Order determination using the squared magnitude response for a linear system with a time delay

In this paper, an identification method is proposed to determine the order of a linear system with a time delay. The method is based on the estimation of the squared magnitude response (SMR) of the system. It is shown in the paper that the order information about a linear system is retained completely by its SMR. Due to the property that the time delay has no contribution to the SMR with the new technique, the interaction between the order error and delay error can be eliminated. Both simulations and experiments are performed to verify the new technique, which show that the method can be used to determine system order without taking the delay into account, and is superior to the conventional techniques for systems with no a priori knowledge about the order and the delay