Process Control (Part 2): Even Smarter Control

Written by Joe Evans, Ph.D.

Page 2 of 2

The blue curve in Figure 1 plots the percent change in system pressure over time. The red, horizontal line at zero on the Y axis is the set point pressure. Here is what happens. At time 0, the controller receives a message that the system pressure has dropped 10 percent, so it immediately initiates a proportional speed increase. After about one second, the pressure returns to the set point, but then it increases for another second and hits its max at 5 percent over set point. By this point, the proportional controller realizes that it has made a mistake and instructs the drive to slow the pump. Yet again, it overcorrects in the opposite direction. Over the next few seconds, it continues to adjust speed until pressure finally remains near the set point.

The curve in Figure 1 represents the total error that occurred during the pressure correction and can be broken down into three different pieces of information. The first is rise time, or the time it takes for the pressure to increase from its low point to the set point. The second is overshoot and represents the maximum pressure that occurred. The third is settling time, or the time required for pressure to settle about the set point.

The beauty of the integral function is that it can calculate the area under this complex curve and come up with a numerical value that describes the total error that occurred. It can then use that quantity to police the proportional controller the next time a pressure change occurs. For example, if the controller sees a 10 percent drop in pressure and decides to increase speed by 10 percent, the integral will say, "Nope, can't let you do that. Based on your past performance I am going to limit your increase to 7 percent." The integral tracks the error quantity continuously, and its response will continue to increase until the error is reduced to zero. This probably never happens but it does substantially reduce the total error that results from proportional control alone. In fact, many VFD processes-including some pump applications-find PI control more than adequate and don't even use the D in PID.

The Derivative

As I said earlier, the derivative function (or D) allows us to calculate the rate of change of some quantity that is undergoing a nonlinear increase or decrease. In our example, this quantity is pressure, and pressure seldom changes in a linear fashion. More often its change is in the form of a complex curve. The derivative continuously monitors the rate at which pressure is changing and informs the controller as to how quickly it should react to some change. You can think of it as the "how quickly" function.

Figure 2 below contrasts the curves generated by a 10 percent pressure drop that occurs over a period of 1.5 and 2.5 seconds. As you can see, the blue curve-generated by the 1.5 second drop-is quite a bit steeper than the red one that occurs over 2.5 seconds, and the steeper the curve, the faster its rate of change. Since the rate of change is much greater for the 1.5 second drop, the derivative function would cause the controller to respond more quickly to that drop and more slowly to the 2.5 second drop.

I said the feedback seen by the VFD is usually one-dimensional, but that single source provides a continuous stream of information. Depending upon the processing power of the controller, it might be monitored anywhere from 5 to 10 times each second. Since the controller is continuously updated with new pressure information, both the integral and derivative functions can drastically increase the accuracy of the proportional algorithm by providing it with real time guidance.

One of the advantages of the typical VFD is that the P, I, and D logic is an integral part of the system. If your particular application works well with P and I alone, there is no need to use D. If reaction time is critical, D is always available.

Joe Evans is the western regional manager for Hydromatic Engineered Waste Water Systems, a division of Pentair Water, 740 East 9th Street Ashland, OH 44805. He can be reached via his website at www.pumped101.com. If there are topics that you would like to see discussed in future columns, drop him an email.

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