System Identification Under Relay and PI Control

TLDR: On-line identification scheme is proposed where the system characteristics is extracted with respect to proportional-integral (PI) controller dynamics in terms of sustained oscillatory responses broadly known as limit cycle at the system output.

Abstract: This brief presents a symmetrical relay-based identification scheme for a class of linear time-invariant systems with time delay. During off-line identification, the adverse effect of static load disturbance may lead to erroneous system model parameters. Therefore, on-line identification scheme is proposed where the system characteristics is extracted with respect to proportional-integral (PI) controller dynamics in terms of sustained oscillatory responses broadly known as limit cycle at the system output. Utilizing the relay settings (amplitude and hysteresis width), controller parameters and limit cycle information, an explicit set of mathematical expressions for on-line parameter estimation of system dynamics in terms of a stable first order plus time delay (FOPTD) model is deduced from frequency domain and state space analyses. As compared to recent relay-based identification methods, the proposed set of explicit expressions does not require any prior guess of initial values of the system model parameters for the simultaneous solution of a nonlinear set of mathematical equations. Simulation of a benchmark example from literature and experimental results from the coupled tanks system are included for validation of the proposed identification algorithms using the deduced set of mathematical expressions.