I have two questions regarding solving the problem (http://
i50.tinypic.com/33usrqs.png) and comparing with the textbook's
solution manual's approach (http://i45.tinypic.com/wtxahe.png
)

1. I have noticed that the PID controller shown in equation 6.6.16 is used to cancel out the plant's poles. Do you happen to know why the controller is used to cancel the plant's poles?

2. For second order systems, I recall the characteristic equation is (http://latex.codecogs.com/gif.latex?s^2%20+%202 \zeta\omega_%20+ %20\omega_^2=%200). However, as the problem provides the specification that the bandwidth is 2 rad/s, I was under the impression of making the middle term in that equation to be 2. However, the solutions made it to be 2.08, and the third term to be 2.56. Do you think these two terms can be anything that would work in terms of making the controller?

Thanks in advance for your comments.

1. I have noticed that the PID controller shown in equation 6.6.16 is used to cancel out the plant's poles. Do you happen to know why the controller is used to cancel the plant's poles?

2. For second order systems, I recall the characteristic equation is (http://latex.codecogs.com/gif.latex?s^2%20+%202 \zeta\omega_%20+ %20\omega_^2=%200). However, as the problem provides the specification that the bandwidth is 2 rad/s, I was under the impression of making the middle term in that equation to be 2. However, the solutions made it to be 2.08, and the third term to be 2.56. Do you think these two terms can be anything that would work in terms of making the controller?

Thanks in advance for your comments.