# Data-Driven Model-Free Adaptive Sliding Mode Control Based on FFDL for Electric Multiple Units
###### Abstract  
The electric multiple units (EMUs) have become a very convenient and powerful means of transportation in our daily life. Safe and punctual trajectory tracking control is the key to improve the performance of the EMUs system, but it is difficult to realize due to the influence of environmental uncertainty, coupling and nonlinearity. In this paper, a model-free adaptive sliding mode control (MFASMC) method is proposed for the EMUs. This method can solve the dependence of the model-based control method on the train model and eliminate the influence of external disturbances on the robust performance of the system. In this method, the running process of the EMUs is equivalent to a full format dynamic linearization (FFDL) data model, and a model-free adaptive controller (MFAC) is designed based on the data model. Then, to reduce the influence of measurement disturbance and improve the robustness of the system, a discrete sliding mode control (SMC) algorithm is introduced. Furthermore, to prevent the control input from being too large, the parameter estimation error is introduced as an additional correction term of the algorithm. In the end, the simulation experiment is carried out with CRH380A EMUs as the object. Compared with the traditional MFAC and the traditional SMC, the speed tracking effect of each power unit of the MFASMC algorithm is more effective, the change of control force is stable, the acceleration meets the requirements of driving, and has a strong inhibitory effect on external disturbances. electric multiple units; model-free adaptive control; discrete sliding mode control; full format dynamic linearization; robustness +
Footnote †: journal: Applied Sciences  
the multi-input-multi-output (MIMO) system is more in line with the actual situation of the train. In Reference [4], the dynamic process of train operation is analyzed, and a nonlinear multi-particle model of the train is established considering the carriage type and operation state, then an adaptive robust nonlinear predictive controller is designed for it; in Reference [5], a model parameter estimation method based on adaptive update law is introduced to avoid wheel idling or skidding during train operation, and a dynamic surface-based terminal SMC strategy is proposed; Reference [6] established a coupling model of high-speed EMUs and designed a distributed neural network SMC strategy; similarly, References [7;8] established the prediction controllers based on the ANFIS model and distributed model for trains, respectively. Although the subspace identification methods used in References [6; 7; 8] require less model structure information, they are still essentially model-based control methods. The above studies often need to obtain the system model structure and parameters when designing control algorithms and stability analysis, or need to estimate the nonlinear part of the system. If the system model information is unknown or the model structure is complex, it is difficult to apply the above methods. Firstly, for a multi-power unit EMUs system, its accurate dynamic model is difficult to construct, but its input and output data can be obtained easily. Secondly, for the existing multi-particle train model, decoupling must be considered when designing the controller, which undoubtedly increases the difficulty of design. Therefore, this paper adopts the data-driven algorithm to realize the operation control of the EMUs. MFAC is a typical data-driven control method proposed by Professor [PERSON] in his doctoral dissertation [9]. The general idea of this method is that, based on satisfying certain assumptions, an equivalent dynamic linearized model is established at each sampling point of the discrete system by introducing the concept of pseudo partial derivatives, and then the model is used for controller design, structural adaptive law design, stability analysis, etc.