## 1 Introduction  
Radiofrequency ablation (RFA) is a minimally invasive method of treating tumours by heating tumour tissue to 50-100 \({}^{\circ}\)C using radiofrequency signals, and is widely used in clinical practice [1; 2; 3]. Temperature control during ablation has a significant impact on the effectiveness of the treatment [4; 5; 6]. When the temperature between the radiofrequency electrode and the tumour tissue exceeds 100 \({}^{\circ}\)C, the tumour tissue will carbonicise, resulting in a sharp increase in the impedance of the tumour tissue, which reduces the radiofrequency current density and limits the final ablation effect [7; 8]. In addition, different temperatures can affect the ablation volume, and inappropriate temperatures can cause thermal damage to the normal tissue surrounding the tumour, which can lead to a range of complications [9; 10; 11; 12; 13; 14]. Therefore, stable and accurate temperature control needs to be achieved to improve the therapeutic effect of RFA.  
Proportional-integral-derivative (PID) controllers have a wide range of applications in the field of RFA temperature control due to their simple structure and easy implementation [15; 16; 17; 18]. However, the temperature system for RFA has characteristics such as non-linearity and hysteresis, whereas PID controllers are designed based on linear systems. Therefore, when dealing with non-linear RFA temperature systems, PID controllers may not be able to achieve the desired control effect [19]. In addition, PID controllers have shortcomings such as reliance on high-precision mathematical models and time-consuming parameter adjustment [20, 21].  
The adaptive network-based fuzzy inference system (ANFIS) controller implements the neural networking of the fuzzy inference process by integrating the learning ability of artificial neural networks and the decision-making mechanism of fuzzy logic [22]. The controller uses fuzzy inference parameters to represent the weights of the neural network, updates the parameters through a learning algorithm, and exhibits Takagi-Sugeno (T-S)-type fuzzy inference behaviour, which gives the controller the ability to approximate non-linear functions [23, 24]. The ANFIS-PID controller, which is formed by combining the ANFIS controller with a PID controller, has advantages over the PID controller alone in terms of stability and tracking capability. In [25], an ANFIS-PID controller was constructed using three separate ANFIS to update each of the three parameters of the PID controller, which was applied to the temperature control system of a 3D printer, and simulated and compared with the PID controller. The results show that the ANFIS-PID controller outperforms the PID controller in terms of overshoot and steady-state error with better stability. In [26], the PID controller was combined with ANFIS in the form of selection and switching to form the ANFIS-PID controller, which was applied to the temperature control of a polyethylene reactor, and the performance of the three controllers, ANFIS, PID and ANFIS-PID, was comparatively analysed in terms of tracking and disturbance suppression. The results show that the ANFIS-PID controller performs better in terms of stability compared to the PID and ANFIS controllers.  
Based on the above analysis, in this paper, the incremental PID is used to construct the ANFIS-PID controller instead of the rule output of ANFIS. At the same time, the hardware language Verilog is used to implement it in FPGA, and the calculation method of the input value error and the learning rate are set in segments according to the test, in order to improve the control accuracy of FPGA in the implementation of ANFIS-PID.