RPM Tracker — Control Systems/Vibration

RPM Tracker

Control Systems / Vibration

The shaft speed of a machine, read out of the machine's own vibration – no tachometer. A rotating order writes itself across a time-frequency map as a ridge at f = order · rpm / 60, so following that ridge from frame to frame is the speed measurement.

This is the coarse ridge of MATLAB's rpmtrack, transcribed from R2026a's signal.internal.rpmtrack.computeRPM. Every hop samples the last Window Length samples are windowed and transformed, and the ridge takes one step: from the previous two rows r₁ and r₂, the search band is [r₁+s−3 … r₁+s+3] with s = r₁−r₂ the slope, and the row taken is the one minimising

S[i] + λ·(i − 2r₁ + r₂)²

where S is the cost map −10·log₁₀(col/Σ + eps) and λ is Frequency Penalty scaled by half the bin width, exactly as rpmtrack scales it. When the power penalty is finite the band then grows one row at a time until the chosen row's power is within Power Penalty decibels of the previous ridge's.

Ports

• u – the vibration signal, scalar. One block per channel.
• rpm – the tracked speed in revolutions per minute.
• f – the ridge frequency in hertz, (row − 1) · f_s/L.
• row – the 1-based bin the ridge sits in, which is a discrete answer: the smallest speed change this block can report is one bin, 60·f_s/(L·order) rpm.

Parameters

• Sampling Rate (Hz) – the rate the signal was sampled at; it sets the frequency axis and nothing else.
• Window Length – L, the frame the transform runs over. The bin width is f_s/L, so this is the resolution of every speed this block can report.
• Window – Hann, Hamming, Flat Top or Rectangular, periodic sampling (the one to take a spectrum with).
• Overlap (%) – how much of each frame the next one repeats; the hop is L − round(overlap·L/100), at least 1.
• Order – the shaft order the ridge represents. 1 is the shaft rate itself; 2 is the second harmonic, and the rpm it reports is half the frequency's.
• Initial Frequency (Hz) – the seed, and it is the one parameter this block cannot guess. The walk opens on the bin nearest this frequency and never searches more than three bins per frame, so a seed on the wrong ridge tracks the wrong ridge for the whole run.
• Frequency Penalty – λ before scaling: the price of curvature. Larger keeps the ridge straighter and less willing to follow a jump.
• Power Penalty (dB) – how far the ridge's power may move between frames before the band widens to look further. ⚠ A value of zero or less means INFINITE – no power test at all, which is rpmtrack's own default, and it is also what switches the slope extrapolation on.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period. ⚠ It is not the same number as Sampling Rate (Hz): this one is how often the block is called, that one is what the frequency axis is read in. Setting one does not change the other.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text, from one statement list, so every target runs the same arithmetic in the same order as the simulation. The window taps and the bin spacing are numbers at export time; the transform, the two maps and the ridge run as loops. The three HDL targets carry it in simulation-only real arithmetic, quantized at the port.

Simulink bridge

None. rpmtrack is a Signal Processing Toolbox function and that toolbox ships no Simulink library at all, so there is no path a diagram could name.

Notes

• ⚠ WHAT REPLACES rpmtrack's RIDGE POINTS. rpmtrack is handed (time, frequency) pairs on the record's absolute time axis and walks outward from each in both directions. A stream has neither an absolute time axis nor a future, so this block takes one seed and walks forward only. Given the same columns and the same first row, every row after it is rpmtrack's own.
• ⚠ THE NORMALIZING SUM CANNOT CHANGE THE ANSWER, and that is measured. rpmtrack divides the map by the sum over the whole observation window before the log, which a stream cannot do without holding the window. It does not have to: dividing by a positive T shifts every row of one column by the same +10·log₁₀(T), and every comparison the step makes is between two rows of the same column, so the shift cancels. Checked by adding a random constant to the cost map on the 600 reference cases below – the ridge moved on 0 of 600. This block therefore normalizes by the current column's sum and keeps O(M) state instead of O(W·M).
• ⚠ THE FIRST TWO FRAMES ARE DIFFERENT STEPS, because they are in rpmtrack: frame 1 is the plain minimum of S within ±3 rows of the seed, frame 2 adds the frequency penalty but no power test, and the general step starts at frame 3.
• ⚠ VERIFIED AGAINST MATLAB'S OWN STEP. 600 random cases spanning 8 to 40 rows, both penalty regimes, and an infinite power penalty on 179 of them, generated by calling the R2026a local functions directly: 600 of 600 identical, with the band-widening loop firing on 276 of them over 5827 iterations. ⚠ One defect this gate caught that reading could not: MATLAB builds its band as max(1,c−3):min(c+3,M−1), which is EMPTY when the slope throws the centre clear of the map – and that empty range is exactly what triggers its fallback to r₁±3 with the slope off. Clamping both ends into [1, M−1] instead makes the empty case unreachable and silently searches a single row. It cost 27 of the 600, every one a large slope at an infinite power penalty.
• Stateful, and discrete by nature (setDiscreteOnlyBlock(true)): a shift register of L samples, a frame counter, and the ridge's own memory. No state space – a ridge index is not linear in the window.
• Not the whole of rpmtrack. That function refines this ridge with a Vold-Kalman order waveform and a second transform. Both of those are blocks in this library already – Order Waveform and Time-Frequency Ridges – so the refinement is a diagram, not a missing feature.