Consider the nonlinear system:
x˙ 1 = x2
x˙ 2 = cos(x3) + x1 + u
x˙ 3 = x4
x˙ 4 = x1 + u
y = x1
Find the relative degree of the system and convert it to the normal form. Design a feedback
linearization control law for this system. Is the system stable? Plot relevant phase portraits/state
trajectories to justify your answer.
2. Design a sliding-mode controller for the system given below, to track xd(t) = sin(t)
x¨ + a(t) ˙x
2
cos(5x) = b(t)u
Where 1 ≤ a(t) ≤ 2 and 4 ≤ b(t) ≤ 8. Introduce a boundary layer to remove chattering. Plot s(t),
x˙(t) vs x(t) and u(t).
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