Identification of processes with direction-dependent dynamics

The identification of systems which have different dynamics when the output is increasing compared with those when the output is decreasing is considered. The dynamics in each direction will be assumed to be linear. It is shown that when such systems are perturbed by pseudorandom binary signals based on maximum length sequences, there are coherent patterns in the input-output crosscorrelation function, but there is no coherent pattern in either the gain response or the phase response in the frequency domain. The crosscorrelation terms are developed in detail for a process with first-order dynamics in the two directions, perturbed by a maximum length binary (MLB) signal and the results are confirmed by simulation. Similar theoretical expressions and simulation results are given for such a process perturbed by an inverse-repeat signal based on an MLB signal. The crosscorrelation function patterns obtained using an MLB signal are not present when other classes of pseudorandom binary signals are used. The linear dynamics for the process perturbed by an MLB signal and its corresponding inverse-repeat MLB signal are estimated, and found to agree more closely with the theoretical value when the latter type of signal is used. The theory cannot be readily extended to processes with direction-dependent dynamics of higher order, but simulation results presented for such second-order processes show that the departure from linearity can still be detected from the crosscorrelation function when an MLB perturbation signal is used