The PID structures with proportional on error cause a step change in the PID output for a large setpoint change. For structures with derivative on error there is also a sharp bump almost looking like a spike unless you zoom in. The question is whether these abrupt changes are beneficial and if detrimental what can be done to make the initial response of the PID output smooth. The solution involves intelligent choices of PID structure and tuning.
This is the 3rd in a continuing series of practical and useful questions on PID tuning raised by Brian Hrankowsky a knowledgeable process control specialist in the pharmaceutical industry after having been present at a panel session on controller tuning at ISA Automation Week 2010 developed by Michel Ruel. Brian is not representing his company in these posts. The questions and answers in all of these blogs will be addressed in much greater detail in the long overdue 4th edition of my book Tuning and Control Loop Performance being published by Momentum Press.
Whether a step or bump in the PID output is useful depends upon your process type and objectives and system capabilities. Let's look first at how equipment, piping, and automation system limitations would affect your decision.
If a final control element has deadband, a threshold sensitivity limit, or a resolution limit, there is an additional deadtime created that is the deadband or limit divided by the rate of change of the controller output. The additional deadtime does not show up on typical tuning tests because a step change is made in the controller output. A step or bump in the controller output for a setpoint change eliminates this deadtime. The effect is particularly noticeable for small setpoint changes. The best solution is to reduce the deadband setting in a variable speed drive and the backlash and stiction in a control valve and improve the threshold sensitivity of the actuator and positioner and above all avoid on-off valves posing as control valves. See the November 2012 Control article "Is your Control Valve an Imposter", the December 2012 Control Talk column "Diagnosing Control Valve Problems", and the May 3, 2012 Control Talk Blog "Checklist for Control Valves"
If there is a significant transport delay of the manipulated stream, a step change in the flow of a stream for a setpoint change will help reduce the process deadtime. The effect is particularly significant for the small reagent flow associated with pH control. The best solution is to reduce the volume of piping between the control valve and the point of entry into a pipe or vessel and the volume of an injector or dip tube.
A step change in the flow and temperature of stream can cause a more immediate increase in the heat transfer coefficient and driving force, reducing the heat transfer lag. For surfaces that tend to coat, the avoidance of low flow can keep the surface cleaner and the heat transfer coefficient larger.
I seem to remember boiler control systems purposely introduce a lead-lag on output changes to a coal pulverizer to improve the response to changes in coal demand.
Abrupt changes are detrimental to some processes. Sudden changes in liquid flow can cause liquid hammer. Sudden changes in flow controllers off of a header can upset other users on the header and the compressor. Sudden decreases in user flows can cause compressor surge. Sudden changes to inline blend and composition systems can cause off-spec material unless there is a large or agitated volume downstream to attenuate the short term excursions.
Large changes in the addition of heat can cause hot spots that burn product or trigger side reactions in chemical processes or kill cells in biological processes. Overdesigned heating systems accentuate the problem. Large change in chilled water flow can cause cold spots that cause the formation of crystals on heat transfer surfaces.
Let's look at some process types and objectives where a step or bump on the controller output is useful.
For integrating processes, such as batch composition and temperature, vessel pressure, and level, the controller output must be driven past the balance point or final resting value in order to change the process variable. This requirement is most easily visualized for level. For a level controller manipulating a flow out of the tank, the flow must be increased to be greater than the flow coming into the tank before the level will drop. The reliance on integral action to do this task is not advisable from many view points. First of all putting two integrators in series has some undesirable effects including causing limit cycles from deadband and creating a low controller gain limit. Last week we discussed how you need to increase the reset time as you decrease the controller gain for integrating processes and that most level and batch loops are in violation of the relationship.
For highly exothermic reactors, there is also a low controller gain limit with disastrous consequences for even approaching this limit. I have seen where polymerization batch reactors use a proportional plus derivative (PD) structure (no integral) because of safety concerns.
For an one sided response in batch reactors which occurs in heating a batch when there is no cooling split range, negligible heat loss, and no heat consumption from vaporization or endothermic reactions, a PD structure is needed to prevent overshoot.
The side graphics on slide 21 in the "Emerson-Exchange-2012-Effective-Use-of-PID" show the considerable benefit achieved by Hector Torres by going to PD on error control in batch temperature eliminating an overshoot of 30 degrees by omitting integral action.
