Other considerations of scale effect occur in control systems as well. When considering a control system problem, the bandwidth or scaling of the control parameters themselves are often a major issue.
What happens when the velocity of a system needs to be controlled over a range 1000 to 1 or greater?
This was the exact problem in the 1970’s when researchers at Corning and Bell labs were attempting to make glass fibers thin and pure enough to carry digitally encoded light signals to replace voltages on copper wire. The concept itself is one in which scale effect is part of the merit of the technology, the possibility that communications bandwidth could be expanded by 65,000 times the density of a copper dominated infrastructure. In the scale up of the technology, cost for the laser and the fiber have become so low, that few people remember the ancient dial-up modem and audio tones required for computer based communications.
Scale effect in motor control systems becomes a significant parameter of merit when wide bandwidths of control are required. In the case of fiber optics, it was necessary that a servo motor be able to pull a bead of molten silica from a pot starting at zero speed. Then by ramping the speed with precise control, pull and thin down to a fragile fiber of extremely small diameter without breaking the glass.
Nice trick if you can do it! And, in fact, it was available technology at the time. Expensive, yes, and a little uncommon. But to specialists in the servo world, it was known and reliable technology. The credit goes to the Electrocraft company for making the only servo system on the market at the time, that would do the job with 1000 to 1 speed control and super accurate speed control at any set speed. Still a significant trick even in today’s market.
Scale effect can drive lots of different issues. What happens when position feedback tolerances are increased by several orders of magnitude? For most situations one millionth of an inch would seem excessively precise, but this is an off-the-shelf technology from vendors like Renishaw and Heidenhain. These vendors have been doing it for years and 1/2 millionth and beyond are available solutions. The real challenge comes when facing the requirements set by semiconductor lithography equipment. And honestly, I don’t know how they do it.
When it comes to manufacturing, scale effect has it’s impact. Extremely large and extremely small electric motors come with unusual price tags. This is because at either end of the spectrum, extremely large and extremely small machines are extremely difficult to manufacture. For entirely different reasons.
When attempting to control extreme situations, the challenges are significant. Those challenges can be compounded significantly by operating across extreme ranges or by virtue of the added complexity of scale effect at the extremely large or extremely small end of the spectrum. All part of the engineering challenges faced every day by men and women engaged in some very noble pursuits. Like making life better for the rest of us.