Audible Frequency Response of Stable and Unstable Control Algorithms
A teaching lab that lets you hear a control loop go unstable. Much of a power converter’s transfer function lives inside the audible band, and the ear reads sound as a frequency spectrum — so a boost converter wired to a speaker turns loop stability into something you can identify by listening, before you have read a single Bode plot.
The idea
The converter switches between two operating points once a second. Every time it steps, the output rings according to the transfer function, and that ringing is audible. Change the control and the sound changes with it — same circuit, same operating point, different character.
- Open loop — duty cycle alternating between 20% and 60% at a fixed 10 V input, with no feedback to correct the overshoot.
- Closed loop — reference voltage alternating between 14 V and 18 V, with \(K_p\) and \(K_i\) swept from wildly unstable to critically damped.
- Frequency sweep — available in either mode, walking the step rate from 20 Hz to 5 kHz over 5 or 10 seconds.
Hardware
A conventional boost converter on ECE 469 boards into a 50 \(\Omega\) load, with a speaker in series with a 220 \(\mu\)F capacitor to block the DC. Switching signal, output current, output voltage and the mid-point sense node are all probed, so the scope trace and the sound can be read against each other.
The closed-loop controller borrows the buck implementation and inverts the integral term, which behaves closely enough to a true boost controller for the purpose. The topology is incidental here — what matters is being able to dial the stability margin freely, and that a boost output swings hard enough to drive a speaker at a useful volume.
What it sounds like
| Mode | Control | Sound |
|---|---|---|
| Open loop | no feedback | a bouncing rubber ball — impact, then reverberation |
| Mode 0 | unstable, eventually settles | a turbine winding down, high to low |
| Mode 1 | stable but uncontrolled | an alarm; grainy, resonant, unclear pitch |
| Mode 2 | near the stability edge | the same pitch as Mode 1, much less sibilance |
| Mode 3 | critically damped | near silence; a faint low thump on each step |
Mode 1 and Mode 2 are the useful pair. Their waveforms look alike and they measure the same loudness, so nothing on the scope separates them at a glance — but the resonance and grain that Mode 2 removes are immediately obvious by ear. Mode 1 overshoots to nearly twice the intended output and still reads as a single clean impulse, because a stable controller does not sustain the ring; Mode 0, which is genuinely unstable, is the one that keeps going.
The sweeps make the same point on a longer time base. In Mode 2 the peak-to-peak output grows as the step rate climbs, and the sound picks up chirps and digital artefacts exactly where the waveform jumps. Mode 3 holds its amplitude across the whole sweep and stays quiet throughout, apart from one brief chirp where the sweep resets.
Why it works as a lab
The diagnostic is the point: stability margin becomes a perceptual judgement rather than a measurement. A student who has heard Mode 1 and Mode 3 back to back has a reference for what an underdamped loop does, and can recognise it in a converter that has no speaker attached at all.