Suppose that we are asked to design a unity-feedback closed loop position controller for the plant (a spring- mass-damper system) below: 1 G(s) = 10s² + 6s+ 3 where G(s) is the transfer function between the position output and the actuator force input. Later, we noticed that the actuator in the system (the component that generates the input when commanded by the controller) has a delay! The actuator itself has a first-order dynamics, making the plant as shown below: G(s) 0.5 1 (s+ 0.5) (10s2 + 6s+ 3) 3) Use MATLAB to check whether the previously designed proportional controller would work on this new system, using Bode Plot. Please describe the effects of having an additional first-order dynamics in the plant on the phase-gain margins. 4) Update the controller so that the closed-loop system would satisfy the steady-state error requirement above. (Hint: combine a lag, lead, or another type of controller with the proportional controller we had originally designed.) Show that your design works as desired by plotting its response in time, using MATLAB.