digital-brain/content/zettels/right_half_plane_zeros.md

+++ title = "Right Half Plane Zeros" author = ["Thomas Dehaeze"] draft = false +++

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Right Half Plane (RHP) Zeros are present in a broad range of systems.

• SISO RHP zeros:
  • \(G(z) = 0\). The real part of \(z\) is positive
• MIMO RHP zeros:
  • RHP zeros of the determinant of the transfer function matrix
  • For MIMO plants, the zero is associated with an output direction
• Consequences:
  • Non minimum phase
  • Usually, if looking at the step response, at first the response goes in the wrong direction
  • The frequency of the RHP zero should be outside the controller bandwidth. It therefore impose a fundamental limitation to the controller bandwidth. The reason is that inside the control bandwidth, the controller basically inverts the plant, and the inverse of a RHP zero is an unstable pole.