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Zeros and Step Response αlaracteristics in LTI SISO Systems

선형시불변 단일입출력 시스템의 영점과 계단응답 특성

  • 이상용 (인하대학교 전기공학과)
  • Published : 2009.08.01

Abstract

This paper deals with the relationship between zeros and step response of the second and third order LTI(Linear Time Invariant) SISO(Single-Input and Single-Output) systems. As well known, if a system has a single unstable zero, it shows the step response with undershoot and, on the other hand, a stable zero slower than the dominant pole causes the system to have the step response with overshoot. Generally, in the case of a system with two unstable real zeros, it is known to have B type undershoot[7]. But there are many complex cases of the step response extrema corresponding to zeros location in third order systems. This paper investigates the whole cases depending on DC gains of the additive equivalence systems and they are to be classified by the region of zeros which are related to the shape of the step response. Moreover, monotone nondecreasing conditions are proposed in the case of complex conjugate zeros as well as the case of two stable zeros.

References

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