Unlike self-regulating processes that will line at a steady state after disturbances have died out, integrating processes will ramp until a physical limit is hit. The ramping response is caused by the lack of negative feedback (e.g. self-regulation) in the process as defined in Advanced Application Note 4. In other words an increase in the process variable does not increase a counteracting effect to make the response bend over and reach a equilibrium.
The most common integrating process is level. Since the discharge flow is not appreciably affected by level (except for the rare case of gravity flow), any difference between the feed and discharge flows causes the level to ramp. The low limit is the vessel running dry and the high limit is the vessel spilling over or flooding a vent system.
Other common examples are
(1) Gas pressure control of columns, furnaces, and vessels when changes in operating pressure does not appreciably affect the vent flow rate
(2) Batch temperature control when changes in vessel temperature does not appreciably change the heat transfer rate
(3) Batch pH control when there is no reagent reaction or consumption or reagent concentration does not appreciably change reagent reaction or consumption rate
(4) Batch dissolved oxygen control when the change in oxygen absorbed does not appreciably change the oxygen transfer rate
(5) Batch product composition control when a change in product concentration does not appreciably affect side reaction or degradation rate
(6) Vessel solids concentration control when changes in solids concentration does not affect the evaporation or precipitation rate
(7) Bioreactor biomass or cell density control before the stationary and death phases
Many processes due to a long process time constant or large process gain, will appear to ramp because the steady state is beyond the time range or control region, respectively. What the user sees on the trend charts and what the controller sees as a response from the process variable is a ramp. These processes called “near-integrating” or “pseudo-integrating” processes are better analyzed and tuned as if they were integrating rather than self-regulating processes. Temperature control of any continuous process with a large residence time (volume/flow) can be treated as a “near-integrating” process.
Most of the more important loops have an integrating or “near-integrating” response. Furthermore the ramp rate (%/sec) for a % change in controller output (integrating process gain) is often incredibly slow. These slow ramp rates require exceptionally high controller gains and large integral times.
The test results for a single use bioreactor (SUB) with what would appear to be a small volume (100 liters), revealed an integrating gain of 0.000008 %/sec/%, that was 30 time slower than a bench top bioreactor. The SUB volume was about 30 times larger than the bench top bioreactor volume. The relative size of the volumes is a strong factor but the relative size of other parts such as heat transfer area play a role. This was the first time temperature control was tried on a SUB in this lab. Fortunately an adaptive controller was in service that identified the unexpectedly slower integrating process gain. The best response was achieved with a controller gain of 80 and an integral time of about 10,000 seconds. A Lambda factor of 0.05 was needed. The test results are shown in “BioreactorTemperatureTuningTestResults.pdf.”
The principle opportunity for integrating processes is realizing and using higher controller gains and larger integral times. We tend to use too much integral action (too small of an integral or reset time) because we are impatient and integral action provides a continual driving action to eliminate error. We don’t normally think of using higher gains because the problem of instability from high gains is drilled into us in all our courses and books on process control, our older measurement systems often gave flaky signals, and before we had structure and set point filter options, high controller gains caused the controller output to peg on a set point change. Properly installed smart transmitters with integral sensors and primary elements have a noise level that is low enough and a sensor sensitivity and repeatability high enough so that the amplification of small changes provides corrective actions rather than amplification of noise or extraneous actions. The proper use of the many PID parameter, control options, and structure today allows the user to minimize the disruption to the operator and other loops.
Most people don’t realize there is a window of allowable controller gains. As I mentioned we all know too high of a gain causes instability. For many integrating processes, this controller gain is way above our comfort level (e.g. gain > 100). More often we run into the low limit for controller gain (e.g. gain < 10). Too low of a controller gain causes overshoot and slow rolling oscillations. The correction is non intuitive. You need to increase the controller gain. Even with a high gain and integral time and rate action, it is difficult to prevent overshoot with an integrating process unless you take a very slow approach by using a PID structure that provides no step change in the controller output on a set point (e.g. proportional and derivative action on PV and integral action on error). The overshoot and speed of approach problem was the primary motivation for the simple control strategy for making a temperature go as fast as possible and then stop right at set point as discussed in the article "Full Throttle Batch and Startup Response“
The Lambda tuning equations for integrating processes automatically makes the controller gain large enough to stay above the low limit in the window of allowable controller gains. This is accomplished by keeping the product of controller gain and integral time to larger than 4 divided by the integrating process gain as seen the last slide of “LambdaTuningEquations.pdf.” However to get an acceptably fast enough response, Lambda factors much lower than the user is accustomed to must be used. Not shown is the fact that derivative action is helpful. The rate time should be set to the next largest time constant for a self-regulating process and the largest time constant in an integrating process. These rules are consistent for a “near-integrating” since the integrating process gain is the process gain divided by the largest process time constant leaving the next largest time constant as the one used to set the rate time.
Temperature control of exothermic reactors where the reaction rate increases with temperature and particle or crystal size control where the formation rate increases with particle or crystal size can have an integrating followed by a runaway (positive feedback) response where is it is critical to maximize the controller gain and integral time.