A funny thing happened to me while I was doing my calc homework. It happened that I had to do the following problem in my textbook:
The formula for the power output P of a battery is P = VI - RI^2 where V is the electromotice force in volts, R is the resistance, and I is the current. Find the current (measured in amperes) that corresponds to a maximum value of P in a batter for which V=12 volts and R = .5 ohm. Assume that a 15-ampere fuse bounds the output in the interval 0 <= I <= 15…
Anyways, the point is to use the derivative to find the critical point, and then plug that in to the origional equation to find the maximum value. What it comes down to is the maximum power of 72 (joules?) is achieved at 12 amperes. I’m guessing what that means is peak efficiency is at 12amps, 12 volts, and .5 ohms.
What I want to know is can you apply this to robotics somehow? Can we, for example, find the voltage and the amperage for a certain component and adjust the resistance to get it closest to peak efficiency for the battery? Or is there more to this concept than a mere problem in a textbook implies?
If you were to do that, it would involve calculating the surface areas, normal forces, coefficeints of friction, weights, and a lot of other stuff for ALL moving parts of your robot. It’s not worth the trouble.
Your math problem is just a typical unconstrained optimization question, nothing to get excited about.
Multivariable calculus…ugh! It would be nice to use math equations for everything, but there are just too many variables and chance opportunities that math can’t predict
No, this is just a single-variable problem.
However, in the real robot, there are many more things to take into consideration. If your model is complete, anything can be predicted. The most practical and the simplest application appears to be the “dice probabilities” for the boxes. Maybe we should try tossing our box tommorrow? I don’t feel like integrating.
The problem actually seems like doing multivariable equations with the single-variable calculus rules becaues of the many different things you would have to take into account. I agree with the dice rolling, forget the integrating.
The problem with just tossing the boxes is that we can’t account for falling from stacks with our one box. Others have said that when falling in satcaks, boxes tend to fall on their sides. I think we’re better off doing the math, at least until we get more boxes.
Super,
What this problem addresses is the maximum terminal voltage of the battery in real world conditions. For our robot systems the voltage available at the terminals of the battery is affected by the voltage drop across the internal resistance, R in your problem. Although you are calculating for output power maximum we are more concerned with terminal voltage since a fall below 8 volts will reset the controller. As the battery discharges the internal resistance rises. If the current draw remains the same then the output voltage must fall due to the drop across the internal resistance. Increase the load current and the voltage drop internally also rises making less voltage available for the robot. The result is RC reset and 2-5 sec of lost match time.
As a side note, there are other resistances in the overall system. Mostly those are resistance in wire and connectors. The bottom line is to power your RC from a point as close to the battery as possible, and not at the end of a string of high current devices.
I’m pretty sure that it’s in the rules that the robot controller must have it’s own dedicated circuit (nothing in series with it), so the voltage shouldn’t be an issue.
However, our robot did some funny things on a low battery.
What I’m implying is this…Don’t wire the power to the RC after several feet of wire and two power distro panels that are feeding high current motors. The current flowing in the wiring harness is enough to drop the voltage supplied to the RC below 8 volts when the currents in the motors are high. Take off the power for the RC from the first distro as close to the battery as you can get and keep battery wires short.
While I defer to Al on matters electrical, I disagree with those posters who said “forget the analysis”. Analysis is a tool. Like any other tool you need to figure out where and when to use it. That’s the tricky part.
The first year we built a lift, I did a fair amount of analysis to ensure it wouldn’t break. The next year, when we had to hang a robot from the bar I did more. The year after that I said “what we did last year worked and the loads are much lower this year” so I did no analysis but used the same sized elements. I chose, based on experience, not to use a tool that had been successful in the past because there was no need for it.
This year we will probably be radically changing our lift concept and the new concept will be more weight critical. That is weight in the wrong spot will have a greater adverse effect. So I will be analyzing our lift not to ensure that it doesn’t break, but to ensure there is no excess weight. Though if I have to choose between weight and break I’ll take weight anyday.
Engineering is an exercise in continuing judgement calls. You are constantly faced with “What’s the best way to do this?”.
If your problem is to figure out how to make a robot go fast, you could buy alot of gears, shafts and wheels, put them together and measure the resulting speed.
Or you could sit down and say “My motor has these characteristics, what gear ratio range will give me acceptable operation?” Figure that out and you have greatly reduced the number of combinations to try out. You might even save time doing it that way.
Like any other tool, using analysis requires time and thought. It is all a matter of balancing resources vs requirements. How long it will take to do the analysis and what effect it will have on the overall design are things you need to weigh. Don’t spend days figuring out whether to use a 3/16 or 1/4 inch bolt, but it might be worth a few minutes to figure out whether or not 1x1 aluminum tube will support a 5 lb box cantilivered 5’ out.
If actually testing the scenario is simpler, faster, and more accurate than doing the analysis, why bother?
The robot has som many moving parts that it is very impractical to try and calculate and optimize the efficiency. The 5-10% gain won’t be worth the weeks you put into it.
I don’t know how to really word this so if it sounds weird, sorry. It is not always the best robot (insert any noun here) that wins but it usually the one who has performed their homework, eeked out the slight edge or practiced, practiced, practiced. 5-10% better is huge when it only takes one more point to win. As to testing vs. calculating, we must always be testing ourselves. Make the calculation and run the test, if they are close then proceed. If they are far apart check the calculation again then test again. Something has to be wrong and you need to find out why. Many teams last year asked for our assistance to find problems with their robot. In some cases we encountered teams who had made the calculations and tested and were still blowing breakers. They had all the data that something was wrong they just couldn’t find it. These cases were usually two motor drives where one of the motors had failed or was accidentally wired wrong when replaced.
BTW, We are always glad to help if we can. If you are having a problem let us know. Especially if we are at the same event, come and get one of us to help. If you came to play, I want to help you make that happen.
I’m glad that you agree that practice is good. In fact, I think that the extra 10-12 hours practice you will get driving outweighs the slight efficiency boost you will get by measuring and tweaking the wiring. In a game that close, the extraq driving practice will make a much bigger difference.
Perhaps you should do the math before you construct, and discover, for instance, the torque required is about 5 times what is available. Once the calculations say you are in the ballpark, proceed to make something to test. You may save some time and some aluminum.
