12.4 Split-Range Control

A split-range strategy is often used in situations where one or more valves may be used, depending on the operating scenario. An example application is a batch reactor. Batch reactors must often be heated from ambient temperature to a desired operating temperature. Particularly if the reaction is exothermic, then cooling will be needed to maintain the desired reactor temperature. In the split-range control strategy shown in Figure 12-4, if the jacket temperature controller output is between 0 and 50%, the cold glycol valve is open; if the jacket temperature controller output is between 50 and 100%, the hot glycol valve is open. For safety reasons we wish the cold glycol valve to fail-open and the hot glycol valve to fail-closed. The diagram in Figure 12-5 more clearly shows the relationship between valve positions and the jacket temperature controller output.

The implementation is as follows. Let u represent the output of the jacket temperature controller (0–100%). Also, let v_c and v_h represent the cold and hot glycol valve positions, respectively. The split-range algorithm can be stated as

Equation 12.6

Sometimes there is a small deadband, where the cold glycol is open between 0 and 45%, while the hot glycol is open between 55 and 100%. This adds the equivalent of a small time delay to the control strategy but avoids situations where both cold and hot valves are open owing to small miscalibrations.

Example 12.1: 1000 Liter Stirred-Tank Heater

Here we show results for a 1000 liter jacketed, continuous stirred-tank heater, operated at 85% of capacity. For clarity, we consider only the jacket temperature controller, which is split-ranged as shown in Figure 12-5. Ordinarily this jacket temperature controller would be the secondary (inner-loop or slave controller) where the output of a vessel temperature controller (outer-loop or primary controller) is the setpoint to the jacket temperature controller.

The modeling equations are

where the jacket make-up flow rate (F_j; of either cold or hot glycol) is the process input. Numerical values are shown in Exercise 5.

The responses for setpoint changes in jacket temperature are shown in Figure 12-6. A positive setpoint change is made at t = 0 minutes, followed by a negative change at t = 10 minutes. The middle plot shows the jacket temperature controller output and the bottom plot shows the individual valve positions. All variables are in deviation form. When the controller output is positive, the hot valve is activated; when the controller output is negative, the cold valve is activated.