RC18T and Transfer Functions

Well, blogging is for telling about all the things on your mind, no matter how obsure or unintelligible to potential readers. My little brother's blog is a particularly gratuitous example of this concept. Today however, I wish to discuss the two things that have most recently spent too much time contemplating. The first is my new Team Associated RC18T and the concept that I am studying in mechatronics, namely transfer functions.

First, the RC18T. Team Associated has long held one of the top postitions among the ranks of the makers of the best RC cars. It seems that ever since I have known the difference between Tamiya and Team Associated, I have wanted one of these. The RC18 is part of the class of 1/18 scale cars that have come about in recent years due to the kindness that has been done upon the RC industry by advances in microprocessor and battery technology. For instance, I'm thinking of buying for this car a brushless motor system. The motor itself is pretty neat, but the real kicker is the motor controller. This tiny controller (about the size of 4 quarters stacked on top of each other) helps this motor produce pretty incredible power despite its small size. Also, should I so desire, I can buy the USB adapter (only about $25) and use my pc to download different performance curves for the motor, download upgraded firmware as new versions are released, as well as adjust forward and reverse top speeds, traction control, and certain braking options. That's right folks, this car is 8 inches long and has similar forms of computer control that today's newer cars enjoy.

If my wife is reading this, she just finished shaking her head. Many of you out there are probably thinking right along with her: "Don't you think you're spending a little too much time and energy on this?" The answer is no. I don't think that. As it turns out, making an electric motor do just what you want it to do is much less trivial than it seems. And that brings me to the second portion of this post--Transfer functions.

Right now in mechatronics we are finally getting around to something that requires more than a design handbook to figure out. All last semester, we were taunted with promises that we would learn about control systems, and now we have finally begun. First, I will attempt to describe how transfer functions make our lives easier, then I will show how it relates to the RC18 and its amazing motor controller.

Basically, any phenomenon in nature can be described through mathematics. Newton identified the major laws that define the universe. It also turns out that if you espress these laws mathematically, instead of verbally, you end up with an equation. most of these equations usually tend to be fairly a complex and are classified as differential equations. When an engineer attempts to design a system he/she must use these differential equations to model the system and anticipate how this machine is going to behave under given circumstances. As an example, I will use a garden variety back-hoe. The components of this system are (simplified) a set of switches that controls the electrical circuit that controls the hydraulic valves, and these valves control the hydraulic circuit that produces motion at the end of the digging arm. Each of these small systems plays their part in making the system work. You could imagine each as a box on a flow chart. The "signal" would move from one box to the next as it moved through the system. Now suppose we wanted to take all these small boxes and combine them into one big box. Each of the subsystems would have been modeled by a differential equation and combining them would require a mathematical operation called a convolution, which is even more nasty than it sounds. However, years ago, a brilliant man by the name of Laplace (la-plaaz') came up with a trasformation (Called a Laplace transform) that allows us to turn these differential equations into fairly basic polynomials. Expressing these polynomials in terms of output over input yeilds the transfer function of a system. By this method, transfer functions of subsystems can be combined into an overall system simply by straight multiplication. It's much easier.

Anyway, that's what a transfer function is in a nutshell. That fancy RC car motor controller is programmed based on what the designers thought the transfer function of the motor and driveline systems would look like. From the standpoint of a future designer, the elegance of the system is undisputable. The challenge that these designers are faced with, however, is the definition of this differential equation. Each term in a DE has a coefficient that is a number or a function and determining these coefficients has been the subject of countless doctoral theses, as well as the ruin of many a system. Getting it right wins success, while getting it wrong can cost people their lives. But no pressure. As for me, I just want my RC car to go FAST.