Abstract : For typical industrial process control objects, a two-degree-of-freedom fuzzy PID controller design method is proposed, which decouples disturbance rejection characteristics and setpoint tracking characteristics. This method uses a fuzzy adaptive PID controller to achieve disturbance rejection, and adjusting the parameters of the outer loop setpoint reference model can enable the system to obtain good setpoint tracking characteristics. Simulation results show that this method is superior to other methods. Keywords : Fuzzy PID ; Decoupling; Two degrees of freedom Keywords : fuzzy PID; decoupling; two-degree-of-freedom 1 Introduction In the field of industrial process control, many controlled processes have complex mechanisms and exhibit characteristics such as high nonlinearity, pure time delay, and open-loop instability. Under load disturbances and changes in some parameters, the model parameters of the process will change, resulting in a certain degree of uncertainty in the actual process system. Using fixed parameters to address such uncertain processes is clearly insufficient to achieve satisfactory control results. Furthermore, tuning the PID controller parameters involves trial and error and is difficult to achieve. With the continuous development of modern control theory and the widespread use of computer technology, algorithms for industrial process control systems, such as grey prediction algorithms, neural network control, and fuzzy adaptive control, have emerged to meet the requirements of high-performance systems. References [1][2] combine two-degree-of-freedom control with fuzzy control for speed control of AC systems and position control of servo systems. To improve the robustness of the system and obtain better target value tracking response, reference [1] proposes to introduce a system reference model in the forward channel and a fuzzy controller in the feedback channel on the basis of a two-degree-of-freedom control system, thus forming a fuzzy adaptive mechanism, and realize online adjustment through it. Reference [2] proposes a fuzzy two-degree-of-freedom controller design method for speed controllers. This method uses two fuzzy controllers to realize setpoint tracking characteristics and disturbance suppression characteristics respectively. Reference [3] proposes a two-degree-of-freedom internal model control method. This method has certain robustness, but the response speed is slow and the overshoot is large. Reference [4] proposes a two-degree-of-freedom PID parameter tuning method, but this method requires tuning many parameters and is not easy to tune. Reference [5] proposes a parameter tuning method for a PI controller based on fuzzy inference, but this method is a one-degree-of-freedom control and cannot simultaneously take into account setpoint tracking performance and disturbance suppression performance. Based on the paper [1], this paper proposes a completely decoupled two-degree-of-freedom PID controller. The system uses a fuzzy adaptive PID controller to suppress system disturbances and can achieve setpoint tracking control by adjusting the filter parameters of the reference model. The main design idea of ​​this method is: under nominal conditions, a two-degree-of-freedom controller is designed according to the system's expected tracking performance and disturbance performance requirements, so that the closed-loop transfer function of the system is a set reference model. By adjusting the parameters of this model, the system can obtain good setpoint following characteristics. At the same time, a fuzzy adaptive PID controller is added to the two-degree-of-freedom control system. This controller is used to suppress disturbances and reduce the impact of parameter changes on system performance. Its specific working principle is: under nominal conditions, the model tracking is accurate and the fuzzy PID controller does not work. However, when the parameters of the controlled object change or there is a disturbance, the fuzzy controller will automatically generate an adaptive signal to compensate the system, thereby improving the robustness of the system. The two-degree-of-freedom controller designed by this method does not require mathematical derivation in the design of the fuzzy controller, so it is easier to implement than the conventional controller. At the same time, this method can improve the robustness of the system. 2. Design of a Two-Degree-of-Freedom PID Control System 2.1 Improved Two-Degree-of-Freedom Control Structure This paper proposes a new two-degree-of-freedom control structure for a first-order inertial process with time delay, as shown in Figure 1. [align=center] Figure 1. Two-Degree-of-Freedom Control Structure with Modified Structure [/align] In the figure, r is the setpoint, y is the system output, d1 is the disturbance signal, P is the process object, G[sub]MP[/sub] is the reference model for the setpoint following characteristic, G[sub]GP[/sub] is the fuzzy adaptive PID controller, and G[sub]FP[/sub] is the system's feedforward controller. In this two-degree-of-freedom control structure, G[sub]MP[/sub] adjusts the system's setpoint following characteristic, and the G[sub]CP[/sub] fuzzy controller suppresses disturbances and ensures good robust stability of the system. 