Any process with split ranged valves is prone to limit cycling for many reasons. The periods are unpredictable. Some are process related. For example, the transition between steam and coolant creates a severe discontinuity. There is a change of phase and disruptive change in magnitude and sign of the effect. There is no happy medium for a small cooling or heating requirement. When the steam replaces the coolant in the jacket or coils or vice versa, by the time the controller sees that the consequence of its action is too large, it is too late.
The real behavior of control valves also make the transition at the split range point less than smooth. The resolution (stick-slip) at the seat at process conditions is often an order of magnitude larger than the stated resolution of the valve. Tight shutoff specifications and designs, high temperatures, solids, and fouling increases the friction and stick-slip as the valve trim, ball, or disk tries to break free of the seat or seal. Tests done by the manufacturer are usually done far away from shutoff (e.g. 50%). There are exceptions as noted in the blog “Control Valves on the Skids” on May 10 in the Plant Design category.
The slope of an installed characteristic of a control valve is also typically largest near shutoff and smallest near the wide open position. So besides the difference in valve gain due to valve capacity, there is also a change in valve gain due to the installed characteristic.
When a small control valve is split ranged with a large control valve, there may be an improvement in rangeability when you are throttling just the small valve but there is the increase in stick-slip in the transition to the big valve and a loss of sensitivity when throttling the big valve. Model predictive control can eliminate the need for this split ranging by simultaneously manipulating both valves as described in Advanced Application Note 2 available at http://www.modelingandcontrol.com/repository/AdvancedApplicationNote002.pdf
When the split ranged valves are for different streams that have opposite effects, the limit cycle across the split range point poses a significant loss in process efficiency. The cycling between coolant and steam wastes energy and the cycling between acids and bases waste reagent. Here not only is there difference in the valve gain, but also in the process gain, dead time, time constant, and sign. Adding a dead band in the split ranged point adds dead time in all processes and creates a limit cycle for integrating processes.