Lab Station: Air Heater
Description of the system
Figure 1 shows an air tube with heater and temperature sensor(s). University College of Sout-Eastern Norway, Department of Electrical Engineering, IT and Cybernetics on campus 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
An input-output mathematical model that has proven to describe quite well the dynamic behaviour of the outlet air temperature is given by Eqs. 1 and 2 given below.
Tout = Tenv + Theat (Eq. 1)
· Tout [C] is outlet temperature (C is Celcius). (On the real air heater, Tout is measured with a Pt100 sensor.)
· Tenv [C] is the environmental (room) temperature.
· Theat [C] is the additive contribution to the outlet temperature Tout due to the heater.
Theat in Eq.1 is given by the following differential equation model representing "time-constant with time-delay" dynamics:
thetat * d(Theat)/dt = - Theat + Kh * u(t-thetad) (Eq. 2)
· u [V] is the control signal to the heater.
· thetat [s] is time-constant.
· Kh [C/V] is heater gain.
· thetad [s] is time-delay representing air transportation and sluggishness of the heater.
Note that the above model is not derived by mechanistic (first-principles) modeling based on energy balance. In stead, the model expresses the typical "time-constant with time-delay" dynamics of thermal processes. In the literature, Eq. 1 is often referred to as a “First Order Plus Time-Delay” (FOPTD) model. (However, under idealized assumptions, mechanistic energy balance modeling of the contents of a heated tank with inflow and outflow and heat transfer with the environment through the tank walls, actually gives a model like Eq. 2.)
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 C/V
· thetat = 23 s
· thetad = 3 s
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,