The net result of this behavior is that the same air pressure signal to the valve top corresponds to two different stem positions, depending upon whether the valve is the process of opening or closing.
The hysteresis described in the previous paragraph should be distinguished from the dynamic lag of a valve discussed in Chap. 9. The dynamic lag discussed in Chap.9 is caused by the volume o space above the valve diaphragm, the resistance to flow of air to the valve top, and the inertia of the valve stem and plug; such a lag is expressed by a first-order or second-order transfer function. On the other hand, hysteresis, which is caused by the friction between the stem and the packing, is a nonlinear phenomenon and cannot by expressed by a transfer function. A valve can exhibit both dynamic lag and hysteresis.
The presence of hysteresis in the valve can cause the controlled signal to exhibit an oscillation or ripple called a limit cycle. Since this limit cycle is usually considered objectionable and contributes to the wear of the valve, a method is needed to eliminate it. Since the limit cycle is a nonlinear phenomenon related to the hysteresis, controller tuning is not a solution to the problem.
To reduce the deleterious effect of hysteresis and to also speed up the response of the valve, one can attach to the control valve a positioner that acts as a high-gain proportional controller that receives a set point signal from the primary controller and a measurement from the valve stem position. In this sense, the addition of a valve positioner introduces a form of cascade control, which was discussed in a previous chapter. A sketch of a control valve with a positioner attached is shown in Fig. 19-8. The positioner, bolted to the valve actuator, has an arm that is clamped to the valve stem to detect the stem position.
Notice that the valve positioner shown in Fig. 19-8 has the usual connections for a controller: a set point that calls for a desired stem position in the form of a signal from the primary controller pc, a measurement in the form of stem position x, and a pneumatic output in the form of a pressure to the valve top pv. Some positioners are now electronic microprocessor-based controllers, while others are still pneumatically based. Valve positioners are especially important for speeding up the valve motion and eliminating hysteresis and valve stem friction.