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What are Stiffness Estimate (SE) and Control Effort (CE) in Dynamic Testing?

Owned by Diogo Teles (Deactivated)
Last updated: May 03, 2024 by Dan Zanet
3 min read

 

This article was written for dynamic systems that use the Stiffness Estimate (SE) parameter for dynamic load-controlled tests. However, the same principles apply for systems that use Control Effort (CE) directly instead of SE,  (e.g. VDDCSS)   CE = 1/SE

 

Stiffness estimate (SE) is a parameter that scales the base PID values of your dynamic system.

This means that it scales the aggressiveness of the system. The base PID values are divided by the SE, and the resulting values will be used in a test.

 

For example, if your system has a base aggressiveness of 100 (default internal value):

  • you use a stiffness estimate of 5 => the aggressiveness during the test will be 100 divided by 5 = 20 => 5x Less aggressive compared to the default of 1. 

  • you use a stiffness estimate of 0.5 => the aggressiveness during the test will be 100 divided by 0.5 = 200 => 2x More aggressive than compared to the default value of 1. Ten times more aggressive than an SE of 5.

This aggressiveness, the combined value of PID, can be seen as Control Effort (CE). CE is inversely proportional to SE.


The softer the sample => the more CE is needed to reach targets => a lower SE must be used.

The stiffer the sample => the less CE is needed to reach targets => a higher SE must be used.

The required SE will depend on:

  1. Sample stiffness

Sample stiffness has the largest influence on this. There is an interval of SE values for which you will get good results. The higher the frequency the narrower this interval becomes. 

  1. Amplitude

Amplitude is a moderate to small influence (the higher the amplitude the lower the SE).

  1. Frequency

Frequency influences the margin of error while defining SE. The higher the frequency the lower the margin.

  1. Effective stress (which influences sample stiffness)


For example, you find through a trial test that for an amplitude of 0.1kN and a datum of 0kN on a sample at specific effective stress, you can use a SE between 0.6 and 1(with the ideal being 0.8) when testing at 0.1Hz. You will see that when going up to 1Hz SE values between 0.7 and 0.9 work well. But if testing at an amplitude of 0.2kN you may find that you now have to use a SE value between 0.8 and 1 (with the ideal being 0.9).