Figure shows a proposed scheme for controlling the position of a mechanical system such as a link in a robot arm. It uses two feedback loops-one for position and one for velocity-and a feed forward compensator transfer function s2.
a. Suppose that the estimates of the mass, damping, and stiffness are accurate so that me = m, ce = c, and kc = k. Derive the expressions for the transfer

Functions X(s)/X=(s) and X(s)/Fd(s). How well does this control scheme work? Obtain the expressions for the PID gains to achieve a damping ratio of ζ = 1 and a closed-loop time constant of specified value Td.
b. Discuss any practical limitations to this scheme.

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Control algorithm FA S) X(s) + X(s) Feedback gains Sensors