Exercise 9*: Lead-Lag design using Root Locus Recall the disc drive problem from Tutorials, where we demonstrated that the open-loop system can be written as (s)o Gc(s) Figure 8: Disc Drive System Block Diagram We will now try to design a lead-lag compensator with the requirements that • Overshoot < 10 • Ts < 75ms • era„,p(a)) 5 0.001 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 Ge = b) Use MATLAB to draw the region where the dominant dosed-loop poles must be to satisfy the transient requirements. Comment on your ability to achieve these requirements with a gain-only controller. c) Design a lead compensator(s) to meet the transient requirements (i.e. overshoot and settling time) d) Design a lag compensator to achieve the steady-state tracking requirement e) Use MATLAB to compute the resulting closed-loop poles and discuss second order dominance. Some Hints: • You may need to place more than one lead compensator for part c) • When assessing second order dominance of the dosed-loop system, be sure to cancel poles and zeros (i.e. use minrea:.)