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## ← 05ps-04 Hydraulic Braking Solution

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Showing Revision 2 created 10/24/2012 by Amara Bot.

1. The first thing we did in order to model the zigzagging oscillation of the brake pressure
2. was to create this perimeter called brake change.
3. Just for simplicity,we set the initial value of brake change to zero.
4. If you move down to the far loop, you can see that brake change
5. alternates between having a value of 1 and -1.
6. If the wheel slip falls below the constant low slip, then the brake change value switches to 1.
7. And as soon as the wheel slip passes high slip, they change, switches signs, and becomes -1.
8. An expression for b after the next times step
9. We've ensure that b will not drop below zero
10. by setting zero as the minimum value that it can take on.
11. Then using this min method right here, we are assuring
12. that its magnitude will not exceed max brake.
13. However, anywhere in between zero and max brake, it will take on this value right here.
14. We take the value of b at the previous step and add it to the step size times brake change,
15. which is either you're going to make this a positive or negative quantity
16. and multiply that by the hydraulics speed.
17. Remember that hydraulic speed is just the rate of change of the strength of the brake.
18. To visualize what we've done, let's look at our plots.
19. This bottom graph shows how the brake strength changes with time.
20. Just as we hoped, we see that our line either has a negative slope or a positive slope,
21. but of the same magnitude just alternating signs.
22. These changes in sign correspond to the flip in the sign of brake change.
23. The crest of the brake strength curve are points at which brake change
24. switches from being positive to being negative.
25. We see that the brake change switches to -1 if the wheel slip exceeds the value of high slip
26. and if you look at the corresponding values in wheel slip, you see that these points of transition
27. in brake strength corresponds to the highest values in wheel slip
28. and the lowest value in wheel slip which we can see signals a switch in brake change to +1
29. correspond to a change in the sign of the slope of brake strength from negative to positive.
30. Zooming out and looking at these plots as a whole, they say that the wheel slip is controlled very nicely
31. but the value of b does oscillate very strongly
32. and this would look pretty stressful for the brake mechanism.
33. What we would want instead would be a value of b that will be close to the correct value.
34. One option for this would be to limit the range of b by holding the pressure constant
35. or keeping the value of b constant then b gets either too large or too small.
36. Let's try that out by making a small change in our code for just a second
37. I'm going to comment out this line and instead infinite this line.
38. Our original line of code kept the value of b between 0 and max brake.
39. We are now going to replace those respectively with 100 and 150
40. so b is going to be within a much smaller range of values.
41. Now, let's see what happens with this change.
42. The first thing that I noticed when I looked at this is that as you would expect
43. the graph of the brake strength, it doesn't look like it will
44. put much strain and stress in the braking system as our previous system did.
45. The wheel slip also still stays within a very nice range and their car does come to a complete stop.
46. Despite the improvement that this would allow, it will require some additional knowledge
47. that may be difficult to find.
48. We have to be able to project a reasonable range for b depending on current road conditions
49. and we also have to measure the hydraulic pressure of the brake.
50. There are cheaper options that we could consider such as looking at the deceleration of the wheel
51. to decide when to stop increasing or decreasing the pressure and to hold the pressure constant instead.
52. I hoped you enjoyed this brief introduction into the intricacies of actuators with the speed dynamics.
53. Unfortunately, this is the end of our work for now with cars and braking systems.
54. We're moving on to something very exciting, wild fires.
55. I know that playing with fire is risky, but luckily we are doing all that on computers
56. so we don't really have much to worry about.
57. Get ready for some very interesting problems and great job on this unit.