# Neglect Level Control at Your Peril

## This first article in a four-part series examines reset mode tuning issues.

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The lag observed in Figure 2 is roughly the sum of these lags. The combined effect often is approximated by a transportation lag or dead time. In the simple approximations of the dynamics of a level process, the process lag θ is considered to be entirely transportation lag.

Unfortunately, for many level loops, conducting a test such as in Figure 2 is impractical due to the presence of noise on the measured level value and variability in the feed flow to the vessel.

Testing procedures are available to determine KF and θ in face of both measurement noise and flow upsets. One approach is to use a pseudo-random binary signal (PRBS) for the output to the control element. Model predictive control technology relies on such tests to find process characteristics. However, such tests are long-duration (days) and difficult to justify for level control applications.

TUNING EQUATIONS
When a proportional-integral (PI) controller is used, the relationships between the tuning coefficients and the process characteristics are:

Controller gain, KC: inversely proportional to the process gain KF; inversely proportional to the lag θ.

Reset time, TI: not affected by KF; directly proportional to θ.

Especially for large tanks with long residence times, tuning equations often suggest unreasonably large values for KC. Most tuning relationships link the product KFKC (the loop gain) to the process dynamics. The large value for KC results from two factors:
1. For responsive processes, the tuning equations suggest a large value for KFKC. For a vessel with a residence time of 1 hr, a lag of 0.4 min is trivial.
2. For large vessels, the process sensitivity KF is small.

Using the Ziegler-Nichols tuning equations, the suggested values for the tuning coefficients are:

KC= 1/(KF θ) = 0.9/{[0.049 (%/min)/%] × (0.4 min)} = 46 %/%

TI= 3.33 θ = 3.33 × (0.4 min) = 1.33 min

The performance objective for the Ziegler-Nichols tuning equations is a response with a quarter decay ratio, which usually provides a rapid response to a disturbance. Figure 3 presents the response to a 10-min 50-L/min increase in one feed for the level process in Figure 1. These tuning coefficients maintain the vessel level very close to its set point — the maximum level deviation is approximately 0.2%. The response period, P, is 2.7 min. Also note the feed flow change is translated quickly into a discharge flow change.

A controller gain of 46 %/% is unreasonable in a level controller. A high controller gain amplifies any loop imperfections, such as the consequences of a finite resolution in the measured variable. In the example here the measured level value has resolution of 1 part in 4,000 — this means that 0.025% is the smallest possible change in measured level value. Using a controller gain of 46 %/%, a change of 0.025% in vessel level alters the controller output by (0.025%) × (46 %/%) = 1.15%. This, not surprisingly, leads to the abrupt changes seen in Figure 3, especially as the vessel level approaches its set point. Between the abrupt changes, the controller output exhibits ramp changes. (The finite resolution gives a constant control error that is integrated by the reset mode.)

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