The previous two articles ("Neglect Level Control at Your Peril" and "Be Levelheaded About Surge-Tank Control") examined issues pertaining to proportional-integral (PI) control of vessel level. Especially for surge vessels, low values of the controller gain are appropriate. This raises two issues:
1. To avoid cycles in the level, reset time must increase as the controller gain decreases.
2. To most reliably avoid trips, the final control element should reach the appropriate extreme before the level gets to the high or low point that initiates a process trip.
Incorporating nonlinear relationships into the control equation can ensure the latter.
The nonlinear option for a PI control equation is implemented as follows:
Proportional mode. The proportional component of the output is a nonlinear function of the control error:
M = KC f(E) + MR
where M is controller output, %; KC is controller gain, %/%; E is control error, %, which equals the difference between the set point (SP) and process variable (PV), i.e., PV – SP for a direct acting controller and SP – PV for a reverse acting controller; and MR is controller output bias, %.
Integral mode. Although incorporating the nonlinear function into the integral mode also is possible, here we'll base the reset action on the control error (the same as for the linear control equation):
where TI is reset time, min; and MR,0 is the initial value for controller output bias, %.
Bumpless transfer calculations determine the value of MR,0, which is the initial condition on the reset integrator.
Despite basically unlimited possibilities, only two nonlinear relationships commonly appear:
• error gap or error deadband; and
• error squared.
In a true error deadband, the sensitivity within the deadband is zero. However, level control applications require a low sensitivity within the gap. Here, we'll call this relationship "error gap" and the value of the control error at which the sensitivity changes the "error deadband," EDB.
Figure 1 illustrates the desired relationship for the proportional mode. When PV equals SP, E is zero and M equals MR. As the PV deviates from SP in either direction, the sensitivity initially is low. But when the control error exceeds the value of the EDB, the sensitivity abruptly increases.
The relationship in Figure 1 involves three adjustable coefficients: