## 1 Introduction  
Belt conveyor systems are critical equipment for the continuous transportation of bulk materials in many industrial fields [1, 2]. With the advantages of long distance, high speed, and large capacity, belt conveyor systems are used widely. A typical belt conveyor system consists of an endless belt for traction and bearing components driven by a high-power redundancy electric roller. Idlers, conveyor belts, and other inertial equipment require less power for smooth transportation than the start-up. In addition, the \"big horse pulls a small carriage\" phenomenon can occur during the process of conveying bulk materials due to the load changes on the belt and the mode of constant speed operation, as shown in Figure 1. More than 60% of the total energy consumption of bulk material handling and production is spent by the belt conveyor system [3]. If the belt conveyor system starts with no load or operates at nominal speed with unevenly distributed and intermittent bulk materials, a lot of energy is wasted. Therefore, it is necessary to improve the energy efficiency of belt conveyor systems. A belt conveyor system is a complex electromechanical coupled system. Its energy efficiency can be improved mainly at the equipment level and the operational level. At the equipment level, a variety of techniques of local motor controls have been developed to optimize the operational process of belt conveyor systems, for example, start-up process optimization [4], soft-start device addition [5; 6], less motor operation [7; 8], asynchronous motor Y-\(\Delta\) switching [9], and material flow automated control. In addition, a reduced-order model based on a balanced truncation method was proposed in [10], and a predictive controller model based on a reduced-order model performed well in controlling a belt conveyor system. To quantify the energy and cost savings, a motor sequencing controller was installed in [11] to reduce the energy use and to perform initial saving calculations. Generally, a belt conveyor is a continuous transport machine consists of a conveyor belt and a bearing mechanism. Energy efficiency improvements that occur only at the equipment level may inhibit the production capacity of a bulk terminal or limit certain scenarios since the conveyor belt is usually coupled closely with other mechanical equipment [12]. Operation is another aspect for energy efficiency of belt conveyors. Many researches have explored the effect of optimum control parameter prediction at the operational level. These studies were performed mostly using the global optimization by adjusting the belt speed according to the bulk material flow to reduce energy consumption [13; 14; 15; 16]. With the development of the variable frequency technique, the variable speed drive (VSD) strategy has the most potential for energy savings and can be categorized into three categories. Recent decades have seen the rapid development of intelligent controls [17; 18; 19], including fuzzy logic control [20; 21], and neural network control [22; 23; 24]. In terms of fuzzy logic control, [PERSON] [25] established an expert diagnosis system of belt conveyors to predict the potential fault information in the belt speed condition. [PERSON] and [PERSON] [26] developed a speed-regulating controller for open-pit mine remote control based on VSD technology. To optimize the speed control strategy, a fuzzy logic method was applied to classify the material feeding rates and the reference speed could be defuzzified based on the linear relationship between belt speed and conveyor capacity [27]. Nevertheless, it is not well adapted to the situation since the relationship is mainly by experience or trial and error. Based on the system optimum loading rate principle, [PERSON] et al. [28] deduced an optimal belt velocity by making the cross-section of the material flow reach the optimal loading rate of the belt conveyor. The remote control of belt conveyors for energy savings in open pits has been realized through direct torque control (DTC).