The spiral torsion spring-based mechanical elastic energy storage (MEES) device presented previously with inherent characteristic of simultaneous variations of inertia and torque is disadvantage to be actuated by conventional control method. This study proposes an improved non-linear backstepping control scheme based on combination of recursive least squares (RLS) and differential evolution (DE) optimisation to regulate permanent magnet synchronous motor (PMSM) at a very low speed and control MEES device effectively. For this presented control scheme, first, a single RLS method with forgetting factor is presented to simultaneously estimate the time-varying inertia and torque of MEES device. Second, on the basis of estimation results, an improved non-linear backstepping control algorithm considering parameter variations in derivation process is proposed to drive PMSM to operate at a very low speed. Finally, a self-adaptive parameter DE method is designed to optimise the several control parameters. The performance of the proposed methodology is verified through simulations and experiments.