What a Line-of-Sight Stabilisation Figure Actually Costs

Stabilisation accuracy is the specification buyers compare most and understand least. A figure of 0.05° and a figure of 0.003° differ by more than a decimal point: they are different mechanical architectures, different sensors and, usually, a different price class. This paper explains what separates them.

Stabilisation is an error budget

A stabilised line of sight is the sum of several independent error sources, combined in quadrature. Reducing the total means finding the dominant term and attacking it; polishing a term that is already small buys nothing.

That last sentence is worth stating as arithmetic, because it decides where money goes. In a root-sum-square, a term half the size of the largest one contributes about a tenth of the total. Halve that term and the total moves by a percent or two — an improvement no test will resolve. Until the largest term has come down, every other improvement is invisible. Most stabilisation budgets that fail to close have been optimised in the wrong place, and the budget itself is what tells you where the right place is.

The principal contributors are:

Bearing and structural compliance. Every mechanical joint deflects under load. At long focal length, an angular deflection of a few tens of microradians is visible in the image. This is why stiffness, not mass, is the design driver, and why the analysis chain — static, modal and random vibration — exists before the first part is cut.

Backlash. Any lost motion in the drive train appears directly as pointing error on a reversal. This is the reason zero backlash is published as a specification in the positioner range rather than offered as an option: a drive with backlash cannot be stabilised, only averaged.

Encoder resolution and accuracy. The control loop cannot correct what it cannot measure. Axis resolutions in this range run from 0.084° down to 0.002°. Resolution is not accuracy: an encoder can report finely and still be wrong, which is why the tighter architectures use a secondary encoder closer to the load.

There is a third term in that family that gets left out. Repeatability is not accuracy either, and the difference decides what can be fixed after the fact. A system that reports the same wrong angle every time is repeatable and inaccurate, and a calibration table removes the error completely. A system that reports a different angle each time it approaches the same point is accurate on average and not repeatable, and no table will help it. When comparing two units, ask for all three figures; suppliers quote whichever of them is best.

Inertial sensing. The loop needs to know how the base is moving. A MEMS IMU is compact and adequate for moderate requirements. A fibre-optic gyro has lower noise and drift, and it is what appears in the architectures that publish the tightest figures.

Control bandwidth. Disturbance rejection falls off above the loop’s bandwidth. A loop that is fast enough for a vehicle on a road may not be fast enough for the same vehicle cross-country, because the disturbance spectrum has moved.

Every stabilisation figure has a clock attached to it

A stabilisation number is a statistic, and a statistic is taken over a window. The window is almost never printed next to the number, and it changes what the number means.

Measure over a short window and you are measuring the loop’s rejection of vibration. Measure over a long one and slow terms enter that were not in the first result at all: gyro bias drift, thermal movement of the structure, settling of the mount. Both are honest measurements of the same system and they will not agree. Two suppliers quoting the same figure over different windows have not made comparable claims, and the shorter window always flatters.

This is why the dwell requirement belongs in the specification. Holding a mark for the flight time of a round and keeping a picture watchable for an hour are different problems, and a system bought for one may fail the other while meeting its published figure.

The error that arrives with the weather

One term is missing from most published budgets because it is not a control problem at all. A gimbal’s boresight moves with temperature. The structure expands, the optical path expands with it, and the two do not necessarily move together. A system aligned on a bench at room temperature carries a boresight offset at the cold end of its operating range, and another at the hot end, and neither appears in a stabilisation figure measured on a shaker in a laboratory.

This is not a defect; it is a property of building things out of materials. It matters because it is an angle, and angles at long focal length are the subject of this whole document. If absolute pointing has to hold across an operating temperature range, the specification must say so, because it drives material choice and it may require an in-service re-boresight capability that nobody costed.

Why dual-loop control changes the answer

A single-loop architecture closes the position loop on the motor-side encoder. It is simple and robust, and everything between that encoder and the optic — gearbox, coupling, structure — is outside the loop and therefore uncorrected.

A dual-loop architecture adds a second sensor at the load and closes an outer loop around it. Now compliance and lost motion inside the drive train fall inside the loop and are corrected. This is the step that takes an architecture from the hundredths of a degree into the thousandths, and it is why the specification appears as “dual-loop control to 0.001° with secondary encoder” rather than as a bare number.

The cost is not only the sensor. Two loops interact; the inner loop must be substantially faster than the outer one or the pair oscillates. That requirement propagates back into motor selection, driver bandwidth and processor headroom.

Verifying it before there is hardware

An error budget written on paper is a hypothesis. The way we test it before committing to parts is hardware-in-the-loop: the real control algorithm runs on its target microprocessor against a simulated mechanism, so loop gains, sampling rate and filter design are exercised against realistic disturbance before a prototype exists. Multi-body dynamics supplies the plant model and, in the same run, the loads that bearings, actuators and end stops will actually see — which is how those parts get selected rather than guessed.

How to specify stabilisation without over-buying

1. State the disturbance, not just the accuracy. “0.01° on a wheeled vehicle at 40 km/h on a graded road” is specifiable. “0.01°” alone is not.
2. State the focal length you will use. Stabilisation requirements scale with magnification; a figure that is generous at wide field is inadequate at full zoom.
3. State the dwell time, and with it the averaging window. Holding a mark for the flight time of a round is a different problem from keeping a picture watchable, and the two are measured over different windows.
4. Separate stabilisation from pointing accuracy, and both from repeatability. They are different specifications with different causes, and buyers frequently ask for a tight version of one when the mission needs another.
5. Say whether the figure has to hold across the temperature range. If it does, say so before the architecture is chosen rather than at acceptance.

Over-specifying stabilisation is expensive in a way that is invisible at quotation and obvious at delivery: it drives the architecture, and the architecture drives everything else.