Lab Station: Air Heater
Description of the system
Figure 1 shows an air tube with heater and temperature sensor(s). University College of Southeast Norway, Porsgrunn, has 26 copies of this lab station, being used in several control courses in both bachelor and master programmes in technology.
Video presenting the air heater
A mathematical model that has proven to describe quite well the dynamic behaviour of the outlet air temperature (where one of the temperature sensors are mounted) in simulations is as follows:
Tout = Tenv + Theat
· Tout [C] is outlet temperature.
· Tenv [C] is the environmental (room) temperature. It is the temperature in the outlet air of the air tube when the control signal to the heater has been set to zero for relatively long time (some minutes).
· Theat [C] is the additive contribution to the total temperature Tout due to the heater. Theat is given by the following "time-constant with time-delay" differential equation model:
thetat * d(Theat)/dt = - Theat + Kh * u(t-thetad)
· u [V] is the control signal to the heater.
· thetat [s] is time-constant.
· Kh [K/V] is heater gain (K is Kelvin, which is the temperature unit used for temperature increments).
· thetad [s] is time-delay representing air transportation and sluggishness of the heater.
In a simulator based on this model a proper initial value of the state variable Theat must defined. If you assume that the heater has been turned off for a while, you can set the initial value to zero.
The parameter values vary somewhat between the lab stations. However, the following values are typical and can be used (e.g. in a simulator) unless you have found other values from experiments:
· Kh = 3.5 K/V (K is Kelvin)
· thetat = 23 sec
· thetad = 3 sec
Furthermore, you may assume
airheater_logfile.txt contains data from an experiment on the air heater. (The fan speed was kept constant during the experiment.) The file containes three colums of data:
Each air heater consists of the following items:
1. One plywood plate on which the devices are mounted
2. Plastic box containing all electrical devices
3. One plastic tube
4. One air fan (originally a PC fan)
5. One potensiomter (variable resistance) for manual adjustment of the voltage controlling the fan speed.
6. One electric power cable (for connection to mains outlet, e.g. 220 V)
7. Two temperature sensors, type Pt100, with measurement signal converter from resistance to current: INOR miniPack-L
8. One heating element (coil) for electric heating of air. The coil is originally used in a shoe dryer. Power (assuming 220 VAC) is 250 W.
9. One electrical AC-DC converter from 220 VAC to 24 VDC. Datasheet_power_supply.pdf
10. One Pulse-width modulator (PWM): Carlo Gavazzi RN F23V30. Datasheet_ssr_pwm.pdf
· F. Haugen, Fjelddalen E, Edgar T., Dunia R., Demonstrating PID Control Principles using an Air Heater and LabVIEW,