# temperature control; electronics analogy **URL:** http://discourse.iapct.org/t/temperature-control-electronics-analogy/15148 **Category:** CSG1996 **Created:** [January 25, 1996, 10:07pm UTC](http://discourse.iapct.org/t/temperature-control-electronics-analogy/15148 "1996-01-25T22:07:15Z") **Posts on this page:** 1 **Page:** 1

### Author: ![William\_T\_Powers4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/977dab/32.png) [@William\_T\_Powers4](http://discourse.iapct.org/u/William_T_Powers4) #### Post date: [January 25, 1996, 10:07pm UTC](http://discourse.iapct.org/t/temperature-control-electronics-analogy/15148/1 "1996-01-25T22:07:15Z")

[From Bill Powers (960125.1430 MST)] Remi Cote 012596.0945 -- I tried to simulate the system suggested by Bill and here is the result. I think I made a mistake. I need detective here: 1) 0.1\*(20-0) - cooling of 0.3 = 1.7 of heat output 2) 3.23 = 0.1\*(20-1.7)=1.83 + 1.7 = 3.53 - cooling 0.3 = 3.23 3) 4.61 ... it is an asymptote heading to 17... not 20 degree. I think I made a mistake but don't know what. You did it perfectly. Reason it out. When the temperature reaches 17 degrees, the heat output is 0.1(20 - 17) = 0.3 units. This is exactly enough to balance out the disturbance of -0.3 units, leaving no heat output to add to or subtract from the previous heat output. So the temperature remains the same from then on. The first lesson to learn is that control systems are not perfect. It is true that 17 degrees is not 20 degrees, but it is 85% of 20 degrees. This shows that there is a modest amount of control. If you increase and decrease the heat loss, you will see that there is an effect on temperature, but the temperature stays near 20 degrees -- not equal to 20 degrees, but close to it. If you vary the reference temperature T' with the cooling at 0.3, you will see that the final value of T remains at 85% of T'. So varying the reference temperature does make the actual temperature follow it reasonably well, and the cooling is resisted. We can easily improve the performance of this control system. The number 0.1 is called the output gain or output amplification of the control system. It determines how much heat output there will be for any given difference between T' and T. For now, just try increasing the output gain. Raise it to 0.2, 0.3, and so on, and see what happens to the asymptotic temperature. After you have experimented with this but before we go on, it would be best to make your simulation a little more physically correct. A heat output is measured in calories. When you put a certain number of calories into an object, its temperature rises by a specific amount. If the object is a one milliliter volume of water, its temperature will rise by 1 degree centigrade for each 1 calorie of heat input (4.18 joules). Let's assume that we're dealing with just this situation so we don't have to worry about physical scaling factors for the present. The heat output produced in one round of calculations (minus the loss in the same iteration) is H = G\*(T' - T) - 0.3 calories Where G = output gain Heat output is measured in units of energy, not temperature. When we put this many calories into one milliliter of water, the temperature will rise from the former temperature this way: T(new) = T(old) + H degrees centigrade You were adding the new heat output to the old heat output, but you got the right answer because you then set the temperature directly equal to the heat output. With this more correct approach, we first calculate the heat output, and then add it to the old temperature to get the new temperature on each iteration. If you try it this way with the same numbers you used, you will see that the results are the same. When you use these steps in doing your calculation, each step describes a physically realistic process: the generation of heat energy, and then the use of this energy to raise the temperature of an object. As you continue increasing the output gain G from 0.1, you will eventually run into a problem. After you have seen it, tell me about it and I will tell you what we do next to prevent the problem. > **···** > > ----------------------------------------------------------------------- > Bruce Abbott (960125.1035 EST) -- > > There's nothing you can learn from your electronic analogy that you > can't learn directly from the equations. If using this analogy puts you > on more familiar grounds, fine -- but let's not start naming even more > entities by analogy with other situations. What we need to do is to get > rid of superfluous entities. > ----------------------------------------------------------------------- > Best to all, > > Bill P.