The key aspects of good vessel temperature and pH control are often not recognized. Here we provide some simple guidance and overview of the benefits of a particular strategy and implementation guidelines that should be commonly used. A fundamental understanding is provided that may also be beneficial for other primary control loops.
In case you are busy let’s cut to the chase. Let’s start with pH. The cascade control of vessel pH to inline pH provides a simple well known open loop gain for the vessel pH loop (primary loop). The effect of the nonlinear pH titration curve is isolated from the vessel pH loop and dealt with by the fast inline pH loop (secondary loop). The open loop gain (also commonly known as the process gain) for the vessel loop is simply dependent upon the scales of the vessel and inline pH loops. If the pH loops have the same scales, the open loop gain is simply one.
The well-known open loop gain makes the tuning of the much slower vessel pH loop much easier. The biggest benefit is that you can much more easily avoid having a vessel PID gain that is too high or too low. The less recognized problem of too low a vessel PID gain stems from the vessel loop response being near integrating and true integrating for continuous and batch operations, respectively. A near or true integrating response will cause incredibly slow oscillations (e.g., period that is 40 times dead time) if the PID gain is too low. In some ways violation of the low gain limit is worse that violation of the high gain limit because the oscillations are much larger besides being much slower, which means they are not as effectively smoothed out by downstream volumes. They are also continuative.
The minimum PID gain is inversely proportional to the product of the open loop integrating process gain and PID reset time. You don’t want this to be dependent upon the slope of the titration curve that varies enormously with pH and feed concentrations or how well you tuned the reset time. Most reset times are set way too small since people tend to use too much integral action and not enough proportional action on vessels or columns (any volume with mixing either due to turbulence or agitation). Often the reset time needs to be increased by two orders of magnitude. By simplifying the open loop gain to a number that is constant and easy to calculate, the PID gain can be more readily set to be above the minimum besides below the maximum. The reset time is simply a factor of the vessel dead time. For an arrest time (lambda) of two deadtimes in lambda tuning for integrating processes, this corresponds to a reset time of 5 deadtimes. Note that smaller arrest times can be used by making the process gain linear and relatively constant by the recommended cascade control.
For a well-mixed vessel, the process time constant is approximately the residence time that is simply the vessel liquid mass divided by the process input mass flow. For inline pH loops on the influent, this is the influent feed flow. For inline pH loops on a recirculation line, this input flow is basically the recirculation flow since the recirculation flow is typically much greater than the feed flow. The near-integrating process gain is the open loop gain (dependent upon primary and secondary scales) divided by the process time constant (dependent upon residence time). If the pH loops have the same scale, the integrating process gain is simply the process input mass flow divided by the liquid mass in the vessel. This calculation can be done on a volumetric basis. You just need to have consistent flow and liquid inventory units.
The cascade control of vessel temperature to inline feed temperature or recirculation temperature, the computations are similarly simple. If the secondary loop is jacket inlet temperature with constant jacket recirculation flow, the open loop gain is again simply dependent upon primary and secondary loop temperature scales. The residence time is the liquid mass divided by the process input mass flow. Note that the jacket input temperature loop is an inline loop where the jacket temperature is a blend of a manipulated makeup coolant flow with a constant jacket recirculation flow where increases in the manipulated jacket coolant makeup flow result in corresponding changes in coolant return flow by jacket outlet pressure control. For jackets that require some heating, the inline temperature controller manipulates the steam to an inline injector and the return flow is a hotter return water flow.
The secondary pH and temperature loops are left to deal with the nonlinearities of the process. They should be tuned for an aggressive setpoint response minimizing rise time even at the expense of an increase in overshoot. Setpoint feedforward can help where 50% of the inline loop setpoint change is translated to the corresponding change in inline PID output to achieve this setpoint change. The setpoint feedforward is simple added to the inline PID output via the PID feedforward summer.
