Air Conditioning Unit for a Room

[Siddhat]

Hello everyone,
I am designing a closed loop control system for an air conditioning unit for a room. Attached is the block diagram that I came up with. The aim is to control the room temperature (TR) and make it follow the desired temperature (TD) set by the user. So, a transfer function relating the desired temperature and the room temperature is needed. In order to relate the room and the desired temperature, transfer function of the individual components is needed. How do I relate the input temperature with the output voltage of the temperature sensor? and how can the transfer function of the individual components be found?

[Mechatrommer]

How do I relate the input temperature with the output voltage of the temperature sensor?

you find the electrical model for your thermistor. if the manufacturer doesnt provide it, you probably can derive from general thermistor model such as...
https://en.wikipedia.org/wiki/Thermistor
http://www.ecircuitcenter.com/Circuits/therm_model1/therm_model1.htm

and how can the transfer function of the individual components be found?

similar to the thermistor, you figure out whats inside the component and start laying out their equivalent circuit model or mechanical relationship to your desired target, ie temperature from desired control variable, such as V or I or F etc. then you have the model. since the model usually involve first or second order derivatives, you'll need to transfer it to Z-transform, shuffle the Z-transform so the other side is output/input, there goes your transfer function. then you draw bode plot or find the zeros and poles to figure out stability. but then you are going to experiment to see if real life behaviour match closely you derived model/transfer function and then adjust accordingly and repeat again, find transfer function in mathematical mode, bode plot, zeros and poles, experiments, repeat X times....

if this for hobby purpose, just buy ready made ACU. if this for academic purpose, you may want to buy Control Engineering book from Beginner to Advanced (or practical) level. if you want to impress your professsor, get one about Robust Control System (be ready for the headache) in the end most of us laymen will resort back to simple PID control model. trying to get transfer function that is in no way guaranteed match real world behaviour will be a PITA experience, just look in the book how they modelled a simple motor is enough to make a brain hurt. ymmv.

[Siddhat]

If the input and output variables are both voltages then the transfer function can be found by using KCL, KVL and nodal and mesh analysis. But during modeling, if the input and the output variables happen to be analogous quantities, say for a potentiometer if I want to relate input temperature to the resistance of the potentiometer,  can the resistance (R) be set equal to the temperature (T) by introducing a proportionality constant (K)? i.e. R is proportional to T and thus R=KT where the unit of K is Ohm/degree Celsius. In this case  can the transfer function be written [R(s)/T(s)]=K? If so, how can the value of K be determined? Hope you got what I said. Thanks.

[Mechatrommer]

can the resistance (R) be set equal to the temperature (T) by introducing a proportionality constant (K)? i.e. R is proportional to T and thus R=KT where the unit of K is Ohm/degree Celsius. In this case  can the transfer function be written [R(s)/T(s)]=K? If so, how can the value of K be determined? Hope you got what I said. Thanks.

nop! according to the...

or

from the above link... https://en.wikipedia.org/wiki/Thermistor

[Siddhat]

The relation you showed is absolutely correct for a thermistor which is a temperature sensor.
But I meant this: Let's take a different example; there is a subsystem that takes voltage as an input variable and has the output variable as velocity. Basically what the subsystem does is it maintains the velocity of that subsystem according to the input voltage which may be from a control unit. So in that case can the velocity be set equal to the voltage by a proportionality constant Kv provided that the subsytem will be designed in such a way that the response will be linear? i.e Vel(s)/V(s)=Kv? Thank you.

[ace1903]

The procedure to obtain transfer characteristic is called identification in control system lingo.
Basically, you provide input to the system step function or PRBS sequence and by analyzing the response you can obtain transfer caracterisitc.
Air conditioning most of the time is described by a nonlinear transfer function. Often humidity is the second input to transfer function.
That is why most of the examples in books are with heating and not cooling.
If you try a lot, you can find a linear function that will be a good approximation in theory. In practice doing AC control with purely linear components does not provide good results.

My recommendation is to choose some transfer function with random parameters and do calculations as an exercise.
You professor will appreciate if you identify all the room parameters that will affect transfer function like room volume, heat isolation on the walls, windows, sun outside ....
ACs that you can buy in stores are of ON/OFF type. There is no metering device that will control refrigerant flow and amount of cooling.


 

[Mechatrommer]

The relation you showed is absolutely correct for a thermistor which is a temperature sensor.
But I meant this: Let's take a different example; there is a subsystem that takes voltage as an input variable and has the output variable as velocity. Basically what the subsystem does is it maintains the velocity of that subsystem according to the input voltage which may be from a control unit. So in that case can the velocity be set equal to the voltage by a proportionality constant Kv provided that the subsytem will be designed in such a way that the response will be linear? i.e Vel(s)/V(s)=Kv Vel(s)/V(s)=K? Thank you.

in the very simplistic form of PID control, yes thats the P term (proportional). your formula above is corrected.

[Siddhat]

How can the value of K be found for the type of subsystems that I stated? Can I just take some constant number?

[Mechatrommer]

yes take constant number, test it. if too much oscillation, reduce it. if its too slow to reach target point, increase it, and do it X times. much more simplistic form of what you originally asked. soon you'll discover I, and D term. google "adjusting PID" parameter or simply google PID control in youtube, as soon as you start to appreciate them.

[Siddhat]

Thanks. That really gives confidence to model a system. Using MATLAB in a design process is usually a good practice. Yeah, P, PI and PID controllers are really interesting topic to look forward for. Thank you.