Question

Recall the disc drive problem from Tutorials, where we demonstrated that the system can be written as e(s)+ 1000 Ge(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 1096 ii. Ts S 100ms ii. eramp() s 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 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 Ge to meet the transient requirements, i.e. i and above c) Compute the steady-state error to a ramp, eramp (0). Is it below your requirement in ili)? If not, design a Pl compensator to satisfy ii) 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)

Answer 1

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