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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
𝑥̇2 = − 𝑏 |
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𝑥̇3 = − |
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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