Consider the split ranged loop reactor temperature loop shown on slide 100 of "ISA-Edmonton-Effective-Use-of-Measurements-Valves-and-PID-Controllers." The temperature PV is 48 and the SP is 50. Should the steam or cooling water valve be open? Looking at the faceplate or digital value or even a dashboard dial on their graphic display operators and engineers say the steam valve should be open. Interesting enough, my experience is technicians may not be fooled as easily. If you look at a trend chart with the proper time frame, you realize the cooling water valve should be open to prevent overshoot due to the acceleration of temperature trajectory. Today the typical trend chart available from the faceplate is next to useless because the process variable (PV) span and time frame are not intelligent. A short time frame would not have shown the acceleration. The cited example was actually reported to me from two control rooms as something wrong with PID algorithm. I got the report only because I knew the people at the plant very well. I would venture the same problem is experienced to some degree in almost every control room. It leads to manual tuning of too much reset action and not enough gain action because the integral mode has no sense of direction and would work to open the steam valve even if overshoot was eminent, whereas the proportional mode would work towards getting the cooling water valve open as the temperature increases. The lack of understanding of trajectories explains why most manually tuned temperature loops have too much reset action (too fast of a reset time) and not enough gain or rate action. The June 26, 2012 Control Talk Blog "Future PV Values are the Future" shows the benefit of projecting a PV value one deadtime into the future for operator understanding, the fastest setpoint response, and adaptation of the reset time.
The benefit of derivative action on error is rather marginal and in most cases not worth the wrath of operators when they see a spike in controller output whenever they make a setpoint change. The DCS I work with has a default structure of PI on error and D on PV.
The step change in output for setpoint change will reduce the rise time (time to reach setpoint) to speed up a startup or a batch cycle time. In the bottom equation on slide 131 of the ISA Edmonton presentation we see this can be achieved by proportional action or setpoint feedforward. The benefit of setpoint feedforward is mostly seen for a low PID gain. The equation also shows the reduction in rise time is limited by the maximum allowable change in output established by output limits.
When the PID output is saturated, the PID output does not come off the limit even though the PV is accelerating towards the setpoint until the integral contribution is less than the total of the proportional and derivative contribution to the PID output. Too much integral action can cause the output to remain saturated until the PV crosses setpoint.
A general method for an intelligent reset time uses the computation of the rate of approach to the setpoint and the setting of the reset time to make the integral contribution less than the proportional and derivative contribution when the PV is within a specified error per the equations and discussion on pages 14-16 in the ISA 2012 Automation Week paper "Effective Use of Key PID Features." If the near or true integrating process gain can be identified, the method can automatically achieve fastest rise time and minimum overshoot.
The reset time can be adapted online to include the aforementioned calculation and feedback correction based on future PV values. The reset time is increased if the PV overshoots the setpoint and is decreased if the PV falters or hesitates in the approach to setpoint. This feedback correction accounts for nonlinearities and unknowns.
PV overshoot can occur if the PID gain, reset time, or rate time is too low. While the PID gain could be increased, there may be good reasons why the PID gain is less than the entitlement either to absorb variability or to provide robustness to nonlinearities. The more conservative approach is to increase the reset time. This agrees with the fact that the reset time is too small in most slow continuous and batch processes. Often we can make a big improvement by simply increasing the reset by an order of magnitude. There is very little downside to this practice.
PV faltering or hesitation can occur if the PID gain, reset time, or rate time is too high. The module I have for an adaptive reset focuses on decreasing the reset time. The faltering is most noticeable for deadtime dominant self-regulating processes where the deadtime is larger than the open loop time constant (largest time constant) and the controller gain is tuned with rules designed for other types of processes. The faltering occurs if the loop is stable and the proportional and derivative contribution overwhelms the integral contribution. For loops where the deadtime is much larger than the open loop time constant, the reset time can be reduced by factor of 8. Equation C-13 in the InTech Jan/Feb 2012 "PID Tuning Rules-Appendices" provides this reduction in reset time.
Lambda tuning automatically decreases gain and increases integral action going essentially to integral-only control for processes with a small time constant. Brian has found almost eliminating proportional and derivative action to be useful for fast loops. Flow loops become deadtime dominant due to the module execution time unless a PV filter or transmitter damping is added. These loops are nonlinear due to an installed valve characteristic and tend to be noisy and erratic at low flows near the rangeability limit. Also, the slower movement of the output helps avoid violating the cascade rule from having a positioner on the flow loop. Here essentially integral-only control is the right solution as Brian found out.
Integral-only control has also traditionally been used for valve position controllers (VPC) and analytical control loops (AIC) dominated by a large analyzer cycle time. Slow integral only type of action eliminates interaction and overreaction. However, the VPC and AIC is vulnerable to being too slow reacting to disturbances. Feedforward control and an enhanced PID developed for wireless can help. The enhanced PID suppresses limit cycles from valve and analyzer resolution limits and can be used with setpoint rate limits for directional move suppression as noted in last week's Control Blog. The key feature of the enhanced PID is the intelligent suspension of integral action. For more on VPC features and opportunities see the Nov 2011 Control article "Don't Over Look PID for APC"