Arduino is a digital mikrocontroller. But I wonder if it's possible to implement an continuous time feedback regulator in an Arduino microprocessor?
Continuous time feedback regulators such as PID:
$$ K = P(e(t)-D\frac{\mathrm{d} }{\mathrm{d} x}e(t) + I\int_{0}^{\infty} e(t) dt) $$
Or LQG regulator (this is a LQR with kalmanfilter only, not the model): $$ \dot{\hat{x}} = (A - KC)\hat{x} + Bu + Ky + Kn - KC\hat{x} $$
$$ u = r - K\hat{x} $$
Or do it need to be a digital feedback regulator? I mean....those feedback regulators works exellent by using operational amplifiers.
I know that operational amplifier works in real time. But an Arduino working in 16 Mhz speed, and that's very fast too.