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PID tuning

The process controller’s job is to maintain the process variable at setpoint, regardless of whether the setpoint is constant or has just been changed.

The controller contains the “control algorithm,” or control logic equation. The most common control algorithm is called PID, which stands for Proportional (P)-Integral (I)-Derivative (D).

When the process is not at setpoint, the PID controller will calculate an output change based on the sum of the Proportional, Integral, and Derivative terms. Determining the appropriate settings for P, I and D can be a difficult task, given the array of process types.

The first tuning method was developed in 1942 by Ziegler and Nichols and is known as Quarter-Amplitude-Damping (QAD). Yet many practitioners still prefer to use trial and error or “tune-by-feel” techniques. Default tuning values abound and are written in “black books” for future reference. A Proportional gain of 1.0 and an Integral (reset) time of 1.0 minute/repeat are typical “good numbers.” However, it is difficult to achieve excellence in manufacturing through “feel” alone and a more scientific method is required.

“Lambda Tuning” refers to all tuning methods in which the loop speed of response is a selectable tuning parameter. Lambda tuning is of critical importance in the process industries, because it is the only method that allows the tuning of all loops to be carried out in a coordinated manner. The Lambda tuning method is straightforward and consists of the following steps:

• Perform a series of manual bump tests to determine the type of process response. The bump tests usually reveal control element deficiencies and a host of other problems that should be corrected to allow the process to work correctly.

• Choose the desired speed of response of the loop based on process requirements and apply the Lambda Tuning equations to calculate the PID controller gains.

• Test the tuning by performing a setpoint bump.

As an example, consider the Reactor feed problem shown in Figure 1, where the need is to maintain the reagent ratios and reaction stoichiometry constant. A level controller cascades down to the setpoints of the two reagent flow control loops (A and B) via ratio stations. In the example, the reagent flows have target ratios of 68 percent for “A” and 32 percent for “B.” The flow controllers were tuned using both the QAD and Lambda tuning methods. Figure 2a compares the flow responses to a setpoint change and Figure 2b illustrates the reagent ratios of flow A to flow B.

Using QAD tuning (heavy red lines in Fig 2a and 2b), both loops oscillate with an initial overshoot of 50 percent and flow B is slower than flow A. Fig. 2b shows that this causes a significant disturbance to the ratio of reagents A and B. Oscillatory tuning offers no benefit for uniform manufacturing. Operating a reactor with such tuning leads to lower reaction conversion efficiency, lower product purity, lower operating constraints and increased cost.

Clearly, the requirement for the two flows is to respond in a non-oscillatory manner, with exactly the same speed of response. This requires Lambda Tuning with both Lambda values set exactly equal (in this case, 20 seconds) as shown in Figure 2a and b (blue lines). In Figure 2a, the transient lasts about 80 seconds, while the flow ratios are absolutely constant (Fig. 2b). This is only one example of how the selection of a specific speed of response for multiple control loops impacts uniform manufacturing.

The benefits of the Lambda tuning method are clear:

• The method provides “smooth” control over a large range.

• It allows coordinated tuning of cascaded control strategies, loops that are interactive and that require identical response times.

• The manual bump test identifies control element problems that will degrade control loop performance.

Ellen Palmer,, is a Process Control Consultant with Emerson

Process Management, EnTech Division, in Toronto.

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