CAD.Reference:4.6 - Worked joint revision

The running example begins with two different concerns: a planner needs two fast ticks of computation, while an inexpensive feedback law runs every tick. CAD.1 makes the reason for separation explicit. The separation does not yet decide the command: a held target and a timed segment remain alternatives.

CAD.2 derives how their meanings change the error. A held target creates a boundary jump; a joined segment supplies bounded increments at every fast tick. CAD.3 turns that difference into actuator reserve. At the doubled demand, the four-tick held target has a direct violating first input; the joined-segment command has a sufficient input bound of 0.05 under the toy model. Its limited reference interval also has an explicit continuation by holding the reference.

CAD.4 returns the result to the practical choice. The segment design fits the declared computation arrangement but requires a clocked generator, continuity at handover and an admitted initial error. The engineer cannot keep only its attractive input number and omit that realization. If physical actuation is later found to be delayed, the error derivation changes and the bound must be reopened. The reason for separating planning from feedback can remain useful even while that specific realization fails.

During the calculation of an error margin, the immediate mathematical work contributes to constructing a command domain, which contributes to choosing a viable control architecture, which contributes to the engineered system’s required behavior. A changed whole requirement alters what counts as a useful local margin. This connection explains why a numerically correct sub-result can still fail to resolve the engineering problem.