2.2 Design of Fuzzy Adaptive PID Controller The structure diagram of the fuzzy adaptive PID controller is shown below: [align=center] Figure 2 Fuzzy Adaptive PID Controller[/align] As can be seen from equation (2), the system's interference suppression performance can be obtained by designing G[sub]CP[/sub](s). Since an important aspect of fuzzy control being superior to traditional control is that it can integrate human experience into the control process in the form of rules, without needing to know the precise model of the controlled object, the ideal effect can be obtained relatively easily by using the fuzzy control method to design the system. In Figure 1, G[sub]CP[/sub](s) is the fuzzy adaptive PID controller. In Figure 2, E and EC are the fuzzy linguistic variables of error e and error change de/dt, respectively; Ke and Kec are the quantization factors of error and error change rate, respectively; Kp, Ki, and Kd are the quantization factors of KKp, KKi, and KKd, respectively; and the quantization factor of output variable u is Ku. The fuzzy sets of linguistic variables are as follows: E = {NB, NM, NS, ZO, PS, PM, PB}; EC = {NB, NM, NS, ZO, PS, PM, PB}; Kp = {ZO, PS, PM, PB}; Ki = {ZO, PS, PM, PB}; KKd = {ZO, PS, PM, PB}. These represent {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}, respectively. The membership function curves corresponding to each linguistic variable are shown below. [align=center] Figure 3 Membership function curves of error and error change rate Figure 4 The membership function curves of the output variables proportional-integral-derivative (PI) and output variables are shown. The universes of discourse for E and EC are both [-3,3], while those for Kp, Ki, and Kd are [0,3]. The membership functions for E, EC, Kp, Ki, and Kd are a combination of Gaussian and triangular types. The median method is used for defuzzification. Rules are the core of the fuzzy controller. Too many rules result in excessively long online inference times, making it difficult to guarantee real-time control; too few rules fail to achieve the desired control effect. Rule formulation is based on human intuition. PI parameter fuzzy self-tuning involves finding the fuzzy relationship between the three PID parameters and the error e and the rate of change of error de/dt. During operation, by continuously detecting e and de/dt, the three parameters are modified online according to the fuzzy control principle to meet the different requirements of e and de/dt for the control parameters, thus enabling the controlled object to have good dynamic and static performance. For large errors, the system should respond quickly; for small errors, excessive overshoot should be prevented. The fuzzy control rules are described in the following form: If {E=Ai and EC=Bi} then Kp=Ci, Ki=Di, Kd=Ei i=1,2……n where Ai, Bi, Ci, Di, and Ei are fuzzy linguistic values ​​in their respective domains of discourse, and their fuzzy control rule tables are shown in Tables 1 and 2. [align=center] Table 1 Fuzzy rule table for Kp Table 2 Fuzzy rule table for Ki Table 3 Fuzzy rule table for Kd[/align] Using the Fuzzy Logic Toolbox in MATLAB, the membership functions of E, EC, Kp, Ki, and Kd are input into the membership function editor, and the values ​​in the fuzzy control rule tables are written into the fuzzy control rule editor one by one. III. Simulation Study This paper refers to the method in reference [5], and selects the transfer function of the industrial object as: The sampling period is 1ms, the system setpoint follows the model, and λ=10 is taken; fuzzy adaptive PID control is used for step response. When the setpoint is 1, the method in reference [5] and the method in this paper are compared and analyzed. The online proportional factor KE=2, KEC=1, KKp=0.5, KKi=0.028 is set. The output proportional factor Ku=0.168. An interference of -0.2 is added to the controller output, and the corresponding curve is shown in the figure below: [align=center] Figure 5 Response curve when the model is accurate Figure 6 Response curve when the model mismatch is 10%[/align] It can be seen from the figure above that, under the nominal condition, the setpoint following performance of the method in this paper is significantly better than that of the method in reference [5]. For interference suppression characteristics, the method in this paper is better than that of reference [5], and the robustness of the method in this paper is better than that of reference [5] when the model is mismatched. IV. Conclusion As shown in Figures 5 and 6, both the method in [5] and this paper have good interference suppression characteristics, but the system setpoint tracking performance of the method in [5] is not ideal. Based on this, a two-degree-of-freedom fuzzy PID control method that decouples the interference suppression characteristics and the setpoint tracking characteristics is proposed. This method improves the structure and fuzzy rules of the PID controller in [5]. This structure can obtain good setpoint tracking characteristics by adjusting the parameters, and the interference of the system can be effectively suppressed by designing a fuzzy adaptive PID controller. This method is simple to implement, convenient and easy to use, and has important guiding significance for actual control. At the same time, the fuzzy controller designed using the fuzzy logic toolbox can easily modify the universe of discourse, membership function and control rules of the input and output, and the simulation time is relatively fast. The simulation results show the superiority of this method. References: [1] CMLiaw, FJLin, Position control with fuzzy adaptation for induction servomotor driver, IEE Pro.-Electr.Power, 1995, Vol.142.No.6, 397-404 [2] CMLiaw, SYCheng, Fuzzy Two-Degree-of-freedom Speed ​​Controller for Motor Driver, IEEE Transcation on Electronics, 1995, Vol.42, No.2, 209-216 [3] ZHANG Jinggang, LI Linsheng, CHEN Zhimei. IMC tuning of two-degree-of-freedom PID regulator[J]. Chinese Journal of Scientific Instrument, 2002, 23(1), 28-30. [4] ARA KI M, HIDEFUMI T. Two-degree-of-freedom PID controllers[J]. International Journal of Control, Automation, and Systems, 2003, 1(4): 401-410. [5] Liu Jing, Lü Lihua. PI controller parameter tuning method based on fuzzy inference. Control Engineering, 1671-7848 (2007) Author's profile: Zhao Runhua (1980-), male, master's student, mainly engaged in advanced process control. E-mail: [email protected] Contact address: P.O. Box 468, Taiyuan University of Science and Technology, postcode 030024 Contact number: 13453177803