Answer Happy

Exercise 2: Disc drive controller using root locus (6 marks) Recall the disc drive problem from Tutorials, where we demonstrated that the system can be written as 0,(s)+ 1000 e(s) Gc(s) s(s² + 110s + 1250) Figure 2: Disc Drive System Block Diagram We will now try to design a compensator with the requirements that i. Overshoot 15% ii. T, ≤ 120ms iii. eramp (0) ≤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 Gc= K. 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 G, to meet the transient requirements, i.e. i) and ii) above. c) Compute the steady-state error to a ramp, eramp (oo). Is it below your requirement in iii)? If not, design a Pl 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 Pl 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)