In circa 400 BC, Socrates held court in ancient Athens. Socrates himself left no written history, but many of his students have, and some have influence today. Zeno of Elia comes to mind.
Zeno proposed that you could never get to the other side of a room. In a simple format, he suggested that an infinite number of steps would have to be required in a finite time. Going halfway would accomplish exactly that – going halfway. Each time you restart the journey, you only divide the future distance in half.
Modern computer software is now being offered utilizing the Zeno Paradox. In this case, we try to do a culpably infinite number of steps performed in a finite time. This is a “super task.” We need to think calculus when we implement physical systems. Zeno helps me rethink control systems using his early calculus concepts.
I assume the reader is acquainted with standard off-the-shelf thinking for motion control. Today, most us use control systems centred around the proportional-integration-differential (PID) loop. I will also assume the reader knows about the PID loop, standards and the simplistic control loops offered today. This column will be an expansion of this platform.
One of the early speed controls was invented by Watts. It consisted of a weighted system and the axially mounted weights. Rotation would throw the weights out from the vertical axis. Doing so would raise the platform along the axis of rotation. The steam input was controlled by a hit-miss (on-off) method.
In my younger days, I lived in Astoria, Long Island. My home was heated by kerosene and cooled by delivered ice. The ice truck had an internal combustion hit-miss control system. We loved to listen to the idling motor. The engine would run and speed up. The local controller would say “too fast.” This would shut the engine off and prohibit ignition. The engine and its large flywheel would then slow down enough to reignite. Hit-miss has a nice rhythm. As an aside, communications were different in those days. To order the ice, we put a rectangular card in the window. It had four numbers around the circumference of the card. The top number told the driver how much ice needed to be delivered today. Ice communication? My good friend, Dr. Wiki, describes all of these references, including Zeno, on the World Wide Web.
In my youth, I helped pay for my college education by being a machinist. In the early 1950s, NC was coming of age. Coupling my machinist and physics backgrounds allowed me to design early lathe applications. We grew into the technology of servos, linear sensors, optical digital encoders, pneumatic and hydraulic actuators, and even printed circuit motors.
We learned a lot. Our fundamental tool was a ball screw driven by a husky DC drive. To increase accuracy, we would use off-the-shelf ball screws and measure their inaccuracies. These measurements surveyed pitch and rotational error. Compensation for these errors was done in the software. We also fixed errors due to tool mounting and warpage of the machine base. We compensated for heat expansion. Accuracy and reliability improved our customer’s ability to have an unfair market advantage. We talked about a rubber machine tool with full compensation.
There is more to life than the PID of optimization. A ball screw is a hardened metal surface between the screw and the ball. High forces that microscopically damage the two services in contact can damage ball screws. High forces are products of continued differentiation. Position, velocity, acceleration, jerk and more. The ones on the other side of acceleration are sometimes humorously called “snap, crackle and pop.” No place on the curve of position displacement should have any sharp edges. These edges damage the ball screw.
For a lathe, never stop at exactly the same spot. Random stop positions improve the life and performance of the screw and ball relationship. A rapid transit to a cutting position need not always stop at the same point. This brinelling (denting of the surface) can occur even without rotary motion. Early automobiles had front-end bearing problems from the jostling of the railroad. It took awhile for the manufacturers of automobiles to understand the problem, and even longer to find a solution.
We found out that there is a big difference between horsepower, torque and speed. We would usually specify a motor without a transmission; usually an error. We needed very high torque at low speeds and almost no torque at high speeds. In large transfer lines, this requirement (at least in history) was with two motors. Each would be geared for optimum performance traversing or cutting. A clutch would choose whether to use the traverse motor or the drilling motor. We could never find an adequate mechanism to do this without a mechanical clutch. As a result, the motor was oversized and heavy. Today, modern rare earth materials and sophisticated solid-state controls can take advantage of these advanced motors.
Designing software and motion control systems is more than the application of simple algorithms. It is the understanding of the problem and the environment. Remember, no sharp edges in the motion profile, and use modern controls and electric actuators. Some of this discussion is applicable to hydraulic systems as well. Eventually, all motion will be run by magnetic forces. After all, these electromagnetic forces and gravity are all that is needed to control our nearby star – the sun.
After reading this, take two aspirin and call me in the morning.
Dick Morley is the inventor of the PLC, an author, speaker, automation industry maverick and a self-proclaimed ubergeek. E-mail him at firstname.lastname@example.org.