# How to model a humidity control system inside a box?

I am a computer engineering student and currently having my undergraduate thesis. My thesis is about a chicken egg incubator and i need to control the humidity inside the incubator.

Right now, i dont know how to calculate the transfer function of the humidity control system. Please someone point me to the right direction.

Is it possible to get the transfer function if i can give a step input (turn on the humidifier) and then get the s-domain of the output, then divide the output over the input because transfer function = output/input? or is this method difficult considering im only an undergraduate computer engineering student?

If a system can be approximated as a (stable) linear time invariant system, than any bounded input which contains all frequencies (for digital signals limited to the Nyquist frequency) can be used to identify the system.

The Laplace transform of a step function is $s^{-1}$, so high frequency behavior might be more prone to be hidden below a noise floor. So you would need more measurements in order to average away this noise, if you are interested in those high frequencies.

Once you have multiple measurements of input data, which contain "all frequencies", and output/system-response data, then you can approximate the frequency response function of the system, denoted with $P(s)$, using,

$$P(s) \approx \frac{\sum Y_i(s)\,\bar{U}_i(s)}{\sum U_i(s)\,\bar{U}_i(s)},$$

where $Y_i(s)$ is the fast fourier transform (FFT) of the $i$th measurement of the output, $U_i(s)$ the FFT of the $i$th input data, and $\bar{U}_i(s)$ means taking the complex conjugate of $U_i(s)$ (which will help reduce the amount of noise in $P(s)$ the more measurements you use). Usually you would also apply a window function to each time domain signal, before calculating the FFT. A common choice is the Hanning window.

• Can you point me to the right direction pls? I mean, what do i need to study, i know about convolution. i know about transfer functions. do i need to use convolution? but convolution is used to calculate the output of the system, the given is the input and the output of the system. just the graph no other else. If i have a step input (logic one of the humidifier), then the output can be graph by using a humidity sensor. Oct 19, 2016 at 0:40
• My main goal is to solve the transfer function of the box which the humidity is controlled. Oct 19, 2016 at 0:41
• @PaulJabines I added an explanation of this to my answer. Oct 19, 2016 at 11:18
• what is the simplest without using the fourier transform? can we get it by using the laplace transform instead? Oct 19, 2016 at 13:31
• @PaulJabines The FFT is not actually the Fourier transform, but a common algorithm to "quickly" calculate the frequency representation of a (discrete) signal in the time domain. It is some what related to the Fourier transform, since it only gives you "information" for imaginary frequencies, while the Laplace transform also allows for frequencies anywhere in the complex plane. Oct 19, 2016 at 15:26