Automatic transfer function synthesis from a Bode plot

A novel algorithm that automatically identifies continuous-time transfer functions from Bode plots is presented. The identification is carried out in two stages: first, the model order and `good´ guesses of the poles and zeros are obtained; and second estimates are refined by means of a modified Newton-Raphson algorithm. Because poles and zeros estimation only requires the magnitude curve, transport delays, if any, can be easily estimated by means of additional information supplied by the phase curve. The major and novel contribution of the proposed method resides in its first stage, where qualitative notions currently `hidden´ in the intuition of the designer are explicitly represented, yielding a simple optimization procedure that is not impaired by the presence of saddle points or local minima, and that converges very fast to the vicinity of the true solution. A detailed example is also provided to illustrate the value of the method