Fitting Discrete-Time Models to Frequency Responses for Systems With Transport Delay

Fitting discrete-time models to frequency-response functions without addressing existing transport delay can yield higher-order models including additional non-physical nonminimum-phase (NMP) zeros beyond those that may appear as a result of sampling. These NMP zeros can be attributed to a discrete-time representation of a Pade´ approximation to account for the transport delay [1, 2]. Here, we explore this idea in greater detail and this discussion motivates the main contribution of this paper, the presentation of a procedure for fitting a discrete-time model to experimentally measured frequency response data. The appearance of NMP zeros in a system model can complicate controller design and limits the desired closed-loop performance. This discrete-time model-fitting procedure presents a technique that will help yield a model that reflects the measured frequency-response functions accurately, while minimizing the presence of non-physical NMP zeros. The key benefit being that, with respect to previous model fits, it may be possible to eliminate all NMP zeros in the discrete-time model. In the case of model-inverse-based control design, this will allow the stable inversion of the model without the use of approximation methods to account for NMP zeros.