# An Improved Data-Driven Integral Sliding-Mode Control and Its Automation Application  
[PERSON]  
1 School of Mechanical and Electrical Engineering, Quzhou College of Technology, Quzhou 324000, China; [EMAIL_ADDRESS] (F.X. ); [EMAIL_ADDRESS] (J.X.) [PERSON]  
2 College of Communication Engineering, Jilin University, Changchun 130022, China 2  
an accurate model of the system. Therefore, model-based control methods have inherent shortcomings [3; 4]. Data-driven control methods are widely used in boiler water-level-control systems because they do not rely on a precise mathematical model and can only rely on system input and output data to achieve system control. Among them, the most typical data-driven control method is PID. Ref. [5] proposed an expert PID method that can still achieve stable control even when the boiler water level is greatly disturbed. Ref. [6] designed an incomplete differential PID to achieve precise control of the boiler-drum water level, thereby ensuring the energy-saving operation of the system. Ref. [7] considers the characteristics of nonlinearity, multivariability and large time delays in the CFB boiler system and uses the fuzzy PID method to control the system, effectively improving the operational efficiency of the system. Ref. [8] combines fuzzy theory to design a fuzzy-PID hybrid control method, which achieves intelligent control of the water level of the thermal boiler drum and effectively avoids the influence of external disturbances on water-level control. Ref. [9] proposes a control strategy that combines the DMC prediction algorithm with feedforward cascade control. DMC-PID feedforward cascade control is used to achieve stable control of the boiler water level and improve its dynamic and static characteristics. However, when using PID to realize the automated operation of the system, due to the fixed parameters of the controller, there are shortcomings that cannot realize the adaptive adjustment. Although the most widely used PID control does not require mathematical modeling, it is more suitable for linear systems and is not suitable for nonlinear, time-varying and strongly coupled systems. In addition, it does not have the ability to learn and adapt to changes in the system structure, so the control performance is poor, slow and prone to overshooting [10; 11]. At the end of the 20 th century, professor [PERSON] proposed a model-free adaptive-control (MFAC) method. This method uses a data model equivalent to the controlled system to design the controller and introduces the concept of pseudopartial derivatives to realize the adaptive adjustment of the controller parameters, thus realizing the adaptive control of the controlled system [12]. Due to the excellent control performance of MFAC, this method has been widely used in many industrial fields. [PERSON]. [13] applied MFAC theory to the heading control system of unmanned surface vessels, achieving precise heading control of the system under model disturbances and system delays. [PERSON]. [14] designed a model-free adaptive fault-tolerant control method that considers issues such as subway speed and traction force constraints, as well as actuator failures, achieving precise control of the subway train. [PERSON]. [15] utilized the MFAC method to realize automobile autopilot, which improved the accuracy, safety and comfort of automobile control. [PERSON]. [16] introduced the MFAC into the self-resistant controller and designed a new type of self-resistant controller to realize the stable heading control of a ship. Ref. [17] designed a new data-driven model-free adaptive robust control law, which was applied the control algorithm to unmanned helicopters and achieved good attitude-control results. Ref. [18] utilized the principle of MFAC to achieve precise control and multiobjective stable control of a continuous robotic arm. In addition, MFAC has been widely used in rehabilitation robots [19], coal-mine belt conveyors [20], linear motors [21], chemical production [22] and other fields.