Use of Stiffness Estimate 101

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 and you use a stiffness estimate of 5, the aggressiveness during the test will be 100/5 = 20. Less aggressive than the default. 
If you use a stiffness estimate of 0.5 the test will be done with an aggressiveness value of 100 / 0.5 = 200 Twice as aggressive as the default values. 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. So you may have to lower SE. A stiff sample will require very little CE to reach target, so will have to increase SE.

This is the base of it. The required SE will depend on: sample stiffness, amplitude, frequency and effective stress (which influences 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. 
Sample stiffness influences the base SE you will have to use greatly. Amplitude is as moderate to small influence (the higher the amplitude the lower the SE). Frequency influences the margin on an error while defining SE. The higher the frequency the lower the margin.

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).

Getting the correct SE is the single most difficult procedure on a dynamic test. If you are testing a completely new sample it may require testing a trial specimen or, doing 2 or 3 cycle trials before the real dynamic test (re-consolidating in between) to find out the correct SE value. Once you find the correct SE for a sample type you will see that it will not change much between samples of the same type. 
Testing experience with this type of system makes getting the correct SE substantially easier over time. It will come to a point when a technician will look at a sample, and considering the stresses and amplitudes involved he will know straight away the approximate value to use as SE.