New chapter of Control Engineer is out! (1/1 chapter)

Model-Based Development (1): A Sudden Motivation

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I returned to the mansion from magic art training. It was still evening, but my room had already become dark. I reached my hand toward the ceiling.

≪Activate! Light on≫

A slight amount of mana was radiated from my arm.

Ah, huh?

The magical lamp shone for an instant, but then, went out.

≪Activate!≫ ≪Activate!≫

Aahhh, no good?

I stepped into the hallway.

“Ursulaaa! Ursulaaa!” (Leon)

Since I just passed by her earlier, she should still be around here somewhere.

“Yes, Young Master. What is it?” (Ursula)

I thought I heard her voice from a bit away, and then the maid came up the stairs toward me.

“The magical lamp in my room went out. Go get me a new magic stone.” (Leon)

“Yes. I will go call Butler Renato.” (Ursula)

“No, it’s fine, I’ll replace it myself. Just bring me the magic stone. The yellow, long one.” (Leon)

The luminous-use magic stones were in the cheap category as magic stones went, but even so, in our mansion they were managed carefully, and Butler Renato held the key to the storeroom.

“Understood. I will go get the long magic stone.” (Ursula)

She went back down the stairs.

Renato is busy, you see. If I asked him, he would bring a hand lantern to light the work, call in a supporting maid, and make a big production out of it.

That aside, this magic stone was short-lived. If I remember correctly, about three months ago I also replaced the luminous magic stone in the magical lamp. They usually last about half a year. Since I had asked Ursula already, I should get ready.

“Step stool, step stool.” (Leon)

I pulled the step stool out from the storage closet, carried it under the magical lamp, and climbed up. From there, I reached upward toward the magical lamp.

I could reach it. I’ve grown taller, after all.

I unfastened one side of the cover and opened the magical lamp. It was dim, but still visible.

Generally, magical lamps are made from three types of magic stones plus other auxiliary components.

My room isn’t that large, so in its magical lamp there’s one yellow, long magic stone for illumination. There are also two bluish ones and one whitish one, four stones in total. The magical lamps in the great hall must use many more magic stones. I’ve never opened one, though.

This was the dead stone. I pinched the long hexagonal prism magic stone and wiggled it… it came loose.

Good, good.

I got off the step stool and carried it over by the wall. I opened the window and held the magic stone toward the outdoors so its interior became visible. The inside, which should have been semi-transparent, was mostly clouded. As expected, it was burned out.

By “burned out”, I mean that the thinned portion of the magic circuit inside the magic stone, the filament, has burned through, and it can no longer produce light. The filament that carries the magic flux has comparatively high magic resistance and produces heat. When an object becomes very hot, it emits electromagnetic waves, and a portion of that is visible light. The magical lamp is a magical tool for illumination that uses this phenomenon. Conversely, this phenomenon requires quite a high temperature in order to radiate visible light.

Huh? I feel like I’ve thought about something similar recently… when was it? I can’t remember. Oh well. I wish Ursula would hurry with the replacement. If it gets a little darker, I won’t be able to see. Well, I could just use magic art, though.

Incidentally, the bluish ones were for mana storage. These absorbed mana from the atmosphere and stored it. This magic stone supplied the luminous-use magic stone, allowing the magical lamp to function. These were also consumable, but a bit more expensive and longer-lasting. Two were used so that mana charging and mana release could be alternated.

The reason we could get by with just two bluish stones was due to the mansion’s location. It was near a dragon vein, where mana was abundant. In other places, more mana storage magic stones were apparently required.

Mana storage capacity depended on the magic stone’s size, so a large stone could suffice. In fact, in the past, magical lamps used to be made with just one magic stone. But large magic stones were expensive, and standardizing the size improved interchangeability. Thus, the current size was adopted for economic reasons.

The last whitish stone was for control.

“Young Master. I have brought it.” (Ursula)

“Yeah. Thanks, Ursula.” (Leon)

I took the item from the maid wearing a white apron and scarf.

“Zorga-san was saying, ‘The Young Master’s room’s one burned out again?’” (Ursula)

“Yeah.” (Leon)

That was something I’d also been thinking.

“I think it’s because you turn the magical lamp on and off without using the magical lamp stick, Young Master.” (Ursula)

“Eh?” (Leon)

“Today, too, you came home and tried to turn on the magical lamp, and it burned out, right?” (Ursula)

“That’s true.” (Leon)

I unwrapped the magic stone from its oiled paper, rolled up the paper, and handed it to Ursula.

“That has nothing to do with it.” (Leon)

Although Ursula was a maid, she had looked after me for a long time, so she spoke to me rather familiarly.

“Is that so?” (Ursula)

She still seemed suspicious, but Ursula fell silent.

I held the magic stone up to the window light. The golden line or the filament looked connected.

Magical lamps are often installed on the wall or in the center of the ceiling. Wall-mounted ones are within reach, making replacement easy and allowing a person to turn them on and off by touch. But that lights only one side of the room, so two or three are needed.

