# Calculating Mass Flow Control Response Specifications

At Alicat, we claim that our mass flow controllers are the fastest flow controllers in the world, but how do we substantiate that claim against our many competitors who also claim to be “fast”? Faster control enables a controller to not only reach new setpoints faster but also better maintain stable flow in the wake of unexpected pressure fluctuations. Clearly, speed of response is important for accurate and stable flow control, and today’s post will examine whether Alicat has any business claiming to be the fastest.

Watch this one-minute video that shows Alicat’s control response between setpoint extremes:

### Physical time constant (Tau)

The Greek letter Tau is used to signify the physical time constant, one of the few standards that exist when it comes to reporting response times. The time constant is the amount of time the controller takes to achieve a percentage of the setpoint defined as 1-1/e, where e is the irrational number that forms the base of natural logarithms. With e having a value of 2.72, roughly rounded, 1-1/e is equivalent to 63.2% of the commanded setpoint change. Although this definition is a physical standard, it may not tell the whole story, since the remaining 36.8% of the setpoint change may take more or less time than the first 63.2% did. The oscilloscope image below shows that the Alicat reached 63.2% of the commanded setpoint in just 7.4 ms.

### Arbitrary setpoint percentage change

Many mass flow controller specifications designate an arbitrary percentage change to define their speed of response. A few of these have become common across manufacturers, such as the time required to move from 10% to 90% of the setpoint. Since the bottom and top 10% of a control response curve can be the most variable, this type of response speed specification may not reveal very much about the actual performance of the control system. For example, the image below shows that the Alicat achieved 100% of the setpoint in 11.4 ms. You can see that the oscilloscope steps are the longest at 50% of the setpoint change and are much smaller below 10% and above 90%. In this image, a 10-90% specification would have resulted in a response time of 6-7 ms.

### Settling time

Because getting to the setpoint does not guarantee that the controller will not also overshoot the intended setpoint, many manufacturers specify control response times based on settling time, the amount of time the controller takes to reach the setpoint and then reduce further oscillations to a given error band. For example, an error band of 2% means that settling is not achieved until the flow rate no longer oscillates outside of 2% of the setpoint. Accuracy specifications for mass flow controllers commonly fall within the 0.5% to 2% range, but some specifications define error bands for settling as large as 10%. At Alicat, we believe that if your flow is supposed to have achieved its designated setpoint, then you should expect it to remain within the accuracy margin of error. In the oscilloscope image below, a common-sense settling error band equivalent to the controller’s accuracy specification (1% at full scale) is achieved after just 27.6 ms.