Ask the experts: How to determine open-loop gain?

Nov. 23, 2016
What to do when the process overshoots the mark.

Q: This is for tuning a control valve on a pipeline. In an open-loop gain test, with a step increase applied to valve opening, the controlled parameter increases, then settles at a number. In this case, flow increased and then decreased to settle at x number. To calculate my Tc, should I use the peak value that PV (flow) reached or the final value that it settled at? If I use x, then 63% of PV happens much sooner.

Our control valve impacts all three: flow, valve inlet (suction) and discharge pressure. The flow and discharge pressure controllers are reverse acting, and the suction pressure controller is direct acting. After a step change from 30% to 35%, flow increases and then decreases to settle at a higher value than what it was before the change was made. My question is: which number should I use to calculate K, Tp and Tc? If I use first peak for the settled value, then my K and Tc will be higher. Since after this peak the flow decreases, if I use the final number, my K will be lower and hence Tc will also be lower.

With everything descaled, my K using final number for flow is 0.3425. Tp and Tc are near 2 sec. If I use the first peak, my K is 0.6225. My Tp, of course, remains the same at 2 sec, but Tc is 4 sec. This is liquid service. I will use lower numbers, so the loop is slower since our process is not that fast.

In this case, I could only do two step tests. Usually, I do the step test by starting from fully open, so I also get a full valve profile. These have been good starting point numbers based on Ziegler-Nichols or GE’s ideal tuning approach. GE’s tuning approach formulas are: Kp gain = 2•Tc / (3•K•Tp) %/%. Ki = Tc rep/sec and Kd = Ki/4. I did not use D since it is liquid service. Of course, I adjust them in closed loop with observation during setpoint changes. Units used in GE block were also important.

The second step is from 35% to 40%. I have your handbook, and have referred to it already. By the way, we use low select at the three separate PID outputs, so the lowest, safest output controls the valve.

Hiten A. Dalal / [email protected]


A: In my answer, I’m assuming that your process fluid is being pumped through your pipeline by constant speed pump(s) and that your goal is to keep the flow and the up and downstream pressures at the control valve within the desired safe limits. I’m also assuming that you want to tune the three controllers, so the one that will be in control will always be the one that requires the lowest valve opening, and you want to use the open-loop method of tuning, which requires the knowledge of the process gain.

In my answer, I will briefly discuss both the process and the process gain determination. Figure 1 shows the system curve of a pipeline and the pump curve of a constant-speed pump. When you step up the flow from 35% to 40%, P1 and ΔP drop, and P2 rises. This is because at a higher flow, the pipe friction rises, leaving less ΔP for the control valve. By applying the low-selecting envelope on the three variables (F, P1 and P2), you’re maximizing flow while protecting the pipe from excess pressure, which might cause leakage. In my view, this goal could be more elegantly accomplished if you used a variable- speed (instead of constant-speed) pump, and just throttled the speed, thereby eliminating both the control valve and the associated waste of energy represented by the pressure drop through it.

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Now, coming to the bump test (Figures 2 and 3), if you’re interested in the open-loop gain (K) of a linear process (such as a linear flow control valve on a pipeline), then you calculate it by the ratio B/A: K = B/A = (% change in flow after reaching steady state) / (bump size in % of full stroke).

In other words, the process gain is based on the final PV value. If you experience an overshoot (which you do), it can be caused by wrong valve characteristics, sticking valve or other causes. In any case, we don’t consider the overshoot in the determination of K, but try to eliminate it. When bump testing, I would make the step change in both directions, to make sure that K also remains unaffected when you apply the step to reduce the valve opening and therefore the flow.

 Please note that I’m using the standard terminology for the various parameters in the bump test:

  • A: Test input[sidebar id =2]
  • B: Test output
  • I: Integral gain setting of controller
  • K: Process gain
  • P: Proportional gain setting of controller
  • Rr: Reaction rate
  • td: Dead time
  • τ: Time constant (defined as Δt or as K/Rr)

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For tuning the controllers, you can use Chapter 2.35 in the 4th edition of my handbook, where some of the most common controller tuning constant and control mode setting recommendations are presented. On flow and pressure applications, we usually end up with control mode values in the ranges listed below:

  • %PB = 50 to 500
  • I = 20 to 200 repeat/min.
  • D = None 

Béla Lipták / [email protected]


A: In addition to the various instrumentation reasons mentioned by Mr. Lipták, you have to consider that your flow is coming from a pipeline. This effect would be more pronounced if it was a gas service.

This means that the line resistance is developed over a length of pipe. Initially, if the pipe carries gas, the pressure in the pipe section nearest to the gas source will be high, but as the flow establishes over the whole pipe work, as the flow (and pressure drop) rises, the pressure will drop at the inlet of the valve (compared to the pressure before making the step change by step-opening the valve).

If you check the pressure just upstream of the valve, you should see the pressure drop (corresponding to the lower flow). I’m not sure if in your case this is significant enough to be considered for the tuning.

Generally, flow loops are fairly straight forward and default parameters are adequate. The only issues I’ve found for flow tuning concerned the characteristics of the valve: linear or equal percentage (EQ%), i.e., if the valve characteristics don’t match the flow range of interest. However, I have not done a lot with pipelines and there may be additional issues. 

Simon Lucchini / [email protected]


This column is moderated by Béla Lipták, automation and safety consultant and editor of the Instrument and Automation Engineers’ Handbook (IAEH). If you have an automation-related question for this column, write to [email protected].