Question: (a) Determine the transfer functions of a controller Gc(s) and a plant Gp(s) that, connected in a unity feedback system, generate the following closed loop transfer function: GCL(s) = 2500/(s2 + 4s + 2500). Considering that the plant is a mechanical system, propose such a system by indicating (sketching) its components together with the input and output.
(b) What changes are needed for this system in the damping ratio p and the natural frequency ~n to obtain a reduction of the maximum overshoot by 30% and a reduction of the settling time by 20%? Sketch the closed-loop poles positions in the complex plane for the two systems.