If you watch a good operator start up or deal with abnormal conditions, you see him or her put the controller output at a value that puts the process at a good operating point based on past experience. The good operator is patient and confident enough to leave the output at this value long enough for it to take full effect. We can take the best operator actions and use the output tracking function of the PID to hold these values for an optimum amount of time.
For start up, the optimum tracking time is the rise time (the time to reach setpoint) minus one deadtime because changes are not seen until one deadtime into the future. The remaining rise time is the absolute value of the difference between the process variable (PV) and the new setpoint divided by the ramp rate (in consistent units). A future PV value can also be used to trigger the end of output tracking. For the fastest possible response, the output tracking value could be an output limit. When the future PV is just short of the setpoint, the final resting value is tracked for one deadtime.
For abnormal conditions, a conservative output or incremental output is tracked. This strategy is called an open loop backup because feedback action is judiciously suspended to take extreme action. The conservative output provides a step change that protects against a worst-case scenario. An incremental output is usually more efficient but causes a slower response. In practice, a combination of an initial output to get a larger, more immediate response and followed by an incremental output may be best. Output tracking is triggered when a PV, future PV, or ramp rate indicates a potentially damaging or unsafe condition or environmental violation is eminent.
To prevent compressor surge, I use an output that I know will get the compressor out of surge. Each compressor surge cycle damages seals and possibly the rotor, causing a loss in efficiency. For axial compressors, the loss in efficiency can be noticeable after just a few surge cycles. Once a compressor gets in surge, a feedback controller usually cannot get the compressor out of surge because the oscillations are normally too fast for attenuation and are very large. Making the surge control loop faster only makes resonance more likely, amplifying the surge cycles. In classic surge conditions, there is a negative swing in the flow in 0.005 seconds that is as large as the positive flow. The flow walks along the negative flow compressor characteristic curve and then jumps in 0.005 seconds to positive flow close to the surge point. This cycle repeats every one to two seconds. I detect the onset of surge by the initial precipitous drop in flow or by an operating point approaching the surge curve and use an open loop backup to position the surge valve open enough and long enough to prevent surge cycles.
To prevent an RCRA pH violation, an incremental output is normally fast enough and saves on reagent use. For an inline pH control system, I found that an incremental output of 0.5 percent per second was fast enough and saved $50,000 per year in reagent use compared to a 50 percent output for tracking.
Concept: Use output tracking to provide the initial change in output necessary to get a process to setpoint faster or to prevent abnormal operation, notably compressor surge or RCRA pH violations. Hold the output long enough to ensure that the full effect of the output change is achieved and the loop has stabilized. The loop may then be turned back over to feedback control to correct for unknowns and disturbances and to provide more efficient operation.
Details: If you want the PV to smoothly reach setpoint about as fast as the open loop response, track the final resting value for the rise time less one loop deadtime. The remaining rise time for tracking at any point in the setpoint response can be estimated as the absolute value of the difference between the PV and the setpoint divided by the current ramp rate. If you want the PV to get to setpoint as fast as possible, track an output limit, and, when the future PV is close to setpoint, track the final resting value for one deadtime. The final resting value can be the best value or last value of a start-up or a batch operation. For a pure integrator with no change in load, the final resting value is the output just before the setpoint change.
To prevent compressor surge, use both a PV excursion past the surge controller setpoint and a precipitous drop in flow as triggers for output tracking. A controller execution time of 0.1 seconds is needed to be fast enough. The major sources of deadtime in a surge loop are the automation system components. Hold the output at a value for much longer than the deadtime (e.g., 10 sec). The deadtime in a well-designed surge loop is too small (e.g., < 1 sec) to use a future PV value to trigger output tracking. To prevent RCRA pH violations, track an incremental output when pH approaches the RCRA limit (e.g., 2 pH and 12 pH). The deadtime is slow enough (e.g., > 5 sec) even for inline pH systems (static mixers) to use a future pH value to trigger the output tracking. Use an initial tracking value that is subsequently incremented to get a more immediate recovery.
Watch-outs: Same as Tip #90.
Exceptions: For frequent and large load changes during setpoint changes, the PID controller may need to stay in automatic. In this case, consider using setpoint PID structure, a setpoint filter, and setpoint feedforward rather than output tracking to optimize the setpoint response.
Insight: The best actions of a process engineer and operator can be replicated by the controller as preemptive actions that are corrected by feedback after the full preemptive effect is achieved.
Rule of Thumb: Use output tracking to get the loop consistently started for the best setpoint response and recovery from an abnormal condition.