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Comments) For transient-response specifications, it is desirable that the transient response be sufficiently fast and be sufficiently damped. Thus, for a desirable transient response of a second-order system, the damping ratio must be between 0.4 and 0.8. Small values of zeta (zeta < 0.4) yield excessive overshoot in the transient response, and a system with a large value of zeta (zeta > 0.8) responds sluggishly. Problem 1-b) You are supposed to use ‘Final Value Theorem’ for steady-state values. Since all poles located in the left-half plane, the system is stable. Therefore, you can use FVT. Otherwise you can not use this theorem. In addition to this, you can double-check steady-state values from step-response plots. Problem 1-d-iv) For a second-order system the rise time (tr) from y=0.1 to 0.9 is approximately wn*tr=1.8 for zeta=0.5. Thus we can use tr=1.8/wn. On the other hand, you may use the linear approximation, tr=(2.16*zeta+0.6)/wn which is relatively accurate for 0.3<zeta<0.8. Keep in mind that it is only accurate for a second-order system with no zeros; for all other systems it is a
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