In deriving a model of an LTI dynamic system, the model of the system does have no RHP zeros, however, when inspecting the step response, it reveals a non-minimum phase system represented by a small negative (backward) time response. How to relate?
Hello Salman, typically, this is associated with zeros in the right half plane (RHP) of the system’s transfer function. However, it’s possible to observe non-minimum phase behavior in the time domain response even if the system doesn’t have RHP zeros. This could be due to the presence of time delays or certain types of nonlinearities in the system.
A time delay in the system can cause a phase lag, which might appear as a non-minimum phase behavior in the time domain. This is because a time delay can cause the system’s output to initially move in the opposite direction before moving towards the final steady-state value.
Nonlinearities can also cause similar effects. For instance, if the system has a backlash or hysteresis, it might show a non-minimum phase behavior in the time domain.
So, while your system might not have RHP zeros, the observed non-minimum phase behavior in the step response could be due to time delays or nonlinearities in the system. You might need to consider these factors when modeling and controlling your system3.
These links could help more.
https://ealizadeh.com/blog/non-minimum-phase-systems/
https://pureportal.strath.ac.uk/files/112787388/Wu_etal_IEEE_TOSE_2020_Impact_of_non_minimum_phase_zeros_on_the_weak_grid.pdf
https://pressbooks.library.torontomu.ca/controlsystems/chapter/8-6the-effect-of-a-non-minimum-phase-zero-on-the-2nd-order-system-response/
For robust systems, this could help too:
Book Applied Mathematics: Theories, Methods and Practices, From s...
Chap 26, pages 383-393, also pages: 375-381
When modeling a non-minimum-phase system, it is necessary to recognize and resolve the special difficulties presented by systems with right half-plane (RHP) zeros or zeros beyond the unit circle. Such systems complicate control attempts by initially responding in the opposite direction from the desired ultimate direction. We first determine the system dynamics, formulate the transfer function, and explicitly incorporate non-minimum phase zeros. We can express the transfer function for continuous-time systems as G(s) = N(s)/D(s), and for discrete-time systems as G(z) = N(z)/D(z). The transfer function also yields the state-space representation necessary for comprehensive analysis. We then examine the system's reaction to varied inputs using simulation programs like MATLAB or Python, focusing on the step response to identify non-minimum phase behavior. For controlling complex systems, efficient controller design approaches, including feedforward control, robust control, and feedback linearization, are essential. This strategy ensures a globally accepted approach to mathematical modeling and optimization.
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