Stan: There are many different opinions on tuning. Aidan O'Dwyer's Handbook of PI and PID Controller Tuning Rules has over 400 pages of equations developed by almost 100 people. Each person is passionate that his rules are the best.
Greg: Most of the reasons for the prolific and diverse sets of rules are the importance of the PID, fundamentally different dynamics and disturbances, and a wide spectrum of processes and objectives. Most of the control literature focuses on balanced self-regulating processes and minimizing integrated absolute error (IAE). There are many other processes and objectives. There are dead-time-dominant, lag-dominant, integrating and runaway processes, and the need to minimize interaction and resonance and promote coordination and absorption of variability. Here we look at how lambda tuning addresses these challenges posed by an incredible variety of applications. To allay any concerns that lambda tuning can't achieve the IAE objective, see my online whitepaper, "So Many Tuning Rules, So Little Time," which shows how lambda tuning can minimize the IAE from unmeasured disturbances for all types of common processes.
Stan: Mark Coughran, who was our interviewee in the June 2010 Control Talk column, "What's Going on with Loop Performance?" has extensive experience in tuning and improving control loops. The lessons learned provide important guidance in tailoring the tuning to the application.
Greg: What have you recently seen in offshore oil and gas applications?
Mark: There are a lot of smaller-to-medium applications. Resources are minimal since control is considered less of an issue. There is a safety and reliability engineer onsite, but the control engineer just visits occasionally. One particularly challenging application was a three-phase separator. The relative amount of water in oil has increased by a factor of five over the past 20 years. Gas lift or water injection rather than pressure is used to get the oil out. The phases must be kept separate in the streams to the downstream units.
There is water cleanup and treatment to dispose of locally or reuse. These vessels need inflow to be as steady as possible. You don't want sheen on the water seen from the helicopter. Oil goes to the distillation column stabilizer to take out lights. You don't want bottoms flow oscillating to tank degassing that would upset heat integration or feed preheat. The gas phase may go to an amine unit for cleanup and resale unless it's being re-injected.
The objective here is to minimize the changes in flow to downstream units from level control. The lambda arrest time for integrating processes was computed to be 800 seconds based on stopping a level excursion before the alarm limit. It was remarkable how downstream unit operations settle down when the absorption of the variability in the flow of phases coming into the separator is maximized by lambda tuning using an intelligent arrest time.
Stan: What is an example of how lambda tuning can be used to prevent interaction problems?
Mark: There were first- and second- stage pressure letdown loops in series with a user flow loop for process water. The control valves were piped in series. Interaction was minimized by lambdas of 6, 30 and 80 for the first stage, second stage and user loops, respectively. In general, you want the tightest control at the source to minimize the start of oscillations. The control valve inherent flow characteristic was changed from equal percentage to linear to help linearize the loops. The nearly constant pressure drop across each valve meant the inherent flow characteristic was the installed flow characteristic, making linear trim the right choice.
Greg: To help minimize interaction for liquid systems, the control valve with the largest pressure drop should be used for the flow loop so that upsets in upstream and downstream pressure have less of an effect on the user flow. This solution is counterintuitive since it means a small upstream valve may be best for the flow loop. Check out the February 2014 Control Talk blogs, "Interaction Perspective" and "Interaction Recommendations," for more techniques.
Stan: How do you stop oscillations in cascade loops for fed-batch control?
Mark: Integrating process tuning rules are not just for level loops. The composition, pH and temperature response in the mixed liquid volumes of continuous and batch unit operations is integrating in the time frame and range for PID control. In a bioreactor cascade of dissolved oxygen (DO) to air flow, oscillations were eliminated by setting the DO integrating process lambda (arrest time) equal to 210 seconds and the air flow self-regulating process lambda (closed-loop time constant) equal to 20 seconds. In general, I've found the arrest time of the primary (upper) loop must be at least three times the closed-loop time constant of the secondary (lower) loop to prevent oscillations.
Greg: The use of external reset feedback of the secondary PID process variable to the primary PID can prevent the primary PID output from changing faster than the secondary PID can respond. Moving on to our favorite subject, the effect of control valve response on control loop performance, how about an example of what you did when stuck with a valve with excessive dead band from backlash?
Mark: When there is a noticeable dead band in the control valve, there will be a nonlinear limit cycle for any controller tuning. However, we can choose the tuning to avoid enlarging the cycle. The reactor pressure in the gasoline hydrotreater unit of a refinery had an integrating process response, which, combined with the integral action in the PID and 0.7% valve dead band, created a limit cycle. In addition, with the "as-found" tuning, the limit cycle peak-to-peak amplitude and period were about 2 psi and 2,000 seconds, respectively. As a result, lambda tuning with an arrest time of 110 seconds reduced the limit cycle amplitude and period by more than an order of magnitude.
Stan: What about continuous and fed-batch operations where flows are ratioed with the leader flow set based on level, production rate or composition control?
Mark: To coordinate the timing of the flow changes demanded by the upper control loop, each flow loop is tuned to have the same lambda (closed-loop time constant). This coordinates the flow changes so that there is no unbalance in the composition of the blend or in the destination vessel as the cascade setpoint of the leader flow changes.
Stan: For more details on these and other applications, see the Oct 2013 Control whitepaper by Mark, "Lambda Tuning—The Universal Method for PID Controllers in Process Control."
Greg: Here's the "Top 10 Reasons to Devise Your Own Tuning Rules."
You get to:
10) Set up test conditions that show you are right and everyone else is wrong.
9) Have your own tuning parameter.
8) Avoid having to do feed-forward control.
7) Focus on integrated absolute error.
6) Complain about tuning rules developed 70 years ago.
5) Discount expertise needed to deal with split range discontinuities, backlash, stiction, installed flow characteristics, interaction, sensor fouling, update rates, disturbance dynamics, inverse response and positive feedback.
4) Become a tuning doctor where you treat symptoms rather than fix the source of the problems.
3) Disregard PID form and structure.
2) See your name in a handbook.
1) Say neat stuff like "My tuning rules rule!"