For both loops, the process gain is inversely proportional to the inline flow which is kept constant for vessel and jacket recirculation flows. For these loops, a linear installed flow characteristic is best. For inline pH and temperature loops on vessel feed flows, an equal percentage flow characteristic helps compensate for the process gain being inversely proportional to feed flow by a valve gain being proportional to flow. Note to insure the installed flow characteristic is close to the inherent flow characteristic and not distorted by changes in available pressure drop, the ratio of valve drop to system pressure drop should be greater than 0.25. Providing enough pressure drop to the control valve also prevents a severe loss in valve rangeability, an aspect of the practical reality due to deterioration from friction and slope of the valve installed flow characteristic near the closed position not discussed by nearly anyone but me. Statements in the literature and catalogs about valve rangeability are generally flat out wrong.
The secondary pH and temperature loop outputs go directly to the control valve. The manipulation of a coolant or reagent flow loop setpoint is not advisable because most of the flow measurements used have insufficient rangeability. In general, the biggest problem with cascade control systems that manipulate a flow setpoint rather than a valve positioner or variable frequency drive speed, is the erratic flow measurement signals at low flows. The signals get noisy and some are simply set to drop out. You can add logic to substitute an inferential flow measurement based on valve position using its installed flow characteristic but this leaves the loop vulnerable to knowledge of the installed flow characteristic and precision of the valve. If you need to use a flow loop, the best solutions are a magnetic flowmeter or even better, a Coriolis mass flowmeter, with a rangeability of 50:1 and 200:1, respectively. Differential head meters with dual range differential pressure (d/p) transmitters and vortex meters have a best case rangeability of 15:1 that is difficult to achieve in practice. A more typical rangeability for dual d/p head and vortex meters is about half the best case (e.g., 8:1).
The valve must be a true throttling valve, not an on-off valve posing as a throttling valve. A diaphragm actuator capable of providing 150% of thrust requirement should be used with a goal of 0.2% resolution, 0.3% deadband and 86% response time (T86) of less than 4 seconds at a starting position of 10% besides 50%. A smart digital positioner tuned with aggressive gain and rate action is needed. The T86 performance and actuator thrust objectives are relaxed here from 2 sec and 200%, respectively that were stated in the March 2016 article “How to specify valves and positioners that do not compromise control” and the associated white paper “Valve Response – Truth or Consequences”. Don’t be surprised if the valve supplier will only provide the resolution, deadband and T86 for a starting position of 50% because of the deterioration of these metrics due to seating and seal friction near the closed position.
The inline pH loop must still deal with the titration curve. Signal characterization can help to translate the controlled variable in pH that is the Y axis to a % reagent demand that is the X axis of the titration curve. The linearization will not be perfect. A simple standard signal linearization block where you enter 20 or so X,Y pairs for a piecewise linear fit is best. Since you are doing the opposite of the process for linearization, the X value is the ordinate (pH) and the Y value is the abscissa (reagent demand) of the titration curve. If just part of the nonlinearity is addressed, you are way ahead in the game in terms of tuning and performance. Plus, the characterization reduces the noise seen by the controller for setpoints on the steeper portion of the titration curve. Even without such linearization, the inline pH loop can usually correct for the disturbances within a minute using mostly integral action.
For more on pH and temperature control, see the ISA books “Advanced pH Measurement and Control 3rd Edition" and “Advanced Temperature Measurement and Control 2nd Edition".
To summarize:
1. Use cascade control of vessel pH and vessel temperature to inline pH and inline temperature control to provide a relatively constant and easily estimated open loop (process) gain that can readily prevent the common occurrence of violating the low PID gain limit for near integrating and true integrating processes. Also more aggressive tuning can be used by a more linear and constant process gain seen by vessel loop.
2. The inline pH and inline temperature controller outputs should directly manipulate precise and fast throttling valves with the right installed flow characteristic.
3. The inline pH and inline temperature controller should be tuned for an aggressive setpoint response.
4. Signal characterization for the inline pH loop PV using a piecewise linear fit should be used to help deal with the nonlinearity of the titration curve when the normal range of inline pH setpoints are on the steeper portion of the curve.
