Tuning is done by hand more often than by theory

What practitioners actually do, and why the textbook method is rare.

Tuning a real control loop is done by hand far more often than by the formal mathematical methods taught alongside PID control, because the theory generally assumes a clean, well-known model of the system being controlled, while most real machines are messy enough, and different enough from their own textbook description, that a practitioner adjusting gains, watching the result, and adjusting again gets to a working answer faster and more reliably than deriving one on paper ever would.

The short version

Formal tuning methods exist and genuinely work, deriving a mathematical model of a system's behaviour and calculating gains that should, in theory, produce a well-behaved response without any trial and error at all. Building that model accurately enough to trust, however, demands knowing a system's mass, friction, delay and every other relevant property with real precision, measured rather than assumed, and most real mechanisms carry small inconsistencies, a bearing slightly stiffer than its neighbour, a cable with a little more stretch than assumed, a motor slightly weaker than its datasheet promised, that no reasonable model captures in full. Practitioners have learned, often the hard way, that starting from a formal calculation and refining it by hand usually beats either trusting the calculation blindly or throwing the model away and guessing from nothing, which is why hand tuning survives everywhere despite decades of formal theory having been available, in principle, to replace it entirely by now.

The guitar-tuning comparison

Tuning a guitar string by ear is a small, familiar demonstration of exactly the same practical wisdom. A guitarist could, in principle, calculate the exact tension a string needs to reach a given pitch, given its length, its mass, and the physics of a vibrating string, and arrive at a defensible number entirely in advance, before ever touching the instrument. In practice, no guitarist does this, because the string's actual behaviour depends on details a calculation would struggle to capture precisely, a slightly worn fret, a string that has stretched unevenly since it was last changed, tiny variations from one instrument to the next that make a calculated answer only ever an approximate starting point rather than a finished result. Instead the guitarist plucks the string, listens, turns the tuning peg a little, and listens again, converging on the correct pitch through a handful of small, corrected adjustments rather than through a single calculated turn of the peg. A control engineer tuning gains by hand is doing exactly this, using rough theory to get somewhere close and then trusting direct observation of the real system to close the remaining gap theory alone could not reliably predict, arriving at a tuning that works rather than one that merely looks correct on paper.

Why the textbook method struggles outside the textbook

Formal tuning methods tend to assume the system being tuned behaves in a simple, well-understood way across the whole of its operating range, but real machines rarely cooperate quietly with that assumption, since friction changes with temperature, a mechanism's mass distribution shifts depending on what it is currently carrying, and a sensor's own noise characteristics can vary between one unit and the next even within the same production batch. A formal calculation performed once, based on a single snapshot of the system's properties, produces gains tuned for that snapshot rather than for the system as it actually behaves across every condition it will eventually meet. Hand tuning, performed while watching the real system respond under something close to its actual working conditions, sidesteps this weakness entirely, since it is reacting to the system's true behaviour rather than to a simplified description of it, and it keeps working even as that true behaviour drifts slowly over the life of the machine, something a one-off calculation performed on day one was never going to track.

One figure worth keeping in mind

An experienced practitioner can often bring a new system's control loop to a genuinely usable, stable tuning within a handful of iterations, adjusting one gain, observing the response, adjusting again, arriving at workable settings in less time than it would take to build and validate a formal model accurate enough to trust on its own, even before accounting for the very real chance that the formal model, once built, still needs hand correction anyway once it meets the actual hardware rather than the assumptions it was built from.

Where extra decimal places stop helping

A formal model built from measured system properties can still leave a controller's real-world response noticeably different from the one the model predicted, sometimes by a wide enough margin that gains calculated to two or three decimal places of precision are, in practice, no more useful as a final answer than a rough starting estimate would have been, since the model's own uncertainty swamps whatever extra precision the calculation appeared to offer. This is not a failure of the mathematics, which is entirely correct given its assumptions, it is simply a reminder that the assumptions themselves, however carefully chosen, are rarely as exact as the real machine turns out to be.

Why this matters in practice

None of this argues that formal theory is worthless, since understanding what proportional, integral and derivative gains are actually doing is exactly what makes hand tuning fast rather than aimless, turning trial and error from blind guessing into an informed search guided by real understanding of cause and effect. Carroll Smith's Tune to Win makes essentially this same case for motor racing, that theory earns its keep by telling a practitioner which direction to turn the dial and roughly how far, while the final, precise setting still has to be found by watching the actual car, or the actual machine, respond on the actual day it is being tuned, under the actual conditions it will actually be asked to perform in rather than the tidy ones a model assumed.