Data-Driven Near-Optimal Reduced Tracking Control of SPSs With Application to PMSM

This brief focuses on the data-driven near-optimal reduced trackingcontrol problem of linear time-invariant (LTI) singularly perturbed systems (SPSs) from noisy data. Based on singular perturbation theory (SPT), the reduced subsystem of the SPSs is obtained, further, an augmented error system is constructed and an optimal trackingcontrol (OTC) problem is formulated. Then, the integral version of the continuous-time augmented error system is constructed to avoid the error-prone problem of derivative calculation. Next, the closed-loop augmented error system is parameterized by the system I/O data, and the data-based semi-definite program (SDP) is proposed for the OTC problem. In addition, considering that the I/O data of the virtual reduced system are actually unmeasurable, the virtual reduced system is reconstructed by the I/O data of the original system, and the system performance is analyzed. Finally, the experiment of speed tracking control of permanent magnet synchronous motor (PMSM) verifies the effectiveness of the proposed data-driven control scheme.