RHPNullstellen

RHPNullstellen, often called right-half-plane zeros, are zeros of a linear time-invariant system’s transfer function that lie in the right half of the complex s-plane (Re(s) > 0). In discrete-time, the analogous concept are zeros outside the unit circle. They indicate nonminimum-phase behavior of the system.

The presence of RHP zeros has important consequences for time-domain and frequency-domain performance. A system with RHP zeros generally exhibits nonminimum-phase response: the initial reaction to a step input can be opposite to the final value, known as an inverse or noncausal-appearing response. This creates practical limits on how fast and how aggressively a controller can move the closed-loop response, because attempting to speed up the response often worsens overshoot and can destabilize the loop. In frequency terms, RHP zeros contribute phase lag and reduce achievable phase margin, complicating controller design and robustness.

Identification and examples: a transfer function G(s) = (s − a) / (s + b) with a > 0 has a right-half-plane zero at s = a. In discrete time, a zero outside the unit circle plays a similar role. Real-world sources of RHP zeros include nonminimum-phase dynamics, transport delays, or internal dynamics that cannot be freely canceled by a stable controller.

Handling RHP zeros in design typically involves robust control approaches, careful modeling to avoid reliance on pole-zero cancellation, and performance specifications that acknowledge the fundamental trade-offs imposed by nonminimum-phase behavior.