I have built a proportional control system to replace the "resume speed" function in the cruise control on my Tesla. It applies an acceleration that is proportional to the difference between the target speed that I have set (50mph) and the current speed. It uses a gain constant K to determine what the acceleration should be. I measured it by turning it on at a certain initial speed and measuring the speed for 0.8 seconds at 20ms intervals. I am having some difficulty determining the best value for K. In the tested situation I would like to reach my target speed in no more than 1 second (preferably without any collateral damage to my brain). The Y axis on my graph is velocity in MPH, the X axis is elapsed time in seconds. Review my data and for each graph, explain in a short, qualitative answer how I should change K based on the measurements. Problem 3: (10 points) 100.0 90.0 80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0.00 0.04 80'0 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 -Speed 09'0 Target 0.64 89'0 0.72 0.76 0.80 0.84 0.88 0.92 96'0 1.00 Here is another implementation I tried. Proportional control is not working as well as I would like. a) What type of additional term should I add to my control equation? b) Will I pass out from this acceleration? Why or why not?