If you have ever set up a levitating display, you know the little plastic or metal frame some systems ship with — the positioning aid you clip on, drop the floater into, then remove. Customers ask us regularly why Gleagle push-up systems do not need one: place the floater by hand, feel a small “click”, and it locks. The short answer is two architecture choices. The long answer is this article.
Three sentences first. 1) A single-direction drive obeys F = ki·i with i ≥ 0 — its control law has exactly two states, push or don’t push; past the sensing point there is no reverse force, the floater overshoots upward, and a mechanical aid must catch it. 2) Bidirectional drive makes the effective stiffness keff = kpassive + ki·Gloop hold on both sides of the levitation point — the potential well turns from a cliff on one side into a symmetric well, and overshoot is braked electrically. 3) The slow servo is an integrator: its steady-state error is zero independent of load, so the system converges by itself to the lowest holding current — and re-converges for any floater weight.
The crux: a single-direction drive can push, but never pull
To save cost, the traditional design drives the coil with a single power device in series:
Current has one direction (on or off), so force has one polarity. The control law has two states — push, or don’t push. There is no third option
Consequence one: past the sensing point, it overshoots
A user lowers the floater by hand; the system detects entry and energizes. If the floater is slightly above the ideal levitation point, the one thing a single-direction drive can still do is push harder — when what is needed is a reverse pull. With no reverse force, the floater runs all the way to a mechanical stop.
Consequence two: heat is architectural, not a cooling failure
Copper loss grows with the square of current; the linear stage’s device dissipation lands directly on the power transistor
The decisive point: both are static. Even with the floater hanging perfectly still, current must keep flowing and the device must keep heating. “Runs hot” and “burns out” are certainties of a single-polarity architecture, not accidents — no heatsink size changes that.
Bidirectional drive: from one-way push to two-way clamp
Force no longer covers only the positive half — it spans the full interval. This is a qualitative change, not an incremental one
In stiffness terms: whether the float is “stable” depends on the equivalent stiffness near the levitation point, and the potential well it forms:
kpassive = passive magnetic stiffness · Gloop = loop gain · E(x) = potential well — the deeper the well, the harder it holds
Under single-direction drive this relation holds on one side of the levitation point only — on the other side Gloop is effectively zero, the stiffness is asymmetric, and the floater is in free fall for half of its travel.
| Dimension | Single-direction drive | Bidirectional drive |
|---|---|---|
| Force polarity | Single (push only) | Bipolar (push and pull) |
| Effective stiffness | One side only | Symmetric, both sides |
| Potential well | A cliff on one side | A symmetric well |
| Capture | Entry from one side only | Captures from either side |
| Overshoot risk | Needs a mechanical positioning aid | Braked electrically by reverse force |
Force versus displacement. Left: the single-direction curve exists on one side only — past the levitation point is a blind zone. Right: the bidirectional curve crosses the levitation point with restoring force on both sides — the point becomes a true lock.
How the “lock” forms: what happens in that one second
Step 1 — floater below the point. The sense loop reads a negative error; the bidirectional stage outputs a large positive current and the coil corrects upward. Large current, but for a very short time.
Step 2 — floater above the point. The instant the point is crossed, the control law reverses the output: the coil pushes downward, braking the motion. A single-direction architecture can do nothing in this step.
Step 3 — lock. Upward and downward forces alternate rapidly, clamping the floater in a tiny neighborhood of the levitation point. Macroscopically: the “click” of a magnetic lock.
Fpm(h) = permanent-magnet repulsion at height h · mg = floater weight · ki·i = coil correction force · h₀ = equilibrium levitation point
The slow-servo loop: why the holding current can be extremely low
By the balance equation, the steady-state current should approach zero in theory. In reality, offsets accumulate: mechanical tolerances in sensor mounting, geometric asymmetry of the magnetic path, offset voltages in the analog stages, temperature drift. Together they form a static bias current — the floater is centered, yet the coil keeps burning power. This is the other half of why traditional designs run hot.
The fix: let the system find its own zero-current point
In parallel with the fast loop runs a slow servo path: it takes the long-term average of the drive signal, integrates it through a large time-constant network, and slowly pushes the static bias back to zero.
i₀ = bias current at capture · τ = the servo’s time constant, deliberately slow so it never fights the fast centering loop
Capture → lock → the slow servo takes over → static current decays exponentially to its minimum.
Why this is the essence of the design
The decisive property of an integrator: infinite DC gain → steady-state error is identically zero.
Whatever the accumulated offset, the servo keeps integrating until the error is gone
The practical meaning is powerful: the servo is insensitive to load. Swap in a heavier or lighter floater and the levitation point moves, the required static force changes — but the servo does not need to know by how much. It watches a single criterion — is the static current zero — and converges to the new optimum by itself.
The combined ledger
| Phase | Single-direction (traditional) | Bidirectional + slow servo (Gleagle) |
|---|---|---|
| Capture instant | Large current | Large current (equally needed) |
| Approaching the point | Keeps pushing → overshoot, aid required | Reverse braking → automatic lock |
| After lock | Sustained static current | Servo pushes the bias toward zero |
| Steady-state power | Baseline | A fraction of baseline |
| Long-term heating | Significant; the main burnout cause | Greatly reduced |
| Different floater weight | Operating point must be re-set | Re-converges automatically |
The power benefit comes from the square law:
Every notch the servo trims off the static current, heat falls quadratically — why auto-seeking is worth far more than its component cost
Formula cheat sheet
| Relation | Expression | Use |
|---|---|---|
| Coil force | F = ki·i | Bidirectional: i can be positive or negative |
| Copper loss | Pcu = I2R | Square law — current cuts pay double |
| Linear-stage dissipation | Ploss = VCE·IC | The static heat source of single-polarity designs |
| Force balance | mg = Fpm(h₀) + ki·i | The steady operating point |
| Equivalent stiffness | keff = kpassive + ki·Gloop | Only bidirectional holds it on both sides |
| Potential well | E(x) = ½keffx2 | Deeper well → harder lock |
| Servo decay | i(t) = i₀·e−t/τ, τ = RC | Static bias decays exponentially |
| Steady-state error | ess = 0 | Inherent to the integrator, load-independent |
Closing
Bidirectional drive answers “can it hold on” — restoring force on both sides of the levitation point, overshoot braked in the electrical layer, and the positioning aid made unnecessary. The slow-servo loop answers “how much power does it cost” — the system converges by itself to the lowest holding current, and re-converges for any floater weight.
Together they turn an operation that used to demand user skill, an aid tool and a tolerance for heat into a single motion: place it with one hand. There is no magic in between — just two explicit architecture choices.
This article is an architecture explainer based on published physics — not a product specification or delivery commitment.
Related reading: the slow-servo loop ships today in our push-up modules — see the PU300G platform — and the forward-looking pieces Next-Generation Push-Up Levitation and Next-Generation Pull-Down Levitation. For module selection, see the Global Adapter Guide Levitation Module Selection Guide.