ODE Parameter Optimisation for early convergence

I have a system which is quite a bit complicated and is a dynamical system with Stiff requirements. There is a particular gain value which controls the settling time substantially in the final output. I want to plot all the outputs from the resulting variations of that gain. How can I achieve this?

More importantly, that gain causes a waterbed effect(tradeoff between settling time and overshoot) how can I optimise to get the gain value which gives a early settle as well as a robust model. Note the minimum value of the gain is 3.

[Subhransu Sekhar Bhattacharjee]

Please note the maximum acceptable value of the gain is 50, sampled at a difference of 5.