InTech magazine - CONTROL FUNDAMENTALS

This article first appeared in InTech, May, 1999

Tuning process controllers starts in manual

By John Gerry

Finding the lag and dead times and the process gain opens the door to PID control, efficiency, and higher profits.

PID controllers are designed to automatically control a process variable like flow, temperature, or pressure. A controller does this by changing process input so that a process output agrees with a desired result: the set point. An example would be changing the heat around a tank so that water coming out of that tank always measures 100° C.

Usually adjusting a valve controls the process variable. How the controller adjusts the valve to keep the process variable at the set point depends on process parameters entered into three mathematical functions: proportional (P), integral (I) and derivative (D). See InTech's January 1999 Tutorial for the details on the mathematics involved in P, I, and D control.

So, how does one set the parameters so that the controller does its job?

Some processes are unruly

First, know that there is more to tuning a PID loop than just setting the tuning parameters. The process has to be controllable. You won't be able to get good temperature in a hot shower if there is no hot water or if the adjusting valve is too small or too large.

Assuming the process can be conquered, then you can begin tuning it. The goal for good tuning is to have the fastest response possible without causing instability. One of the best tools for measuring response is integrated absolute error (IAE).

Honing in on the set point

A control scheme's goal is to minimize the time and magnitude that the process variable strays from the set point when an upset occurs. To calculate the IAE, simply add up the absolute value of the error during each digital controller sample.

Adding these values together yields a number. Adjusting the PID parameters to minimize this number is known as minimum integrated absolute error (MIAE) tuning. Graphically the IAE is the area in the graph between the set point and the process variable. In Figure 1, this area is colored blue.

Figure 1. The error measurement is the area in blue. Minimizing this area maximizes the process's economic benefits.

A poorly tuned process results in sending a richer product than necessary out the door and with it, profits. Or, it causes off specification product, which requires rework and increased cost. With better tuning one can give away less while staying on spec.

For example, methyl tertiary butyl ethylene (MTBE) added to inexpensive gasoline increases the octane number. Because MTBE is expensive, you want to add just enough to reach the target octane level. Add too much MTBE and you give away unnescessarily strong gas. Add too little and the gasoline won't reach the regulated octane level. Ideally, you want to control the added MTBE to give the octane level close to the regulated level without going below it.

Bring in baseline parameters

To perform the tuning chore, certain fundamental measurements must be taken. Specifically the process's lag time, dead time, and gain must be determined. To do this, set the controller on manual. Set its output to somewhere between 10 and 90%. Then, wait for the process to reach steady state.

Next, change the controller output quickly in a stepwise fashion. The process variable will begin to change too, after a period of time. This period of time is called the process dead time.

The process lag time is how long it takes for the process variable (PV) to go 63% of the way to where it eventually ends up. This would mean that if the temperature increased from 100° to 200° , the lag time would be the time it took to go from 100° to 163° .

The process gain, or merely the gain, is found by dividing the total change in the PV divided by the change in the controller output.

Dead time dictates

A process that consists only of lag is easy to control. Simply use a P-only controller with lots of gain. It will be stable and fast. Unfortunately these processes are rare because of another dynamic element of most real processes: dead time.

Sometimes overlooked, dead time is the real limiting factor in process control. Dead time is the time it takes for the PV to just start to move after a change in the controller's output. During the dead time, nothing happens to the PV.

So, you wait. A control loop simply cannot respond faster than the dead time. Hopefully, the process is designed to make dead time as small as possible.

With dead time in the process, gain can be increased to get a faster response, but this will cause loop oscillation. If gain is increased even more, the process will become unstable.

Some like it simple

From the process gain, lag and dead times, we can build a simple tuning table for both PI and PID controllers. Table 1 comes from a controller design method called internal model control (IMC). Each cell yields a numerical setting that an operator plugs into a controller.

Controller Type	Controller Gain (no units)	Integral Time (seconds)	Derivative Time (seconds)
PI control		t	not applicable
PID control		t	q/2

q = process dead time (seconds)

t = process lag time (seconds)

K = process gain (dimensionless)

l = 2q used for aggressive but less robust tuning

l = 2(t + q) used for more robust tuning

Some controller mechanisms use proportional band instead of gain. Proportional band is equal to 100 divided by gain.

The values in the table are for an ideal type controller. The controller computes controller gain, integral time, and derivative time using the formulas shown. Other tables and computational methods, of which there are many, are needed for other systems.

Compare the methods for fun

Figure 2 compares the IMC tuning method outlined above to a more sophisticated method, the MIAE, which uses performance criteria developed using expert systems.

The process described was found to have a 30-second lag time, a 10-second dead time, and gain of 1. The more aggressive setting (l = 2q) was used for the IMC method.

Figure 2. The red line is IMC tuning and yields an IAE of 42. The blue line shows an advanced tuning method which yields an IAE of 8.

The IMC does produce a nice smooth response and it provides a starting place for optimizing the control loop. However, tuning with a more advanced algorithm aimed at minimizing IAE gives an IAE that's better by a factor of 5. The advanced tuning method was much faster as well.

Further, the minimum IAE tuning ensures the minimum amount of excessively rich product production while staying close to and exceeding specifications. Thus, an improvement in IAE is directly proportional to the dollars saved. In this example, the IAE tuning saves the user 500% over the simpler IMC.

Start at ground zero

Assuming a given process and controller are of a specific type, a simple tuning method can get you started in setting PID parameters. Using more advanced optimization methods will enable increased process efficiency and higher profits.

Behind the byline

John Gerry holds a M.S. in chemical engineering from the University of Texas and he's a P.E. He has worked for Foxboro Company, Eastman Kodak, Eli Lilly, and S.C. Johnson. His article on power spectral density analysis appeared in InTech's August 1998 issue. He founded and is the president of ExperTune Inc., located in Hubertus, WI.

Credits

Simulations, figures, and IAE tuning provided by ExperTune Inc.