In my previous article on loop tuning, I discussed the importance of field data collection and the importance of a methodical approach to PID tuning. I introduced the concept of the bump test and how its results help guide the steps and equations used in proper tuning. Here, I will explore that concept in greater detail focusing on self-regulating loops since they are most commonly used in the industrial field.
At ECS we use a visual tool for data collection in every instance. The tool may be part of a controller suite or it may be stand-alone. Regardless, it is imperative to capture accurate information about the performance of your system before planning and programming a solution.
A common example of a self-regulating loop is a flow control which varies flow through a pipe via variable speed control on a pump or a position-controlled valve. In this example, the flow can be managed by speed adjustment of the pump or position of a valve. The result of the change ordered from the controller is stable and is generally fast and repeatable.
I first place the system in manual mode and establish a visual graph which shows the process variable (Pv) and control variable (Cv). I take care to observe both items as a percentage of their overall capability, not in either or both engineering units. Once I can see these elements and understand their safe operating limits, I define an initial Cv and wait for the Pv to stabilize. If the system stabilizes, it is then confirmed that I have a self-regulating loop.
Next, I note an initial time, T1, and modify the control variable with a large step. I measure the time between my modification and when the process variable begins to respond or T2. The difference between these defines the dead time of my system. An ideal theoretical dead time would be zero, but this is not possible. If the dead time is too large, there is likely a physical problem with the system and it is unlikely we will achieve satisfactory results with programming changes only.
I also observe how the disturbance I introduced affects the output, specifically establishing a ratio between the Cv disturbance and Pv response (process gain). A 1:1 reaction, as measured in percentage to my disturbance, would be ideal. But anything that reacts within the range of 0.5to 2 is acceptable. If the process gain is smaller than 0.5, the process is undersized. When it exceeds 2, the process is oversized. It is possible to re-scale the Pv if it isn’t in the desirable range, but this should not be used as a substitute to proper resolution or to mask physical problems. It should be noted that most sensors will perform linearly; however, there are situations where a non-linear sensor is required and it may be necessary to linearize an output within the sensor itself using a conditioner or code within the system controller.
Applying the results
Continuing to watch the system response, I measure the time it takes to achieve a change to 63.25% in our Pv. This is noted as 1 Tau, which is used to establish the system gain. Finally, I observe the Pv’s response curve, noting how the response drives up (or down) towards the Cv setpoint and settles out. This response is our stabilization time and it will be the primary focus of our tuning later. I like to collect and note this baseline information multiple times at varying percentages of Cv to ensure that the system is repeatable at various points.
Armed with this information, I can now select the proper equation(s) to use for my tuning plan. The mathematical equations vary slightly between independent and dependent gain. In either case, you have the variables that you need. Your initial work should be by hand and then later applied to the controller logic.
Using Lambda tuning formulas you can compute derivative, integral and gain. These are your starting points for adjustments within the controller instructions. It should be noted that controller logic varies a bit from brand to brand and even potentially model to model, but the required input information is still there.
Rafael Zapata, lead engineer at ECS Solutions, a certified member of the Control System Integrators Association (CSIA). For more information about ECS Solutions, visit its profile on the CSIA Industrial Automation Exchange.