4. (25 points) Consider the following system with unit feedback. r(s) e(s) Y(s) K(s) G(s) Figure 3: Unit feedback system

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4 25 Points Consider The Following System With Unit Feedback R S E S Y S K S G S Figure 3 Unit Feedback System 1 (29.86 KiB) Viewed 19 times

4. (25 points) Consider the following system with unit feedback. r(s) e(s) Y(s) K(s) G(s) Figure 3: Unit feedback system Suppose the system transfer function is G(8) s(82 +48 + 8) a Now, we want to design a PID controller satisfying the following form: 8 + ZPI K(s) = k(8 + zpp) where k, zpp and zp, are unknown real numbers. Please design the controller parameters such that the closed-loop poles of the system are lo- cated at 8 = -44%, and the system has zero steady-state error when tracking ramp input. (Intermediate steps are required.)