Time-Varying FOPDT system identification with unknown disturbance input

The Time-Varying First Order Plus Dead Time (TV-FOPDT) model is an extension of the conventional FOPDT by allowing the system parameters, which are primarily defined on the transfer function description, i.e., the DC-gain, time constant and time delay, to be time dependent. The TV-FOPDT identification problem turns to estimate these time-varying parameters based on measured control input and system output. This work considers a TV-FOPDT identification problem in the presence of an unknown disturbance input. By regarding the unknown input as one extra system parameter, the considered identification problem is formulated as a Stochastic Mixed Integral Programming (SMIP) problem after discretizing the original problem. The sliding window technique with forgetting factor is employed to cope with time resolution issue, and the Least Mean Square (LMS) method is used to obtain the optimal solution of each individual optimization problem based on different time delay assumptions. The proposed method is firstly tested through a number of numerical examples, and then it is applied to estimate a TV-FOPDT model of the superheat dynamic of a supermarket refrigeration system.