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Find the control law u that linearized model with ℎ(𝑥) = 𝑥2?

1.2. Find a 4th degree approximate state feedback linearization of the following control system:

(10)

(a) 𝑥̇1 = cos(𝑥2)

𝑥̇2 = sin(𝑥1)

The mathematical model of the DC motor is given by following state space equation:

𝑥̇1 = 𝑥2

resistance and induction of the armature coil respectively, 𝑘𝑒 and 𝑘𝑚 are the speed and toque constants, 𝑏 is the viscous friction and 𝐽 is the moment of inertia Design a sliding mode control

to control the angular position ℎ1

b.transform the states and discuss the nature of the equilibrium after the transformation (6)

4.2. Consider the following system: (6)

QUESTION 5: (9) Consider the following system:

𝑥̇1 = 𝑥2
𝑥̇2 = −𝑥1 − 𝑎𝑥1 2𝑥2 + (𝑥2 + 1)𝑢
𝑦 = 𝑥1

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