Optimal FOPDT model fitting to an nth-order all pole process: Impulse response approach

In this paper, an optimal method is proposed to approximate the nth-order all pole systems by the widely used first-order plus dead-time (FOPDT) model. To establish this method, the impulse response approach is used. That is the squared of the 2-norm of the error signal between the impulse responses of the system and the model is chosen as an index function. By minimizing this index function three nonlinear equation are derived in terms of the parameters of FOPDT model. Then these equations are analyzed and proven that these equations always have unique solution for the FOPDT model parameters. Finally by solving the above mentioned nonlinear equations the optimal values of FOPDT model parameters are obtained. Numerical example is included to show the advantage of the presented work.