Controller “stabilising time” (settling convention): In classical instrumentation usage, the stabilising time for a controller is the time required for the response to reach approximately what percentage of its ultimate value?

Introduction / Context:
Practitioners often use practical time markers to describe how quickly a system “settles.” While modern control defines settling time as reaching and remaining within a small band (for example 2% or 5%), older instrumentation texts and many plant heuristics use percentages of the final value corresponding to multiples of the dominant time constant for a first-order response.

Given Data / Assumptions:

• First-order-like response is implied.
• We want the conventional percentage linked to “stabilising time.”
• Ultimate (final) value is well defined for the step.

Concept / Approach:
For a first-order system y(t) = y∞(1 − e^(−t/τ)), standard waypoints are 63.2% at 1τ, 86.5–87% at 2τ, and about 95% at 3τ. Many instrumentation references call roughly three time constants the “stabilising time,” because the response appears practically complete for operators. Thus, 95% is the expected answer here.

Step-by-Step Solution:

Verification / Alternative check:
Many vendor response specifications use “3τ ≈ 95%” as a quick estimate of the time to reach essentially final value for step testing of sensors and transmitters.

Why Other Options Are Wrong:

• 63.2 and 87.5 correspond to 1τ and 2τ respectively, earlier than typical stabilisation.
• 100 is unattainable in finite time for an exponential approach.

Common Pitfalls:
Confusing the strict control definition of settling within a band (2%/5%) with the heuristic “stabilising time” used on shop floors; both are useful but not identical.

Final Answer:
95