Question: (5) A magnetically suspended ball can be modeled by the following nonlinear dynamics: y = 1- u? y2 where y denotes the vertical position of

(5) A magnetically suspended ball can be modeled by the following

(5) A magnetically suspended ball can be modeled by the following nonlinear dynamics: y = 1- u? y2 where y denotes the vertical position of the ball and u an input current. All units have been appropriately normalized. 1 T 22 (i) Compute a nonlinear state-space model for the system with state variable x = and output y. (ii) What equilibrium control input Ueq is needed to suspend the ball fixed at Yeq = 1? Is there more than one control? (iii) Linearize the system around (all) the equilibrium point(s) (xeq, weq) computed above. (iv) Is(are) the linearized system(s) controllable? Observable? (5) A magnetically suspended ball can be modeled by the following nonlinear dynamics: y = 1- u? y2 where y denotes the vertical position of the ball and u an input current. All units have been appropriately normalized. 1 T 22 (i) Compute a nonlinear state-space model for the system with state variable x = and output y. (ii) What equilibrium control input Ueq is needed to suspend the ball fixed at Yeq = 1? Is there more than one control? (iii) Linearize the system around (all) the equilibrium point(s) (xeq, weq) computed above. (iv) Is(are) the linearized system(s) controllable? Observable

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