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When were going to implement the most simple controller I may think of? A p-type controller. P stands for proportional. Its simply going to multiply the error by some number to produce the input for the brake. To be more concrete, lets multiply the error with 100,000 m/s. When doing so, we can, of course, get huge positive and negative numbers that dont make any sense to control the brake so we have to clamp the output. Whenever the result of that multiplication is negative, we return 0 instead. Whenever the result of that multiplication is larger than 200 m/s, we return 200 m/s. Why could that possibly work? Assume that when were fitting this controlled value of 130 m/s into the brake, were actually ending up with the wheel slip of 0.1987. And the difference between the optimum value and the actual value is 0.00130. The controller is going to return the same number again, 130 m/s. So this foot constitutes an equilibrium. One thing to know about this naive version of the p-
