# An Improved Data-Driven Integral Sliding-Mode Control and Its Automation Application
Due to the excellent control performance of MFAC, it has been widely used and developed in many industrial fields, and some scholars have introduced MFAC into the control of the CFB water level. Ref. [23] introduced an improved tracking differentiator on the basis of MFAC and designed a noise-resistant MFAC method, which realized the noise-resistant control of the CFB water level, but the control accuracy needs to be improved. [PERSON]. [24] utilized the MFAC method to achieve water-level control in the boiler water circulation system. A mode search algorithm was used to optimize the MFAC parameters, which greatly improved the accuracy of the water-level control but did not consider the influence of external disturbances. [PERSON]. [25] derived a new control law with an error rate by adding an error rate to the objective criterion and fusing and weighting the error and error rate, and the new control method can not only quickly track a given signal but also has good resistance to noise interference. However, if the signal is time varying, the tracking effect will be affected. Since MFAC relies on real-time sample data for adaptive adjustment, it is sensitive to environmental changes. If the environmental changes are too drastic or the sample data are inaccurate, the MFAC may not be able to adapt to the new environmental conditions in time, resulting in a degradation of the control performance [26]. To further improve the control accuracy and robustness of the CFB boiler control system, it must overcome the influence of large disturbances, multiple parameters and strong coupling in the CFB boiler control system and achieve precise control of the CFB boiler water level. This paper considers introducing the idea of the parameter adaptation of MFAC and combining it with the principle of SMC to design a new model-free adaptive ISMC method to further optimize the control effect of the system. The scheme is based on the FFDL data model in model-free adaptive control, and the discrete ISMC law is designed to realize the control of the system. Finally, the method is simulated and tested on a DHX25-1.25 CFB boiler, which is equipped in the special-equipment testing center. It is then compared with the traditional MFAC and SMC control methods. This proves that the improved control method can quickly track the given signals and has good resistance to noise interference. The specific contributions of this paper are mainly in three aspects:  
1. A new ISMC algorithm is proposed, which alleviates the chattering phenomenon of the system compared to the methods in [26; 27]. The algorithm utilizes the improved sliding-mode surface and the convergence law to achieve more-efficient nonlinear control. At the same time, the algorithm also solves the problems of randomly selecting initial weights and excessive control parameters in traditional neural networks. 2. The FFDL data model used in this paper has the following advantages: High flexibility--the FFDL data model has high flexibility and can adapt to different types and structures of controlled systems. It can handle any amount and type of data sets, and the linearization length can be easily added, deleted or modified. Strong adaptability--The FFDL data model is very suitable for use in scenarios with frequent demand changes or unstable data structures. And, this data model does not require precise parameter information of the system and can handle systems with fast, unknown or unmeasurable parameter changes. It can also automatically learn and adjust control strategies to adapt to new changes. 3. Compared with most of the existing CFB control algorithms, the control scheme in this paper does not rely on the process model of the boiler water-level system and is a data-driven control scheme. The scheme can provide more accurate results, and by analyzing a large amount of real-time data, more accurate and reliable results and predictions can be obtained.