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ODE Parameter Optimisation for early convergence

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

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