sysquake application.
 
In addition, the virtual-lab automates the controller synthesis and analysis. The virtual-lab supports the following user's operations (see Figure 3):
1. To import the TF previously identified.
2. To analyze the TF characteristics using Nyquist, Nichols and Bode diagrams.
3. To choose the controller type (possible options are: PID, lead and lag compensators).
4. To synthesize the controller (i.e., to set the value of the PID's parameters).
5. To specify the error and the phase margin of the system controlled by the lead or lag compensators.
6. To simulate the closed-loop linear and non-linear models.
 
Figure 3: View of the double-pipe heat-exchanger virtual-lab: controller synthesis.
 
An experience using the heat-exchanger virtual-lab will be described below. The operation conditions of the heat exchanger are shown in Figure 2. A change in the value of the the water-flow from 0 to 10E-4 kg/s has been applied at time 150 s to the heat exchanger. A TF has been fitted to the change in the value of the gas exit temperature in response to the step change in the water-flow. A first order identification method, that uses the times to reach 28.3\% and 63.2\% response, has been applied. The following TF has been obtained:
 
A PID to control the plant has been designed. The TF previously obtained has been used in the design process. The PID controller has the following parameters: Kp = 0.05, Ti = 1, Td = 0.01, wp = 1, wd = 1, Ni = 0.9, Nd = 10, ymin = 0 and ymax = 5E-3. The evolution of the gas exit temperature tracking the set-point is shown in Figure 3.
 
References
Cutlip, M. B. and M. Shacham (1999): "Problem Solving in Chemical Engineering with Numerical Methods", Prentice-Hall.
 
Carla Martin-Villalba
Last update: July 2007
euclides web server - Dept. Informatica y Automatica, UNED, Juan del Rosal 16, 28040 Madrid, Spain