Suppose that we are asked to design a unity-feedback closed loop position controller for the plant (a spring- mass-damper system) below: G(s) = 1 10s² + 4s +3 where G(s) is the transfer function between the position output and the actuator force input. 1) Design a proportional controller that satisfies a steady-state error of 0.2 for a unity step reference input. Prove that your design works by plotting the resultant closed loop system's response (in time) to the mentioned reference input on MATLAB. Include your code and plot to your submission pdf file. 2) Use MATLAB to verify the steady-state step error of the closed loop system by checking the Bode Plot of the open-loop system. Also obtain the gain and phase margins of the unity feedback system from the same graph.