Lab Station: Air Heater
Description of the system
Figure 1 shows an air
tube with heater and temperature sensor(s). University College of
South-Eastern Norway (campus Porsgrunn), has 24 copies of this lab station,
being used in several control courses in both bachelor and master programmes
in technology.
Figure 1
Video presenting the air heater
air_heater.mp4
In
the video, the home page of the air heater is erroneously presented as
home.hit.no/~finnh/air_heater. The
correct address is http://techteach.no/air_heater.
Mathematical model
A mathematical model that
has proven to describe quite well the dynamic behaviour of the outlet
air temperature is given by the following differential equation
representing "time-constant with time-delay" dynamics from control
signal u to outlet temperature T:
dT/dt = [(Tenv - T) + Kh * u(t - tdelay)]/tconst (Eq. 1)
where:
·
T [C] is the tube outlet temperature (C is Celcius).
(On the real air heater T is measured with a Pt100 sensor.)
·
Tenv [C] is the environment (room) temperature.
·
u [V] is the control signal to the heater.
·
Kh [C/V] is the heater gain.
·
tconst [s] is the time-constant.
·
tdelay [s] is the time-delay representing air
transportation and “sluggishness” of the heater.
The above model may be
derived from mechanistic (first-principles) modeling principles, i.e. a
simple energy balance of the air, if we make the idealized assumption that
the tube is a so-called CSTR (continuous stirred tank reactor) with air
inflow and outflow and heat transfer with the environment through the
“reactor” (tube) walls, and - in addition - we include the time-delay as
described above. In reality, the idealized CSTR conditions are not satisfied,
but they lead to a useful model structure with parameter values that may be
estimated from experimental data. (Many other stable physical processes show
“time-constant with time-delay” dynamics, and such processes may be
reasonably well represented with models like Eq. 1.)
In a simulator based on
this model a proper initial value, Tinit, of the state variable T
must defined. If you assume that the heater has been turned off for a while,
you can set Tinit = Tenv.
The parameter values vary
somewhat among 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 C/V
· tconst
= 23 s
· tdelay
= 3 s
· Tenv = 20 deg C
Experimental data
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:
- Time, t [s]
- Control signal to the heater, u [V]
- Outlet temperature, T
[C].
Block diagram of temperature
control system with LabVIEW
(Click on the picture for showing picture as
PDF file.)
Technical information
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 a measurement signal
converter from resistance to current (INOR miniPack-L)
8.
Precision resistors for converting temperature measurement current to
voltage
9.
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.
10.
One electrical AC-DC converter from 220 VAC to 24 VDC. Datasheet_power_supply.pdf
11.
One Pulse-width modulator (PWM): Carlo Gavazzi RN F23V30. Datasheet_ssr_pwm.pdf
Publication
·
F. Haugen, Fjelddalen E, Edgar T., Dunia R., Demonstrating PID Control Principles using an
Air Heater and LabVIEW,
Updated 5th May 2023 by Finn Aakre Haugen. E-mail Finn.Haugen@usn.no.
|