bode plot of a magnetic levitator

Magnetic levitation is one of the classic teaching plants in control because of what its Bode plot reveals, so this is a fun one. Let me lay out where the plot comes from, then show it. The plant is open-loop unstable An electromagnet holds a steel ball at gap 𝑥 x below it. The attractive force grows as the ball gets *closer*, which is positive feedback — exactly what makes the thing want to…