Antiskid braking systems present a challenging control problem, since brake/automotive system parameter variations can vary significantly (e.g., due to the brake-pad coefficient of friction changes or road slope variations) and environmental influences (e.g., due to adverse road conditions). The objective of the antiskid system is to regulate wheel slip to maximize the coefficient of friction between the tire and road for any given road surface [8]. As we expect, the braking coefficient of friction is greatest for dry asphalt, slightly reduced for wet asphalt, and greatly reduced for ice. One simplified model of the braking system is represented by a plant transfer function G(s) with a system with

where normally a = 1 and b - 4.
(a) Using a PID controller, design a very robust system where, for a step input, the overshoot is less than 4% and the settling time (with a 2% criterion) is 1 second or less. The steady-state error must be less than 1% for a step. We expect a and b to vary by ±50%.
(b) Design a system to yield the specifications of part
(a) Using an ITAE performance index. Predict the overshoot and settling time for this design.

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Y(s)