A mobile robot uses a vision system for measuring end effector position as shown in the figure below.

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A diagram of the robot dynamics along with a potential PI controller is given below.

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R is the desired end effector position. Y is the actual end effector position. The customer desires a stable system, overshoot to a step position input not to exceed $5\%,$ settling time less than $6$ seconds, minimize peak time for fast response, and zero velocity error $($zero error to a ramp input since velocity is the derivative of position$).$ Does the PI controller given above meet all customer requirements or not? If not, try a PID controller. $($lsim can be used for general purpose time response of a transfer function, given an input defined as a ramp$)$

Document your results by written discussion, equations, calculations, derivations, etc. Include block diagram algebra and any calculations. Include figures of your root locus plots, step response, and ramp response copied from matlab figures into your writeup. Explain your method and results with words. Include an Appendix with a copy of the matlab code that does all the work. create a pdf of your work and upload to this link.