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The flexible mode transitions, multiple power sources and system uncertainty lead to challenges for mode transition control of four-wheel-drive hybrid powertrain. Therefore, the purpose of this paper is to improve dynamic performance and fuel economy in mode transition process for four-wheel-drive hybrid electric vehicles (HEVs), overcoming the influence of system uncertainty.

First, operation modes and transitions are analyzed and then dynamic models during mode transition process are established. Second, a robust mode transition controller based on radial basis function neural network (RBFNN) is proposed. RBFNN is designed as an uncertainty estimator to approximate lumped model uncertainty due to modeling error. Based on this estimator, a sliding mode controller (SMC) is proposed in clutch slipping phase to achieve clutch speed synchronization, despite disturbance of engine torque error, engine resistant torque and clutch torque. Finally, simulations are carried out on MATLAB/Cruise co-platform.

Compared with routine control and SMC, the proposed robust controller can achieve better performance in clutch slipping time, engine torque error, vehicle jerk and slipping work either in nominal system or perturbed system.

The mode transition control of four-wheel-drive HEVs is investigated, and a robust controller based on RBFNN estimation is proposed. Compared results show that the proposed controller can improve dynamic performance and fuel economy effectively in spite of the existence of uncertainty.

The problem of parameter identification for biaxial piezoelectric stages is still a challenging task because of the existing hysteresis, dynamics and cross-axis coupling. This study aims to find an accurate and systematic approach to tackle this problem.

First, a dual-input and dual-output (DIDO) model with Duhem-type hysteresis is proposed to depict the dynamic behavior of the biaxial piezoelectric stage. Then, a systematic identification approach based on a modified differential evolution (DE) algorithm is proposed to identify the unknown parameters of the Duhem-type DIDO model for a biaxial piezostage. The randomness and parallelism of the modified DE algorithm guarantee its high efficiency.

The experimental results show that the characteristics of the biaxial piezoelectric stage can be identified with adequate accuracy based on the input–output data, and the peak-valley errors account for 2.8% of the full range in the X direction and 1.5% in the Y direction. The attained results validated the correctness and effectiveness of the presented identification method.

The classical DE algorithm has many adjustment parameters, which increases the inconvenience and difficulty of using in practice. The parameter identification of Duhem-type DIDO piezoelectric model is rarely studied in detail and its successful application based on DE algorithm on a biaxial piezostage is hitherto unexplored. To close this gap, this work proposed a modified DE-based systematic identification approach. It not only can identify this complicated model with more parameters, but also has little tuning parameters and thus is easy to use.