Often arguments as to whether a linear or equal percentage trim is best are based on the theoretical inherent flow characteristics. Valve rangeability is often stated as simply a deviation of the catalog flow characteristic from the theoretical characteristic. Here we will see how the consideration of the changes in process dynamics, available valve pressure drop, and control valve dynamics can alter what you consider as the best flow characteristic.
The simple rule based on theoretical inherent flow characteristics and types of processes is that for flow, pressure, and level loops a linear trim is best because the process gain and valve gains are linear and for temperature processes an equal percentage trim is best because the process gain is inversely proportional to flow, which is the opposite of the valve gain. The real story requires a greater understanding of the effects at play.
The best trim characteristic is the one that minimizes changes in PID tuning, minimizes the effect of backlash and stiction, offers the greatest rangeability, and prevents abnormal conditions.
First of all, the actual installed flow characteristic of linear and equal percentage trims become more like a quick opening and linear characteristic, respectively as the ratio of the valve pressure drop to system pressure drop at maximum flow decreases as shown in the Installed-Control-Valve-Characteristics-Figures. Due to an increased emphasis on energy savings and an attempt to show variable speed drive valves do not save as much energy as touted, some may say that only 5% of the system pressure drop needs to be allocated at maximum flow (pressure drop ratio = 0.05). While hopefully this gamesmanship is not taken seriously, allocating less than 25% of the system drop can appreciably make the linear trim gain nonlinear and the equal percentage gain no longer proportional to travel losing the assumed benefits of both trims for the processes commonly cited. Additionally, the pressure drop ratio decreases as the frictional losses in the system increase. Fouling of inline equipment can make this a deteriorating situation with time. Hunter Vegas said as much in his reply to the Feb 26, 2015 Control Question “Linear or Equal Percentage Valves: When Should I Use Which?
Not realized as well is the increase in backlash and stiction as the valve approaches the closed position. Tests are typically not done for positions less than 20%. Furthermore, the effect on process flow depends upon the valve gain since deadband and resolution limit are given as a percent of valve stroke. The error in flow for a given deadband or resolution is 4 times larger for a linear valve than an equal percentage valve at a 10% valve position. If you consider the real rangeability is the maximum flow divided by the minimum controllable flow and take into account the installed flow characteristic and limit cycles introduced by deadband and resolution, the equal percentage valve has a better rangeability. This makes more practical sense to me than the official definition of rangeability based on deviation of the catalog inherent characteristic from the theoretical characteristic which in most cases would then make a linear trim the best choice for rangeability. I have been saying this for over 20 years without much traction except for the satisfaction that the users in the plants who have said “Thank You - Now I know why an equal percentage characteristic gives me better control.”
While it is true the process gain of temperature processes increases at low loads, the process time constant also increases at low loads for volumes with some degree of mixing (e.g. vessels and columns) because the process time constant is proportional to residence time (volume/flow). The controller gain is proportional to the ratio of the process time constant to process gain. Thus, for these volumes the effect of flow cancels out in terms of controller tuning and a true equal percentage characteristic would be introducing a nonlinearity that is actually detrimental in terms of tuning. Furthermore, most temperature loops benefit from a secondary flow loop to compensate for pressure upsets and to enable flow feedforward. Here the temperature loop is isolated from the nonlinearity of the valve. These same considerations apply to concentration control loops because the process gain and process time constant are both inversely proportional to flow and secondary flow loops are beneficial particularly for reactors and neutralizers when high rangeability flow meters are used (e.g., Coriolis and magnetic flow meters).
If the pressure drop ratio approaches one (available pressure drop is relatively constant), the installed flow characteristic is the inherent characteristic. If the deadband and resolution is negligible, the minimum controllable flow is solely dependent on the uniformity of the flow characteristic near the seat. For these big “Ifs”, linear trim is best for flow, level, and pressure. For the prevention of surge and gas pressure relief, a linear trim is best regardless of “Ifs” because a more immediate response is essential even if it somewhat like a quick opening characteristic.
For the control of inline temperatures (e.g., heat exchangers) and concentration (e.g., static mixers) control where the lack of back mixing means the process time constant is negligible and the big “Ifs” are true, an equal percentage characteristic will help keep the tuning less dependent upon load (e.g., feed flow).
The advantage of using signal characterization is not straightforward. The characterizer must be based on the installed characteristic that is often unknown and dependent upon frictional losses in the system. Also, whether linearization of the valve gain is beneficial depends upon how the process gain and time constant change with flow, which is often not well understood. Finally, the effect of signal characterization is a mixed bag. For a given change in controller output, the changes in valve signal after characterization are smaller and larger for operating points on the steeper and flatter portion of the installed characteristic, respectively. Small changes approaching the actuator/positioner threshold sensitivity limit will increase the stroking time. Small changes less than the dead band or resolution limit of the valve will increase the dead time associated with the delay until the accumulated changes is large enough to get the valve to start to move.
There is an opportunity for the pressure sensors to measure the valve inlet and outlet pressures and make a fast online calculation of the installed characteristic and flow from knowledge of the valve drop, actual valve position, inherent flow characteristic, and first principle equations. The valve signal then becomes a desired flow providing a linear valve gain. It is not precise enough to replace an accurate flow meter (e.g., Coriolis or magnetic flow meter) but can be used to extend the rangeability of flow meters that get noisy or erratic at low fluid velocities (e.g., differential head or vortex meters). External reset feedback of the fast flow calculation should be used to prevent oscillations from a secondary flow loop trying to change the valve flow faster than the valve can respond.
We can summarize what we have learned as follows: Signal characterization must be done cautiously with knowledge of the installed flow characteristic. An opportunity exists for a fast online calculation of flow and installed flow characteristic. Accurate high rangeability flow measurements in secondary loops are the best way of isolating valve nonlinearities from upper loops, compensating for pressure upsets and providing feedforward control. For applications with a precise valve (e.g., negligible deadband and resolution limit), nearly constant valve drop (e.g., high valve to system drop ratio), and negligible changes in process gain with load (e.g., flow, level, or pressure), or that need an immediate significant flow response to prevent abnormal conditions (e.g., surge control and pressure relief prevention), a linear trim may be best. Otherwise, an equal percentage trim is generally best for many practical reasons reasserting what most technicians and engineers in the field have realized from many years of field experience. Maybe this is a lesson to listen more to these practitioners on the front line. I had already learned this decades ago when I found out why a technician did not want to replace a positioner with a booster on a surge valve as discussed in the 2/09/215 Control Talk Blog “Secondary Flow Loop and Valve Positioner Tips”