All process control gurus cut their teeth on the first-order-plus-time-delay (FOTD) process.  Let’s take a look at what this means.

A first order process is one that shows an exponential response to a step input.  Let’s take, for example, a pot of warm water on a heater.  If you increase the heat input to a higher level, then the temperature will rise.  The temperature rises quickly at first, then it slows down as it levels off at a new, higher temperature.  The shape of the response curve can be represented by an equation:

DeltaT * [ 1-e(-t/T) ]

where t is time and T is the effective “lag time” of the process.  The longer this lag, the longer it takes the process to fully respond.  99+% of the process response will be seen after 4 lag times have passed.

First Order Plus Time Delay Response to Step Change

First Order Plus Time Delay Response to Step Change

The “time delay” is the part at the beginning, where nothing happens for a little while.

Many, many industrial processes behave similar to this FOTD response.  For example, flow controls, pressure controls, and some simple temperature controls all have FOTD responses.  So we can use this same model to understand the process behavior, tune control loops, and train operators about how the process will behave.

In a future post, we’ll get into the mathematical modeling of this process with 3 parameters: Process Gain, Dead Time, and Time Constant.

(image courtesy of ExperTune, Inc. –


As a process control guru, you need to understand process dynamics.  The world does not exist in steady-state.  The sun rises and sets, the weather changes, new batches of raw materials arrive, operators change shifts,  managers change direction, energy prices rise and fall (then rise again!).

All of these factors have a direct effect on the operation of a process.  The primary purpose of process control is to reduce or eliminate the impact of all of these “outside” disturbances.

For the time being, forget about all those Laplace transforms, differential equations, and other math.  We’ll discuss that some other time.  Just stop and think about how the process in your plant changes.

Some things change slowly, like ambient temperature, which rises and falls every 24 hours.

Some things change abruptly, like the operator on the next shift who comes in to work and starts changing setpoints to run the process “his way”.

Some controls can respond very quickly, like flow controllers, and liquid pressure control.

Some controls can only respond slowly, like trying to heat up a large tank, or change the pH of a waste tank.

Fast upsets can only be managed with fast controls.  Slow upsets can be managed by slow or fast controls.

If there is a delay (dead time) between your control action and the process response, then your control will be limited.  Imagine trying to take a shower, and controlling the water temperature.  What happens if the water has to flow through 50 feet of garden hose before it reaches you?  How well can you control it?

Lag time, on the other hand, helps to measure “how long before the full effect is felt”.  So an upset comes, then after the dead time the process starts responding.  The full effect is not seen, however until the lag time has played out.  The good news is that teh controls can respond quickly, even if there is a large lag time – as long as you have an accurate measurement and low dead time.  More on this in another post.

When trying to understand and improve a process, one of the first things a control guru must ask is…How long does it take?  Here are some variations on this question:

* When a new batch is produced, how long is it before we will see the effect here?  How lnog before the full effect?

* How long does it take to process all the material in that tank?

* How long does it take to heat up this (tank, reactor, column, etc.) ?

* How much surge capacity is there?  How long will it last?

* How long between backflush cycles?

* How long does it take before the lab reports back on the quality samples?

* When the biggest upset happens, how long do we have before the process must be back to centerline conditions?

When you combine your understanding of this information with your process understanding, you will be well on your way to thinking about better control strategies.  Always remember to ask about the dynamics.