Recall the disc drive problem from Tutorials, where we demonstrated that the system can be written as Or(s) + 1000 (s) Gc(s) s(s+110s + 1250) Figure 2: Disc Drive System Block Diagram We will now try to design a compensator with the requirements that i. ii. iii. Overshoot 20% Ts 110ms Cramp () = 0 Do the following (you may use MATLAB at your leisure, but be sure to explain your logic for your design choices): a) Use MATLAB to draw the root locus when Gc = Kc. Augment your root locus to include the boundaries of the region where the dominant closed-loop poles must be to satisfy the transient requirements. Comment on your ability to achieve these requirements with a gain-only controller. b) Design a PD controller for Go to meet the transient requirements, i.e. i) and ii) above. c) Compute the steady-state error to a ramp, Cramp (). Is it below your requirement in iii)? If not, design a PI compensator to satisfy iii) above. d) Use MATLAB to compute the resulting closed-loop poles and discuss second order dominance. e) Simulate the step and ramp response in MATLAB and verify that you have achieve the design objectives. If not, discuss you re-design strategy and re-design your PD and/or PI controller to achieve the objectives. Some Hints: When assessing second order dominance of the closed-loop system, be sure to cancel poles and zeros (i.e. use minreal)