System Response with Zeros Now that we have seen the effect of an additional pole, let us add a zero to the second-order system. In this section, we add a real-axis zero to a two-pole system. The zero will be added first in the left half-plane and then in the right half-plane and its effects noted and analysed. 8 System Response with Zeros Adding a zero in the left half-plane: Starting with a two-pole system with poles at −1 ± 𝑗2.828, we consecutively add zeros at −3, −5, and −10. The closer the zero is to the dominant poles, the greater its effect on the transient response. As the zero moves away from the dominant poles, the response approaches that of the twopole system. 9 System Response with Zeros 10 System Response with Zeros Adding a zero in the right half-plane: An interesting phenomenon occurs if a zero is placed at the right half-plane. 11 System Response with Zeros Notice that the response begins to turn toward the negative direction even though the final value is positive. A system that exhibits this phenomenon is known as a nonminimum-phase system. If a motorcycle or airplane was a nonminimum-phase system, it would initially veer left when commanded to steer right. 12

System Response with Zeros

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