A Novel Model-Free Adaptive Proportional-Integral-Derivative Control Method for Speed-Tracking Systems of Electric Balanced Forklifts  
[PERSON]  
1 School of Mechanical and Electrical Engineering, Quzhou College of Technology, Quzhou 324000, China; [EMAIL_ADDRESS] (J.X. ); [EMAIL_ADDRESS] (F.X)  
[PERSON]  
2 College of Communication Engineering, Jilin University, Changchun 130022, China  
electric balanced forklifts, the practical application of autonomous driving is still in its early stages. This is primarily due to the complex and ever-changing operating environments of forklifts. These environments involve diverse cargo types, shapes, and weights, as well as unique operational scenarios, which present significant challenges for implementing autonomous driving technology in the forklift industry. Due to the reasons outlined above, research on automatic driving technology for forklifts has become a hot topic, especially in the areas of visual positioning [8], lidar positioning [9], and adaptive control [10]. For instance, the Vecna company (Cambridge, MA, USA) in the US has launched an automatic navigation forklift that employs multiple sensing technologies, such as lidar, an inertial navigation system, and visual sensors, to achieve accurate positioning and path planning [11]. Similarly, KUKA, a German company (Augsburg, Germany), has developed an automatic forklift based on visual navigation, which captures ground feature points with a camera to enable autonomous navigation and accurate handling of the forklift [12]. In practical research, the tracking of path and time in electric balanced forklifts exhibits a complex nonlinear relationship. On the other hand, the impact of disturbances and load variations makes the vehicle system itself a complex and difficult-to-model nonlinear system. Additionally, traditional forklift operations rely on the driver's experience and skills, which can lead to low operational efficiency and safety accidents such as tipping over [13]. In order to address these challenges, researchers need to develop innovative control methods to enhance the performance and adaptability of electric balanced forklifts. Currently, most of the research is focused on using two- or four-wheeled mobile robots instead of electric forklifts. Refs. [14; 15] applied model predictive control methods based on tracking error models to successfully track the trajectory of mobile robots. Refs. [16; 17; 18] used neural network control methods to simulate the nonlinear movements of robots and applied them to the trajectory tracking of mobile robots. Ref. [19] applied fuzzy control methods to the trajectory tracking control of mobile robots. Ref. [20] combined reinforcement learning with PID algorithms to apply trajectory tracking control of mobile robots. The aforementioned control methods primarily perform trajectory tracking in the time domain and are based on model-based control. However, they have lower control accuracy and adaptability. Electric forklifts experience significant disturbances due to the increasing load during operation, resulting in a time-varying model. This makes it challenging for the aforementioned control methods to meet the high-precision autonomous driving requirements of time-varying electric forklifts. According to the aforementioned literature, when analyzing controller design and system stability, it is necessary to obtain the model parameters in advance or linearize the forklift model. These factors lead to mismatches between the controller and the actual model in model-based control methods, resulting in a significant impact on control performance. To address this issue, some scholars have started exploring data-driven control approaches. PID control is one of the earliest control methods and has been widely applied in industrial processes due to its advantages of simplicity and high reliability [21; 22]. Moreover, the PID is also a typical data-driven control method.