Conversation

“when it feels wrong, is exactly the right moment” — LA mayor Eric Garcetti It’s a good way to informally explain integral control of exponential dynamics. Our instincts are wired to proportional+derivative control which react to “now” instead of recent memory.
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An ounce of gain on I is worth a pound of gain on P and D D gain is the worst. Small noise in signal and you’re thrashing like crazy, like Trump reacting to stock market. D gain in quiet times is like covered calls on a smoothly rising market. Volatility kills the ride.
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Integrating dampens noise and helps forecast under future-like-past conditions. Virus-prep should make a nice homework problem set in model predictive control someday. You wouldn’t want to use an unbounded exponential as an internal model of course, you’d use an S-curve logistic.