How do you know when interaction is going to be a problem? Why would the control loop design need to be changed? Are there hidden loops? What can you do with tuning to mitigate the problem? When do you need to move on to Model Predictive Control? Hopefully, this blog will provide the answers to these questions and more.
The measurement with the greatest threshold sensitivity for the process variable with the largest effect on quality should be selected as the controlled variable. The most notable example is the selection of the distillation column tray that shows the largest change in temperature for changes in both directions of the manipulated flow or flow ratio.
The manipulated variable with the largest effect should be paired with the associated controlled variable. A classic example is where the composition PID should manipulate the small pure component stream flow for a blend composition setpoint of less than 50%. A decoupling feedforward signal may be needed to prevent a PID output from saturating.
Given adequate effect on the controlled variable, the manipulated variable that is least affected by disturbances should be paired with the most important controlled variable. A common example is a pressure loop and flow loop in series with a large and small valve in the same pipeline. The flow loop should manipulate the small valve because the small valve has the larger pressure drop and hence is less affected by pressure disturbances.
Gas pressure and level loops should be paired with the manipulated flows that will keep the gas and liquid inventory within the desired range. Tight pressure control is almost always desired. Tight level control may be needed to enforce material balances and residence time requirements. Loose level control to use up available volume may serve to slow down as much as possible the manipulated flow as a disturbance to downstream operations. For a distillation column receiver, tight level control is needed when reflux is manipulated and loose level control is recommended when distillate flow is manipulated.
Fast loops should be tuned faster to reduce the effect of interaction with slow loops. The feedforward of fast loop process variables to slow loops can eliminate the remaining interaction. The most common example is the use of feed flow feedforward to preemptively change the manipulated flow to maintain a flow ratio. Dynamic compensation is applied so the change in the manipulated flow arrives at the same point at the same time in the process as the change in feed flow. The manipulated flow is corrected by composition, pH, and temperature loops. The same rules applying for setting the feedforward gain and the lead-lag apply for decoupling.
If interaction is still problematic after improvements in control strategy in terms of pairing and mitigating recycle effects, in process and system design and tuning to eliminate oscillations, by the use feedforward control for decoupling and handling production rate changes, and making fast loops faster, the final step is detuning to reduce the remaining propensity for oscillations.
Relative gain analysis is a powerful technique for accessing the type and degree of interaction. The relative gain for a given loop is the open loop steady state gain for the other loops open divided by the open loop steady state gain for the other loops closed. Note that the given loop is open for the tests with the other loops open and closed. A loop is considered open if the mode is manual or remote output or output tracking is enabled or the PID output is at an output limit. For integrating processes, the process variable is translated to a rate of change so the concept of steady state can be used. The relative gain is dimensionless and thus does not depend upon the engineering units of the loops involved. The relative gain does not change when a flow ratio rather than a flow is manipulated. Operating point nonlinearities will affect the analysis but not changes in time constants and dead times. Ideally, the pairing of loops should have a relative gain close to one or slightly higher. Negative relative gains are disastrous.
Full interaction creates additional feedback loops. The type oscillation observed is a clue to whether the loop has positive or negative feedback and to what degree.
If the subject loop’s oscillation is severe showing signs of instability, there is a strong positive feedback loop created from other closed loops. The subject controller action can be reversed and tuned to stop the oscillations but this is not safe because if the offending loop becomes open (could be just temporary residence at output limit), the action sign will be wrong again. Process and/or system redesign is needed to eliminate this extreme type of interaction. Most severe interaction problems are caused by poor process or system design. This scenario corresponds to a negative relative gain.
If the subject loop’s oscillation period and amplitude are larger but with a normal rate of return back to setpoint, there is a parallel negative feedback path created by the other closed loops. The open loop gain and dead time in the subject loop has increased requiring that the PID gain be decreased and the reset time be increased. This scenario corresponds to a relative gain between 0 and 1.
If the subject loop’s oscillation period does not appreciably change but the return back to set point is protracted, there is a slight positive feedback path created by the other closed loops. For setpoint changes, the subject loop will peak below setpoint and very slowly approach setpoint. For both disturbances and setpoint changes, the approach to setpoint is so slow there appears to be an offset and no integral action. For loops with similar dynamics, the subject loop PID gain should be decreased. This scenario corresponds to a relative gain greater than 1.
Furnaces with multiple burners for zone temperature control are a medium scale interaction problem with a medium relative gain matrix (e.g. 5 x 5). Sheets with multiple actuators for cross directional thickness control create an interaction problem grand in scale with a huge relative gain matrix (e.g. 100 x 100). Some multi-variable sheet thickness control systems seek to use a model of the deflection of the die lip when an actuator is manipulated. This is more easily said than done because an exact match is needed to effectively decouple the actuator actions from each other. The implementation requires a lot of trial and error in model adjustment.
- Pick the measurement with the greatest threshold sensitivity for the process variable that shows the greatest sensitivity to both increases and decreases in the manipulated flow or flow ratio.
- Pair manipulated variables with controlled variables that have the greatest effect on the controlled variable and are least affected by disturbances.
- Improve process and system design to eliminate oscillations.
- Tune fast loops faster and slow loops slower to reduce interaction between the loops by providing a greater separation of dynamics. If the loops have similar dynamics, tune the less important loops much slower to provide the separation.
- Add flow feedforward control to decouple and facilitate production rate changes.
- Do a relative gain analysis to access the type and degree of remaining interaction.
- Look at oscillation pattern to access the type and degree of remaining interaction.
- Detune loops whose oscillation period and amplitude is larger due to interaction.
- If decoupling involves complex dynamics, consider Model Predictive Control.
- If decoupling is more than flow feedforward, consider Model Predictive Control.