Try just playing around with weights of different shape and value, and observe (and preferably record) the resultant waveforms.

It's possible you may be able to come up with some "rule of thumb" through empirical analysis. Basically I mean that let your mind do the complex part (like pattern recognition) to reduce the waveforms into a simple equation that can be easily coded into the program. I think thats what Bruce is trying to say too.

For example, you might notice that the final value is approximately some fraction of the first overshoot. Of course that is a biiiit too simple... :D

Bruce's idea about predicting the final value from the over- and under-shoots is a good one too

Alternatively, if you have the option, you could go for a mechanical solution. Increase the damping constant of the system to give a slower but more stable response, hopefully within the specified time. This would involve stiffening the spring a bit. (I am assuming the mechanism is a simple one and can be modelled by a single spring-mass system, so should be easy to analyse...) But then again, why go for hardware when a little extra software might solve the problem? :)

kundi