Order Waveform — Control Systems/Vibration

Order Waveform

Control Systems / Vibration

The time-domain waveform of one or more shaft orders – MATLAB's orderwaveform, the Vold-Kalman tracking filter – over a running window of the last W samples. An order is the component of a vibration whose frequency follows the shaft: order k rides at k·rpm÷60 hertz, so it sweeps as the machine runs up and a fixed filter cannot follow it. The filter finds, over the window, the complex envelope X that makes 2·Re(X·e^jθ) closest to the signal while keeping X smooth – a least-squares problem in which the phase θ[n] = (2πk÷60fs)·Σrpm comes from the speed port and the smoothness weight comes from the bandwidth. The waveform is published for the window's centre sample.

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. Any speed profile is allowed; it is the sample-by-sample phase that the filter tracks.
• xr – the extracted waveforms, [K, 1] with one row per entry of Order List, in the signal's own units. Row k is the value at the sample (W−1)÷2 ticks ago, not at this tick.

Parameters

• Order List – the orders to extract, a vector of up to eight positive numbers; they need not be whole (a 0.5 order is a half-shaft rattle). Defaults to [1 2]. K is its length and sets the output height.
• Bandwidth (Hz) – how fast the extracted envelope is allowed to change, read as the filter's smoothness weight exactly as MATLAB reads it: r = (1.58·fs÷2πbw)² at filter order 1 and (1.7·fs÷2πbw)³ at order 2. A narrow bandwidth rejects neighbouring orders 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.
• Filter Order – the structural equation, 1 or 2: 1 keeps the envelope's second difference small, 2 its third difference. Order 2 follows a curved amplitude more closely at the price of a worse-conditioned solve. Defaults to 1, which is MATLAB's.
• 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 least-squares matrix does not contain the data, so it is solved ONCE at export time and the exported 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, and one accumulation. All five 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 window of a thousand samples. They are not offered as synthesizable.

Simulink bridge

None (Support::None). orderwaveform 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.
• ⚠ The output lags 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. The block reads the centre for that reason and states the latency rather than hiding it.
• ⚠ 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.
• ⚠ This is the whole-record filter applied to a window, and MATLAB's own answer carries a solver tolerance. orderwaveform solves by preconditioned conjugate gradients at a relative residual of 1e−3; this block solves exactly, by a banded Cholesky. On identical windows the two differ by 1.2e−6 to 1.5e−4 for that reason alone.
• Orders are extracted independently of one another, which is orderwaveform'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.
• 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.
• Not Order Track: that block publishes the same filter's AMPLITUDE against time, in rms, peak or power units.