Closed-Loop System Identification Using Parallel PI Controller and Reference Prefiltering: White Noise Case

Some industrial processes cannot have their control loop opened for classic direct system identification, therefore closed-loop system identification is required, thus leading to issues with cross-correlated signals. Instrumental variables can be used to estimate noise-free control and output signals. Typically, a filter is designed to limit high-frequency noise during the identification process. However, an optimal filter can minimize noise without reducing valuable information from the input and output signals. When the output is tainted with white noise, the simplified refined instrumental variable method for closed-loop systems (CLSRIV) can be used. However, in the context of machining with Computer Numerical Control machine tools, the closed-loop of the spindle angular speed is more complex. Indeed, this loop includes a parallel proportional-integral controller, where a prefiltered reference is only applied to the integral component. The aim of this paper is to explore various closed-loop system identification methods in a white noise context by considering such specific prefiltering and parallel controller. A Monte-Carlo simulation is then proposed to analyze the statistical properties of the proposed methods.