Effect of Interactions Perspective Tips
Since most unit operations have multiple loops and streams, interactions can exist where the PID output of one loop affects the PID process variable of another loop and vice versa. Interactions can cause loops to confusingly burst into oscillations. Here we look at how to reduce the consequences and prevent the initiation of interactions. In the process we realize some principles in the design of control strategies for plantwide control.
Often a production rate control loop affects a quality control loop such composition or temperature loop but not vice versa. Here the solution is a feedforward signal of feed rate setpoint to the quality control loop. The composition or temperature PID output corrects the manipulated flow to feed flow ratio. This feedforward signal is a half decoupler where the changes in feed flow loop are passed on as changes to composition or temperature control loop output to preempt the upset. In the literature the decoupling signal is a PID output. Here the decoupling signal is a PID process variable (PV). The dynamic compensation required is the same as for feedforward loops. The decoupling signal must cause a correction to arrive at the same place at the same time as the upset but with an opposite sign. Technically, this case is not true interaction because the effect is one way and not mutual (composition or temperature loop does not affect the feed loop). The addition of a valve position controller (VPC) to optimize production rate would create full interaction by increasing the feed rate to force the composition or temperature control valve to the furthest controllable position. In general the use of VPC creates interactions that in the literature has been typically minimized by using slow integral only control in the VPC. However, this puts the composition or temperature loop at risk of running out control valve for large or fast disturbances because the VPC is too slow to react. An integral dead band can be enabled in the VPC to stop integral action for small offsets of the small valve position from VPC setpoint of the desired small valve position. An enhanced PID can be used with a threshold sensitivity limit and external reset feedback of a rate limited Analog Output (AO) setpoint to provide directional move suppression. For more details on the use of a VPC for a quick and easy optimization checkout my November 2011 Control article “Don’t Over Look PID for APC”
The solutions in preferential order to reducing interaction is the best control strategy in terms of pairing of manipulated and control, decoupling, and detuning. Here we will focus on interactions inherent in the basic control loops.
Consider an upstream pressure and downstream flow controller in series in the same pipeline. There is a small valve upstream and a large valve downstream of the pressure and flow measurements. What valve should the flow loop manipulate realizing the main objective is to control the flow downstream? The “off the cuff” answer is the flow loop should manipulate the large valve. Actually the flow controller should manipulate the valve with the largest pressure drop so that changes in pressure have least effect. Given the valves need to pass the same flow the smaller valve upstream has the larger pressure drop and should be manipulated for flow control. Process dead time and time constant are not a consideration because they are very fast and the same for each valve for liquid flow.
A classic example often cited is inline composition and flow control by the blending of two pure component feeds A and B fed to the inlet of a static mixer. The total flow and composition is measured downstream of the static mixer. If the desired concentration at the outlet of A is less than B, then the concentration controller should manipulate A the smaller stream flow. This analysis also works for static mixer pH control. Consider stream A to be a reagent flow with a relatively high reagent concentration (e.g. 98% sulfuric acid). Stream B is a high flow dilute effluent stream (e.g. 0.1% ammonia). The historical choice of the pH controller manipulating the reagent stream and the total flow controller manipulating effluent will minimize interaction. Consider the unusual but possible case of an extremely dilute waste reagent stream that is larger than the effluent. Here the pH controller should manipulate the effluent stream and the total flow controller should manipulate the waste reagent flow. In both cases, a feedforward of flow controller PV should be added to the pH controller output to further reduce interaction and improve control for production rate changes.
Another example occurs in large recirculation loops where flow and backpressure are to be controlled. Often the flow controller mistakenly manipulates the Variable Speed Drive (VSD) and the backpressure controller manipulates the control valve. The relative gain matrix would say the exact opposite pairing of controlled and manipulated variables.
The interaction between outlet and inlet temperature controllers for kilns that manipulate firing rate and exit gas flow can be reduced by the addition of an oxygen controller. A feedforward of firing rate to the outlet temperature controller as a decoupler can reduce the remaining interaction.
A more complex example showing the importance of first addressing gas and liquid inventory control is distillation column control. When both the top and bottom composition need to be tightly controlled (two point composition control) full interaction occurs between the temperature loops on the top and bottom of the column. Here temperature is an inferential measurement of composition (high boiling point component on bottom and low boiling point component on top of column).
First, column pressure and levels must be controlled. Tight pressure control is needed so that boiling points of components throughout the column change with temperature not pressure. The pressure controller should have a relatively large gain and reset time to rapidly manipulate the split ranged between nitrogen and vent valve. If the gain is decreased and the reset time is not correspondingly increased, slow rolling oscillations will result from integral action dominating proportional action in this integrating process as detailed in my blogs on "Processes with No Steady State in PID Time Frame". The slow rolling oscillations can cause the rest of the loops to perpetually oscillate.
Since reflux flow back to the column is often greater than distillate flow from the column, overhead receiver level PID often manipulates reflux flow. This leaves distillate flow from the receiver to be manipulated for temperature control. Because the column is not affected by a change in distillate flow until the reflux changes, tight level control is essential. Fortunately, tight level control is possible and desirable for the reasons such as inherent compensation of overhead vapor or reflux temperature changes. As with gas pressure control, the level controller should have more proportional than integral action for the integrating process. For the bottom of the column, the manipulation of bottoms flow is preferred for sump level control. However, if the bottoms flow is too small, then sump level PID manipulates steam flow to the reboiler. Here tight sump level control is needed because a change in bottoms flow does not affect the column until the steam flow changes. Unfortunately, a slow secondary lag form heat transfer and an inverse response from bubble formation and collapse prevents tight sump level control. A feedforward signal of bottoms flow that is in reality a half decoupler provides the immediate effect needed in terms of a change in steam flow.
The tray for top and bottom temperature control is selected that provides the largest change in temperature for a change in the manipulated flow in both directions (increase and decrease). By choosing the largest change in both directions, the composition at other trays in the column is more tightly regulated. The manipulated flow paired with the temperature is the one with the largest effect on the temperature. Normally, the top temperature is most affected by reflux flow (directly or indirectly from receiver level control) rather than steam flow so the top temperature is often not paired with steam flow.
After proper pairing, there is still an interaction with the two point composition control. The addition of feedforward of column feed to both loops can provide much of the decoupling needed. Typically the top temperature trims the reflux to feed or distillate to feed ratio and the bottom temperature trims the steam to feed or bottoms to feed ratio.
As detailed in my Control Talk blogs “Causes and Fixes for Fast Oscillations” and “Root Causes of Slow Oscillations”, periodic disturbances should be eliminated where possible by better process and automation system design and better tuning. These oscillations can trigger interactions causing a confusing situation where oscillations at different frequencies are spreading throughout the process.
Recycle streams and heat integration create more opportunities for interactions where disturbances come back with an integrating response from accumulation and at worse a runaway response (snowballing effect) from positive feedback. A good example of this problem is continuous reaction and recovery system. A fixed setpoint flow controller based on production rate needs to be set somewhere in the recycle stream path from a reactor through a recovery system and back to the reactor in terms of recovered reactant.
Separation of dynamics by tuning making fast loops faster can stop full interaction. In particular, the fast loops can correct quickly for a slow disturbance from the slow loop. A feedforward of the fast loop to the slow loop eliminates the rest of the interaction. The remaining concern is setpoint changes to the slow loop that result in large abrupt changes in the slow loop output that upset the fast loop.