This paper presents improved empirical representations of a general class of open-loop unstable systems using closed-loop system identification. A multi-axis magnetic-levitation (maglev) nanopositioning system with an extended translational travel range is used as a test bed to verify the closed-loop system-identification method proposed in this paper. A closed-loop identification technique employing the Box-Jenkins (BJ) method and a known controller structure is developed for model identification and validation. Direct and coupling transfer functions (TFs) are then derived from the experimental input-output time sequences and the knowledge of controller dynamics. A persistently excited signal with a frequency range of [0, 2500] Hz is used as a reference input. An order-reduction algorithm is applied to obtain TFs with predefined orders, which give a close match in the frequency range of interest without missing any significant plant dynamics. The entire analysis is performed in the discrete-time domain in order to avoid any errors due to continuous-to-discrete-time conversion and vice versa. Continuous-time TFs are used only for order-reduction and performance analysis of the identified plant TFs. Experimental results in the time as well as frequency domains verified the accuracy of the plant TFs and demonstrated the effectiveness of the closed-loop identification and order-reduction methods.
