**6. Conclusions**

An adaptive smoothing power following (ASPF) control strategy based on an optimal efficiency map for a series tracked HEB has been proposed by considering its operation characteristics in this research. The three problems of increased fuel consumption presented in previous control studies to be solved by this strategy, including frequent fluctuation of the engine working points, deviation of the genset working points from the pre-set target trajectory due to a lack of response, and interference of the hydraulic pump consumed torque, were analyzed in detail. The whole HEB system simulation model with a novel transient fuel consumption model based on BPNN was established. The HEB HIL platform was then developed to evaluate the real-time performance and the effect of the strategy in a practical application. The methodology of the proposed control strategy is based on fuzzy control theory, real-based control, and the optimization method. The method of effect verification is incorporated on the basis of the adoption of a validated simulation model and an HIL test platform.

The ASPF strategy was compared with two strategies: a power following strategy in a preliminarily practical application (PF1) and a typical power following strategy based on the engine minimum fuel consumption curve (PF2). The results show that (1) the ASPF strategy can significantly reduce the fluctuation and pre-set trajectory deviation of the engine and generator working points; (2) the EFSR can be improved by about 7.8% and 3.4% with the ASPF strategy compared with the PF1 and PF2 strategy; and (3) the ASPF strategy is able to perform well in a real controller. It can be concluded that the proposed strategy can be effective and efficient in practical online HEB applications. The results also show that the discovered problems indeed exist and the corresponding control strategies are valid in HEB.

Filed tests of the HEB with the ASPF strategy will be carried out to further advance the real application value in our future research. The limitation of the ASPF strategy in real applications relative to previous work is that it should obtain the pressure signal of the hydraulic pump as the input for calculation, so a pressure sensor should be placed in the outlet of the hydraulic pump. Nevertheless, the proposed strategy and the problems solved and focused on in this paper are significant references for other types of HECMs. Moreover, future study will also explore comparisons of the ASPF online strategy and the optimization algorithm-based theoretical offline strategy to evaluate its potential for improvement.

**Author Contributions:** Conceptualization, B.Z., S.G., and X.Z.; data curation, B.Z., Q.X., and L.T.; formal analysis, B.Z., Q.X., and L.T.; methodology, B.Z., S.G., and X.Z.; project administration, X.Z.; resources, X.Z.; supervision, S.G. and X.Z.; writing—original draft, B.Z.; writing—review and editing, B.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study is sponsored by the National Key R&D Program of China (2016YFD0700703). The authors would like to thank the anonymous reviewers for their reviews and comments.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Nomenclature**
