The accurate estimation of the state of charge (SOC) for lithium-ion batteries’ performance prediction and durability evaluation is of paramount importance, which is significant to ensure reliability and stability for electric vehicles. The SOC estimation approaches based on big data collection and offline adjustment could result in imprecision for SOC estimation under various driving conditions at different temperatures. In the traditional GM(1,1), the initialization condition and the identifying parameter could not be changed as soon as they are confirmed. Aiming at the requirements of battery SOC estimation with non-linear characteristics of a dynamic battery system, the paper presents a method of battery state estimation based on Metabolic Even GM(1,1) to expand battery state data and introduce temperature factors in the estimation process to make SOC estimation more accurate. The latest information data used in the optimized rolling model is introduced through the data cycle updating. The experimental results show that the optimized MEGM(1,1) effectively considers the influence of initial data, and has higher accuracy than the traditional GM(1,1) model in the application of data expansion. Furthermore, it could effectively solve the problem of incomplete battery information and battery capacity fluctuation, and the dynamic performance is satisfactory to meet the requirements of fast convergence. The SOC estimation based on the presented strategy for power batteries at different temperatures could reach the goal of the overall error within 1% under CLTC conditions with well robustness and accuracy.

An improved rotor position observer based on sliding mode control was proposed to eliminate estimation error and harmonic ripples for PMSM sensorless control. A multi-proportional resonant filter was designed instead of a low-pass filter to filter out the specific harmonics of back EMF. The improved filter can solve the phase delay problem caused by a low-pass filter, eliminate the rotor angle compensator, simplify the system structure, and effectively suppress the system chattering. Then, a fractional normalized phase-locked loop was adopted to calculate the speed and rotor position, further eliminating the influence of noise. Compared with the traditional sliding mode control and the improved sliding mode control, the improved sliding mode observer can effectively suppress the back EMF chattering and reduce the speed estimation error. The correctness and effectiveness of the proposed improved sliding mode observer were verified through the simulation model and experimental platform of PMSM sensorless control.