Order Track — Control Systems/Vibration

Order Track

Control Systems / Vibration

The amplitude of one or more shaft orders against time – MATLAB's ordertrack on its Vold-Kalman path – over a running window of the last W samples. Order k is the vibration component riding at k·rpm÷60 hertz; the filter finds, over the window, the complex envelope X for which 2·Re(X·e^jθ) best matches the signal while X stays smooth, with θ[n] = (2πk÷60fs)·Σrpm taken from the speed port. What is published is the size of that envelope for the window's centre sample: peak = |2X|, rms = peak÷√2 or power = peak²÷2, on a linear or a decibel scale.

Ports

• x – the sampled vibration signal, scalar: one channel and its own window.
• rpm – the shaft speed at the same instant, in revolutions per minute, scalar.
• mag – the order magnitudes, [K, 1] with one row per entry of Order List, in the units Amplitude and Scale select. Row k is the value at the sample (W−1)÷2 ticks ago, not at this tick.
• rpm out – the shaft speed of that same sample, [1, 1]: the magnitudes are plotted against it, and it is delayed by the same (W−1)÷2 samples so the pair belongs together. It is ordertrack's second output.

Parameters

• Order List – the orders to track, a vector of up to eight positive numbers; they need not be whole. Defaults to [1 2]. K is its length and sets the height of mag.
• Bandwidth (Hz) – how fast the tracked amplitude is allowed to change, read as the filter's smoothness weight exactly as MATLAB reads it, r = (1.58·fs÷2πbw)². A narrow bandwidth rejects a neighbouring order and follows a run-up slowly; a wide one does the opposite. Positive; defaults to 40. See the Notes for how it must be sized against the window.
• Window Length – W, the record the filter solves over: an ODD whole number from 17 to 513, odd so that the window has a centre. Defaults to 129. Every generated core carries W-sized arrays and W sine-cosine pairs per order per sample, which is what the upper limit is about.
• Sample Rate (Hz) – fs, the rate the two signals were sampled at: the bandwidth and the order frequencies are in hertz through it. Positive; defaults to 1000.
• Amplitude – what the magnitude means, ordertrack's own three:
  • RMS – peak÷√2, the default there and here.
  • Peak – the envelope itself, |2X|.
  • Power – peak²÷2.
• Scale – Linear (the default) or dB: 20·log10 of an rms or peak magnitude, 10·log10 of a power one. A window in which the order is exactly absent is −∞ on this scale, as it is in MATLAB.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The filter's matrix does not contain the data, so it is solved ONCE at export time and the core carries its W solution weights as numbers; each sample is then the window's cumulative speed, one sine-cosine pair per sample per order, one accumulation and one square root. All six settings are structural, so re-export after changing any of them.

⚠ The three HDL targets run those loops in simulation-only real arithmetic, quantizing only at the port boundaries: a Q16.16 datapath carries neither the sine and cosine of an accumulated phase, nor a decibel, nor a window of a thousand samples. They are not offered as synthesizable.

Simulink bridge

None (Support::None). ordertrack is a Signal Processing Toolbox function and that toolbox ships no Simulink library, so there is no path a diagram could name; the bridge reports this block rather than dropping it silently, and it therefore has no parity testbench. Code export verification still covers it across all ten languages.

Notes

• Stateful, and discrete by nature (setDiscreteOnlyBlock(true)): two shift registers of W samples, zero at the start of the run, so the first W−1 samples of a run are a window that is still filling.
• ⚠ Both outputs lag by (W−1)÷2 samples – 64 at the default window. The least-squares envelope is unconstrained at the edge of its own record, so the window's newest sample is not a usable estimate: measured against the whole-record answer on a 600 to 1800 rpm sweep, the window's centre converges to it (9.0e−4 at (W−1)·bw÷fs = 5.1, 7.0e−7 at 10.2) while its newest sample stays at 1.0 to 2.4 on a true amplitude of 1.4 whatever the window length.
• ⚠ Size the window against the bandwidth. The agreement above is governed by (W−1)·bw÷fs: about 1e−3 at 5, 1e−6 at 10, 1e−12 at 20 – so a narrow bandwidth needs a long window, and W < 5·fs÷bw is a window that cannot hold the filter's own response. The defaults sit at 5.1.
• ⚠ MATLAB's ordertrack only runs this filter in one of its two syntaxes. Given the speed as a plain vector it takes the resampling path instead – an order map, read at the nearest order row – and refuses the bandwidth argument entirely. The Vold-Kalman path is the matrix-speed-and-index syntax, and it is the one this block implements; the resampling path belongs to the RPM-Order Map block.
• Orders are tracked independently of one another, which is ordertrack's default (Decouple false). The coupled solve, which separates orders that cross, needs a K·W system whose matrix DOES contain the data, so it is not offered here.
• The filter order is fixed at 1, as ordertrack fixes it. Order Waveform, whose counterpart exposes it, has it as a parameter.
• An order whose frequency passes fs÷2 aliases, exactly as it would in MATLAB, which refuses such an order list outright; the speed arrives on a port here, so it cannot be checked at configuration time.