A magnetically suspended steel ball can be described by the linear equation

The state variables are x1 = position and x2 = velocity, and both are measurable. Select a feedback so that the system is critically damped and the settling time (with a 2% criterion) is 4 seconds. Choose the feedback in the form
u = - kiX] - k2x2 + r
where r is the reference input and the gains k1and k2 are to be determined.

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