<p>This paper investigates the problem of achieving accurate rotor speed estimation and robust sensorless vector control for induction motor drives, and proposes an integrated solution consisting of a tunable-convergence flux observer (TCFO) and a second-order phase-locked loop (PLL). Conventional voltage-model- or current-model-based estimators typically exhibit sensitivity to parameter uncertainties, degraded convergence characteristics, and reduced numerical reliability, which significantly affect flux-angle estimation and speed-observer stability. Based on the proposed TCFO, the convergence rate of the rotor flux estimation error can be explicitly adjusted through external design parameters, ensuring parameter-independent exponential convergence and improved robustness. The introduced second-order PLL directly extracts the synchronous electrical speed from the measured stator currents, enabling fast dynamic response and elimination of steady-state estimation error under diverse operating conditions. The combined observer-PLL scheme not only provides consistent and stable flux-angle reconstruction but also improves speed-estimation accuracy and disturbance tolerance. More importantly, the theoretically ensured tunable convergence and zero steady-state error enable reliable sensorless operation across varying load and parameter variations. A real experimental platform is established to validate the proposed approach, and the measured results confirm its fast convergence and high robustness, demonstrating the accuracy, effectiveness, and practical feasibility of the proposed sensorless control method.</p>