A magnetically suspended steel ball can be described by the linear equation as shown in the attachment.
The state variables are x1 = position, and x2 = velocity, and both are measurable. Select a feedback format so that the system is critically damped and the settling time (2% criterion) is 2 seconds. Solve for k1 and k2.
Response finds k1 and k2 by finding the characteristic polynomial of a matrix (constructed from given data) and equating that to the desired characteristic polynomial.