The local time constant is 2A√h₀/c and the local DC gain is 2√h₀/c. At a higher level, the same incremental inflow has a larger steady height effect and a slower local decay rate. This follows from the slope of √h; it is not a change in tank area. The display reports the local time constant, not an exact global settling time.
Make one fair comparison
At h₀ = initial = 0.5 m, pin the small flow step. Set both operating and initial height to 1 m, keeping the same Δq, area and outlet. Compare changes from each starting height, not the absolute level alone.
Before moving a setting, write which signal you expect to change and why. A faster-looking curve alone does not explain the mechanism. Keep the initial state and all other settings visible in the pinned run.
A controller still needs flow authority
To hold target r after a constant extra drain d opens, the pump must supply c√r+d. Compare this value with the pump limit before tuning PI. The lab uses qrequest = q₀ + Kp(r−h) + I and continuous integral accumulation. Conditional anti-windup blocks accumulation that would worsen pump clipping. Unlike the thermal lab's zero-bias PI, this experiment exposes the operating-point bias explicitly.
An empty tank and a full tank are physical boundaries, not negative or arbitrarily large levels. This model stops at 0 or 2 m instead of inventing an overflow continuation. The linear prediction is deliberately not clipped: an impossible negative prediction is evidence that the local approximation has been used outside its domain. Replaying a stopped run does not extend its data.
What to change next
When a single tangent model predicts one operating region but misses another, first state the intended height range. A new linearization or a scheduled family of controllers may be appropriate; a nonlinear design is another option. The current lab compares local predictions and one PI controller, not an implemented gain-scheduling algorithm.
The local time constant is 2A√h₀/c and the local DC gain is 2√h₀/c. At a higher level, the same incremental inflow has a larger steady height effect and a slower local decay rate. This follows from the slope of √h; it is not a change in tank area. The display reports the local time constant, not an exact global settling time.
CHECK YOUR UNDERSTANDING: Does the water level return on the same time scale at low and high operating heights?
The local time constant is 2A√h₀/c and the local DC gain is 2√h₀/c. At a higher level, the same incremental inflow has a larger steady height effect and a slower local decay rate. This follows from the slope of √h; it is not a change in tank area. The display reports the local time constant, not an exact global settling time.