Closed Loop System Identification Based on Data Correlation

Abstract

A closedloop system identification method is developed to estimate the parameters of a single input single output (SISO) linear time invariant system (LTI) operating within a feedback loop. The method uses the reference command in addition to the input–output data and establishes a correlation framework to structure the system. The correlationbased method is capable of delivering consistent estimates provided that the specific conditions on the signals are met. The method parallels the instrumental variables four step algorithm (IV4) and is comprised of three steps. First a model is estimated using cross correlation calculations between the reference input signal and the control and measured output signals. In the second step, a prefilter is identified to reduce estimation bias. In the final step, the prefilter, the instrumental variables and the measured signals are employed to estimate the final model. A consistency proof is provided for the proposed estimation process. The method is demonstrated on two examples. The first uses data collected from a diesel engine operation, and an openloop model relating fueling to engine speed is sought. The identification process is complicated by the presence of nonmeasurable external torque disturbances and stochastic sensor noise. The second example uses data obtained from a time domain simulation of a closedloop system where high levels of nonmeasured noise and disturbances were considered and a comparison with existing methods is made.