First Order Plus Frequency Dependent Delay Modeling: New Perspective or Mathematical Curiosity?

The first-order-plus-dead-time model (FOPDT) is a popular simplified representation of higher order dynamics. However, a well known drawback is the rapid decrease of the frequency response accuracy with increasing process order. This especially applies to the higher frequency range. Literature offers solutions by extending this three parameter model with more parameters. Here, a fractional dead time is proposed. As such, a Frequency-Dependent Delay (FDD) is introduced, which offers a better approximation. As the fractional-order term introduces nonlinear coupling between the phase and the magnitude of the process, the fitting of the function becomes an iterative process, so a constrained multi-objective optimization is needed. This novel model, first-order-plus-frequency-dependent-delay or FOPFDD is fitted on a real electrical ladder network of resistors and capacitors of four and eight parts. The classic model, which is clearly a special case of the new model, is outperformed in the entire bandwidth.