# Where's the modern in these loops

## The performance of control loops declines over time.

##### By Martin Emond

We may wonder why the performance of loops declines as time goes by when nobody touches the loop parameters in a proportional-integral-derivative (PID) tuner or the loop programming in a control system.

We have noticed over the years that performance declines at a rate of about 50% every six months. This means that after a year of no maintenance, we have lost 75% of the performance we had right after the maintenance or the implementation. The half-life of control-loop performance is about six months.

So what's the matter with those control loops?

Look at this simple control-loop diagram. The set point is the target measurement we would like the process to be on. The process value is a measurement we get from the process by using an appropriate transmitter. The latter then compares to the set point to generate the error (set-point value - process value).

 A simple control loop

This error calculation transmits to the controller and submits to the PID algorithm to calculate the output effort that is necessary for the process dynamic to correct the error.

This controller output uses an actuator, like a valve, to make the process move in the right direction and get back to set point. People would tend to think that if we do not change any parameters in the controller we should not expect performance decay.

However, people may forget that the process model is changing over time! So, then what exactly does the process model consist of? The process model is a mathematical representation of the behavior according to the physics and the chemistry of the process.

In practice, we try to keep it simple and use only three parameters-the process gain, the dead time, and the lag time.

The gain is the ratio of the change in process value over the change in controller output. Thus, the higher the process gain, the more the process value will react to the controller output changing.

The dead time is the amount of time that it takes for the process variable to start changing after the controller output changes.

Finally, the lag time is the amount of time, after the dead-time period, that the process variable takes to reach 0.632 of its final value after a step change in controller output.

Lag time gives us an idea of the capacity element of the process. For example, the heating control in a house is much easier than the one in a car due to the different capacity. As a matter of fact, in a house we use a simple on/off controller and get good performance, as opposed to a car in which we need a more sophisticated controller.

This simple model is a first order system. It is much simpler than higher order mathematical models and provides enough precision and information to achieve good performance.

 Robustness plot

The robustness plot helps one relate the parameters of a model and its decline with time. This x-y plot shows the trade-off between the robustness or sensitivity to oscillation versus performance or aggressiveness of tighter tuning.

On the y-axis there is dead time, and on the x-axis there is process gain. The blue and orange lines represent the closed-loop process boundary of stability for current and new, proposed tuning.

In other words, if for any reason the process gain or dead time or the combination of both increased enough to be located somewhere above the line, either line, the closed-loop process would be unstable. As a result we would be losing performance.

Conversely, if the process model stays underneath the line, either line, then the system will remain stable. The black cross represents the point of critical oscillation; it is also the actual process gain and dead time.

The cyan zone around the black cross, which the closed-loop system should never be in, represents a prohibited area where the process will start being dangerously oscillatory.

This zone also corresponds to a safety factor of 2. When we tune the process we have to deal with robustness through the safety factor. Consequently, the lower the safety factor, the more aggressive is the control, and the closer the loop gets to the edge of oscillation.

What are the types of situations that might modify a process model, and what are the changes that we should be paying attention to?

Here are several examples that we know can change a process model's gain, dead time, or lag:

• New plant feed
• New operating zone
• New operating procedure
• Modification of the recirculating load
• New filter within the transmitter
• New ramp limiter in a motor drive
• Physical modification-a transport delay increase, tank height or diameter, new valve characteristic, buildup in pipes, or new operation unit
• Valve stiction
• Hysteresis
• Positioner linkage wearing
• Side effect of new programming

These are all part of the day-to-day things we can expect. Even though tuning methods should take place and include a safety factor for robustness, the overstepping of one-day limits is commonplace.

The cost of improper loop performance may be substantial depending on the loop performance's importance in the process. So how can we keep up the good performance?

In the accounting department there exists a software tool to assess profitability in different time spans-monthly, quarterly, and yearly. In control we also need to assess the performance of control loops. However, the time spans in control are much shorter, and the function of the loop is dynamic. We are looking for something like seconds, minutes, or hours.

There is at least one off-the-shelf solution on the market now. This software assesses loop performance according to 20 different indexes for every loop in a plant.

Further it lets the engineer access reports via a network browser, so one can see at a glance which areas can and should improve to reap the most economic benefit.

Moreover, this software is a clever way to target maintenance efforts. This new software is a tool that pinpoints where a process is having problems according to each loop's baseline and threshold.

It gathers data, does statistical calculations, and supplies the graphics necessary to analyze the process completely and efficiently. MP

## Behind the byline

Martin Emond is a registered professional engineer and has a B.S. in chemical engineering. He has fourteen years of plant experience as a process engineer and now works for Top Control in process optimization of continuous and batch processes. Write him at martin.emond@topcontrol.com.

# Ask The Experts

Read questions answered by our experts or join the email list.