Ceiling-mounted ones can light the whole room with just one but are out of reach. They are operated using a magical lamp stick, a rod with a brass ring at the end, which is brought near the magical lamp to turn it on or off. You just bring the ring close.

Of course, as I did, it can also be done with magic art. Ursula doesn’t understand magic arts, so she says such superstitious-sounding things.

Now then, let’s install it.

“Young Master, shall I bring a lantern?” (Ursula)

“It’s fine, it’s fine. I just removed the burned-out magic stone a moment ago.” (Leon)

“Please be careful, Young Master.” (Ursula)

It’s not a ladder, so I’ll be fine.

I climbed onto the step stool and reached up.

“Oof, nn.” (Leon)

Oh, Ursula is holding my legs to steady me. How kind.

“Ah.” (Leon)

Before my eyes, my mental system opened, and a block diagram appeared.

“Are you all right?” (Ursula)

Focus on fitting the magic stone… ah, it went in.

I replaced the cover and fastened the latch.

≪Activate! Light on≫

Good!

“Wow, it’s gotten bright.” (Ursula)

“Yeah.” (Leon)

Ursula let go of me.

“Well then, I’ll take my leave.” (Ursula)

“Yeah. Thanks, Ursula.” (Leon)

She bowed and left my room.

There’s still about thirty minutes until dinner. Too little time to start homework. Magical lamps, compared to candles and oil lamps, are very convenient. But if the magic stone burns out, it’s terribly inconvenient.

I sat in my chair and closed my eyes. The block diagram from earlier was displayed again. What I was seeing was the magical circuit of the entire magical lamp. Inside this circuit were three magic stones.

I see. When an impulse input is applied to the control magic stone’s terminal, the mana storage magic stone generates magic pressure, sending magic flux to the luminous-use magic stone. The magic circuits of each are simple.

Feeling inspired, or perhaps in avoidance mode, I applied an input. On the scope between the magic stones, the waveform that had been flat suddenly rose sharply, climbing higher and higher. This was the graph of magic flux supplied. Since the scope had auto-scaling, the scale kept expanding, and soon another scope’s waveform began to rise.

This one? The luminous output, huh. I see.

Oh, now the magic flux waveform hit a ceiling and began to drop. Yet the luminous output didn’t decrease, and eventually saturated. The magic flux was now less than half of its peak, an overshoot waveform.

Hmm. When the filament’s temperature rose, the magic impedance increased, reducing the magic flux. But since luminous output depends on the filament’s temperature, it brightens smoothly and stabilizes regardless of the magic flux.

Wait a second. Couldn’t the cause of filaments sometimes burning out early be this magic flux overshoot?

A filament is a consumable, constantly exposed to high heat while the magical lamp is lit. It’s surrounded by a hollow for insulation, so it gradually sublimates and thins until it breaks. But the lifespan varies greatly. I now had a hypothesis that the cause was surge magic flux.

That makes sense. When magic flux flows, it generates not only heat but also physical force. If that’s the cause, what should be done? Easy. Let the magic flux flow gradually. That said, surge magic flux occurs because the filament, when cold, has low magic resistance. In the current circuit, the magic pressure is simply switched from OFF to ON, causing a large flux. To prevent that… PWM, pulse width modulation.

By rapidly turning magic pressure ON and OFF, you can control the magic flux via the duty cycle. In electric circuits, this is a standard method for controlling current. It should work fine for magic flux too.

Once I thought of it, I acted immediately.

SimuConnect already has a PWM control block prepared, so it’s easy.

In ten minutes, I had the configuration. I also reduced the gain to prevent magic flux overshoot.

Run… huh? The luminous output scope’s waveform didn’t rise. In other words, it didn’t light. Ah, I see, the filament’s temperature isn’t rising quickly. Without heat, there’s no radiation and thus no light.

After thinking that, about ten seconds later it began to glow, and about twenty seconds in it saturated.

The goal of preventing filament burnout should be achieved, but now, even if you flip the switch, it won’t get bright right away. That’s pretty inconvenient. Needs fixing.

I stretched the scope’s horizontal axis and observed the fine waveform of the magic flux.

Hmm. The magic flux’s rise lags slightly after the magic pressure’s switching timing, so it seems the filament’s magic impedance includes inductance. As expected.

The remaining problem is the average magic flux rise rate. Raise it too slowly and the light is delayed; too fast and lifespan shortens. But this can be handled with variable gain. Right after turning on, use higher gain, then gradually lower it to avoid overshoot.

I built a model for that. I thought it worked with a fixed slope profile, but found it failed if the switch was toggled repeatedly. The gain has to be adjusted to the filament’s initial temperature. I considered using several profiles, but that would be troublesome. In the end, I decided to use temperature feedback.

In about thirty minutes, the modified magic art model on SimuConnect achieved acceptable luminous rise speed and suppression of surge magic flux. The control model grew in scale, but it could now absorb output variations and magic crystal differences, so I’d call it a passing grade.

 

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