Closed loop modelling method for non-linear system using Laguerre polynomials

This paper presents a modelling method for noisy response data of a closed loop with a PI controller. A general pre-£ltering procedure is not required in this method. A three-step procedure for estimating Laplace transfer function of a process is proposed. The true closed loop response is estimated from noisy response data, exploiting orthonormal properties of Laguerre functions. Then the closed loop transfer function model (called the Laguerre model) is represented by Laplace transforms of Laguerre polynomials approximated to a true response. Lastly, the process transfer function model is computed from the Laguerre model and the PI controller. PI parameters are given by gain constant, time constant and dead time of process approximated to £rst-order lag element plus dead-time system. Using this algorithm, the process model is estimated only by the settling time of response data. Simulation and experiment results show that the proposed method is effective for non-linear systems in modelling.