Concept

Collocation — where it appears

Placing a control actuator at the same point as the sensor that measures the motion it responds to. A collocated pair cannot excite a mode it does not also see, which is why such loops are stable for any gain in the absence of delay.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as feedback — the same set of essays touches all of them, so they are one junction rather than several.

$What the actuator pushes against decides its limit. The largest feedback gain, as the damping it would add to the bare mode, at which the loop stays stable, against the delay as a fraction of the period, on a logarithmic scale, for a mode of 1.00 per cent damping carrying a tuned mass of 2.00 per cent of its modal mass at Den Hartog's tuning. Pushing against the ground, fed by the structure's velocity: 2.41 at a delay of 0.05, 0.25 at 0.2. Pushing against the tuned mass, fed by the same velocity: 0.0156 at almost no delay, rising to 0.091 at a quarter of a period. Pushing against the tuned mass, fed by the velocity across it: unlimited with no delay, 0.048 at 0.05, 0.0073 at 0.2.$

The actuator that pushes against the mass

An actuator that damps a structure by feeding back its velocity has to push against something. Against the ground, it is stable up to large gains until a delay of a quarter period removes its damping. Against a tuned mass — the arrangement meant to keep a passive damper underneath — the same feedback goes unstable at a gain of a per cent and a half with no delay at all, makes the structure worse than the passive mass at every gain below that, and drives the mass three or four times as far. What limits it is not when it acts but what it pushes against.

dynamics · Tuned mass damper

Every law with the spring cancelled, stroke against peak. Each point is one law for a structure of one mode with 1.0 per cent damping and a tuned mass of 2.0 per cent of its mass, tuned and damped by Den Hartog's rules with the mass's spring cancelled, its structure-velocity and relative-velocity gains on a grid: its peak response against the mass's peak stroke, both as multiples of the static deflection. Filled, the 731 laws that need no more than 0.50 of the applied force; faint, the 730 that need more. The passive mass is the ring, at 45.3 and 8.72. The lower edge of the filled cloud is the best a law of this kind can do for each stroke; at the passive stroke it is 7.38, and it falls steeply as the mass is given more room.

The law that throws the tuning away

An actuator that pushes against a tuned mass and listens only to the structure pumps the mass's own mode. A law that also listens to the mass can be made safe in one move — cancel the mass's spring, so that it has no mode to pump — and every such law is stable. But cancelling the spring throws away the tuning that made the mass useful, and the actuator has to earn it back: below a third of the force on the structure, the law is worse than the passive mass it replaced. What it buys above that, it buys mostly by letting the mass travel further.

dynamics · Tuned mass damper

Named alongside it

The objects these essays reach for when they reach for this one.

Active control Damping Feedback Resonance Stability Time delay Tuned mass damper

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