New formulas for approximation of multi-inertial systems, by the FOLPD models, based on two-point identification

Jędrzej Byrski and Witold Byrski


Two-point identification, first order system with delay, step response identification, model simplification


In this paper new simple formulas for identification of the time constant T and time delay t of the First Order Lag Plus time Delay model (FOLPD) will be presented. FOLPD model is very useful e.g. for PID controller self-tuning. Two cases will be considered. In the first case, the identified FOLPD model will approximate the dynamics of any unknown multi-inertial system. In the second case, the FOLPD model will be used for approximation of the second order inertial system with known time constants T1, T2. In both cases, the identification of desired FOLPD model will result from the best fitting of the system and FOLPD model step responses. This will be achieved by comparing of these characteristics in two specially selected points. Presented formulas for FOLPD parameters, in the first case, depend on these two selected points. In the second case FOLPD parameters will depend only on the known values of the second order system’s time constants T1 and T2.

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