ASHRAE Journal - June 2009 - 50

• Redesign and replace equipment to attain linearity; • Tune where process gain is high and live with the sluggish response at points of low process gain; • If the control loop does not operate over a wide range, but exists only to account for minor disturbances, there may be no need to linearize the loop; and • Introduce gain scheduling or characterize the output through software programming. The first option is likely the least desirable fix. Replacing equip‑ ment is expensive, although in extreme cases, may be necessary. The second and third options may be viable, depending on the degree of nonlinearity and the amount of time the system operates at the two extremes. Refer to Figure 2. If a system operates between valve open‑ ings of 15% and 70% equally, then the system should be tuned at 15% valve opening (high process gain). If the sluggishness that occurs at 70% valve opening is tolerable, then further at‑ tempts to linearize this subsystem are unneeded. If this loop were to operate at 50% all of the time with only small position changes to compensate for minor process disturbances, then the loop may be gain optimized at 50%. Although a test might show loop instability at 15% and sluggishness at 70%, this would be acceptable since we know the loop will never operate at these points. The final option works well for controllers with programming capability. Using the same example, assume the system must op‑ erate equally at all points between 15% and 70%. Further assume we wished an optimized process response to load disturbance across the entire range of operation. Using some form of gain scheduling is one way to do this. One form of gain scheduling is to establish a table within the controller (provided by the manu‑ facturer) that allows entry of different controller parameters over different ranges of control loop operation. For example, one could establish that a controller requires different tuning parameters when the temperature of the process fluid is less than 40%, is between 40% and 60%, and is greater than 70% of the sensor range. One could tune the controller in each of these three ranges and enter the appropriate parameters into a gain‑scheduling table. Many of today’s controllers allow one to programmatically change controller gain, integral time constant, and derivative time constant based upon a predefined parameter. This is similar to the earlier discussion except the controller parameters are dynamically changed within the code. Alternatively, one may characterize controller output through software programming. Readers interested in such methodology may refer to the March 2003 edition of ASHRAE Journal.3 Sticking Friction Figure 3: Illustration of valve dead band and stick-slip for a typical control valve. The solid line is the driving signal while the stair step line is actual valve movement. This simulation illustrates a 10% valve dead band and a 5% stick-slip. prevents valve movement until the force applied by the driving signal is sufficient to overcome that friction. Once the valve stem moves, frictional forces again overcome the force of the driving signal, stopping valve movement. The result is the staircase move‑ ment of the valve as shown. This is referred to as “stick‑slip.” Once the driving signal reaches a maximum and the signal reverses, the valve stem remains stationary until the driving signal falls below some value allowing the valve stem to move. The amount of signal change after signal reversal required to change the direction of the end device is called “dead band.” In both cases, as the driving signal is changing, valve position does not change for some period of time. The result is no change in the process variable. This effectively injects an artificial dead time into the process. Dead time is the amount of time it takes for a control loop to respond to a disturbance and is the most difficult dynamic element to control. The end‑device should be inspected for excessive manifestations of sticktion and serviced if necessary prior to the tuning process. Noisy Signals Sticking friction, often referred to as “sticktion,” exists in all mechanical end devices. It is due to static and dynamic friction between moving parts; for example, the valve stem and valve packing. Sticktion manifests itself in two ways: dead band and stick‑slip.4 Both phenomena are illustrated in Figure 3. The smooth trace in Figure 3 represents controller output to the valve. As the driving signal increases, the valve will tend to move in the same direction as the signal. However, internal friction 50 ASHRAE Journal Perhaps the most common source of noise in a control loop is that caused by the process itself, such as the inherent noise of flow or static pressure measurement. Such random noise can be difficult to handle. The general consensus is to introduce a noise filter. But whether the filter is a physical piece of hardware or a software filter written into the code, it will introduce a time lag. It is imperative it is applied before tuning the loop. An important consideration is illustrated in Figure 4.5 In this plot, the x‑axis represents the period of an injected sinu‑ soidal wave representing noise. The values are multiples of the ultimate‑period of the control loop, that is, the period at which the closed‑loop will cycle with constant amplitude. The y‑axis represents how well the controller copes with an injected noise signal. Quantitatively, it is the standard deviation ashrae.org June 2009

ASHRAE Journal - June 2009

Table of Contents for the Digital Edition of ASHRAE Journal - June 2009