Q: As I understand it, if the controller output increases when the measurement value rises, it is a direct-acting controller, and if controller output decreases when the measurement rises, it is a reverse-acting controller. In addition, at minimum output of the controller, the desired fail-safe action must be achieved. For example, if we have two controllers on a distillation column—reflux and net overhead—where the reflux control valve is fail-open, and net overhead control valve is fail-close, the reflux controller will be reverse-acting, and the net overhead controller will be direct-acting. Is my understanding correct?
A: Valve failure position and controller actions are independently determined, therefore, let's talk about them separately.
Valve failure position is determined by safety considerations. If, in case of failure, you want your column to go on full reflux, your selection is right (Figure 1). Assuming that the valve actuators are spring-operated pneumatic ones (you did not say what they were), and assuming that you define "failure" as the loss of air supply, the spring will act to open a fail-open (FO) valve and to close a fail-closed (FC) valve, regardless what the controller actions are. (I neglect to mention the role of positioners because I don't like to use them on flow control valves because they can be slower than the flow process and, therefore, they can cause cycling.)
Now let's turn to the subject of controller action. Assuming that your system is as shown in the figure, an increase in column temperature should result in increased cooling, which is accomplished by returning more cold reflux into the column. This means that the temperature controller (TC) has to reduce the reflux flow setpoint, which in turn will increase the level in the accumulator, and to overcome that, the level control (LC) increases the setpoint of the reflux flow control (FC). So a measurement increase requires the TC to reduce its output (reverse action, R/A), while the LC increases its output upon a level increase (D/A). The response of the slave FC controllers is to increase the flow through their valves as the master raises their setpoint, so with the FC valve, it will be D/A, and with the FO valve, it will be R/A.
Naturally, the control system shown in the figure is a very simple one (does nothing about interactions, etc.), but it is sufficient for explaining the issue at hand.