How well does my PID controller respond when you ask it to respond to an upgrade or downgrade? Does it respond as smoothly and precisely as the FL controller? I would love to plan some comparisons. I have yet to connect my controller to a real vehicle. But at least the model of the truck worked well, with plenty of gain to hold negligible error on "upgrades" and "downgrades."
Plus, I didn't need many trims or adjustment to go from one kind of "truck" to another. My standard controller was well-behaved in each case, even if the "actuator" was nonlinear with steeper gain at some settings and less at others.
Now, do you have to purchase op amps and 1-µF capacitors in order to take advantage of my best controller scheme? Heavens, no. You could execute my PID with anti-wind-up with any number of PID controllers. It could be executed with analog circuits, straight digital, DSP, or even FL. But if you want it to work well, you need to understand the signals, the circuits, and the principles behind the analog circuit. If you don't understand all of that, then you might say something foolish, like: "Conventional controllers are OBVIOUSLY inferior. They couldn't POSSIBLY perform this task, so we won't even try one. We'll just build an FL controller." Bad idea!
In fact, I know one guy who started out his planning for an FL system by building an analog system, which is easy to get a feel for. Then he took the best analog system and added refinements, nonlinearity, etc.—and executed it all in FL.
Am I going to put a speed limiter on my Beetle to keep it down below 72 mph? Heck, no. That wouldn't be safe. I have better ideas.
So, what's my point here? As I often say, "The sudden cessation of my stupidity is worthy of some note." And if you see FL Experts claiming that they can do things that nobody else can, QUESTION AUTHORITY.
Is it just possible that they have an "excellent system" that's excellent only in comparison to a mis-applied "conventional" controller? Is it possible that they have designed a steam-pressure controller that won't regulate pressure when you begin drawing steam? Is it possible that they have designed a truck-speed controller that will hold the speed constant only until it comes to an upgrade?
Oh yeah, I was going to explain why I picked the components that I did. The "truck" acts as an integrator with unity gain at 3 mHz from the "gas pedal" to the voltage that represents the speed. If I add a gain of 80, it would make the loop have unity gain at 240 mHz. Then there's a lag of 0.3 seconds (estimated) added into the controller path.
That's seen as a lag at a frequency of 0.5 Hz. If I can keep the loop closure below 0.24 Hz, that shouldn't be too close. It might cause a bit of ringing, but I can tweak that out by adding the differentiator.
The lightly loaded truck now looks like an integrator (i.e., just like an op amp) with unity-gain crossover at 0.24 Hz, plus an extra lag at 0.5 Hz. If the main feedback path is a gain of 80, it would be wise to add a lead (gain boost) at frequencies above 0.5 Hz, which means a differentiator with a gain of 80 at 0.5 Hz. That's what you get with a preamp gain of 5, feeding a differentiator at 3.3 seconds. The effective differentiator is at 16.5 seconds, or 60 milliradians/s, or 9 mHz. When will this gain get up to 80? At about 720 mHz. Not bad! That's what I chose from scribbling on the back of envelopes. It worked the first time with no overshoot. This is for the worst case, with a lightly loaded truck. For a truck loaded much heavier, such as five or 10 times heavier, the integrator has a unity-gain crossover at 0.048 or 0.024 Hz. This kind of "op amp" or "integrator" is even easier to close the loop around. It's even more stable.
All for now. / Comments invited!
RAP / Robert A. Pease / Engineer
rap@galaxy.nsc.com–or:
Mail Stop D2597A
National Semiconductor
P.O. Box 58090
Santa Clara, CA 95052-8090
References:
- Pease, Robert A. "What's All This Fuzzy Logic Stuff, Anyhow?" Electronic Design, May 13, 1993, p. 77.
- Pease, Robert A. "What's All This Fuzzy Logic Stuff, Anyhow? (Part II)," Electronic Design, Nov. 1, 1993, p. 95.
- Pease, Robert A. "What's All This Fuzzy Logic Stuff, Anyhow? (Part III)," Electronic Design, Nov. 11, 1993, p. 105.