LMI-based Robust Design of Back-EMF Observer with PLL in the Loop

This paper presents a gain-scheduled robust back-EMF observer integrated into a quadrature phase-locked loop (QPLL) framework for rotor speed and position estimation in permanent-magnet synchronous motors (PMSMs). While conventional QPLL schemes often employ fixed-gain Luenberger observers tuned at a nominal speed for the back-EMF estimation, their performance deteriorates under varying operating conditions due to speed-dependent observer dynamics. The proposed method overcomes this limitation by scheduling the observer gains as an affine function of the electrical speed and synthesizing them via a Linear Parameter–Varying (LPV) formulation solved through Linear Matrix Inequality (LMI) optimization. By constraining the closed-loop poles within a predefined LMI region, the design ensures guaranteed stability, consistent dynamic performance across the speed range, and enforces that the damping ratio of the observer poles remains above a specified minimum value. Experimental results on a surface-mounted PMSM drive under load conditions confirm the effectiveness of the proposed approach.