Peng Jishen, Su Qingyu, and Song Shaolou of the Department of Electrical Engineering, Liaoning University of Engineering and Technology, found that conventional PID algorithms struggle to track the input signal of a servo system based on the Stribeck friction model. This paper employs a method combining fuzzy PID and traditional PID control, conducting simulation experiments on a flight simulator servo system. Results show that this method is simple to design, effectively controls servo systems with friction, exhibits strong robustness and anti-interference performance, and significantly outperforms conventional PID control. 1. Introduction to the Stribeck Friction Model: In servo systems, we always aim for the output to quickly and accurately track the input to achieve a follow-up effect. In ideal conditions, this might not be difficult, but the problem is that in practical servo systems, mechanical servo systems are inevitably affected by friction, especially in high-precision, ultra-low-speed servo systems. Due to the presence of nonlinear friction, the dynamic performance of the system is greatly affected, mainly manifested as crawling at low speeds and large static error or limit cycle oscillations in steady state. Therefore, establishing a friction model and using dynamic compensation and advanced PID control algorithms on this basis becomes the key to solving this problem. Among them, the Stribeck curve is a well-known friction model. The Stribeck friction model can be represented as shown in Figure 1. [IMG=Figure 1 Schematic diagram of Stribeck friction model]/uploadpic/THESIS/2007/11/2007111611151885196J.jpg[/IMG] Figure 1 Schematic diagram of Stribeck friction model When, the static friction is: When, the dynamic friction is Where: XXX is the driving force, XXX is the maximum static friction force, XXX is the Coulomb friction force, XXXX is the proportional coefficient of viscous friction torque, XXXX is the rotational angular velocity, α and α1 are very small positive constants. 2 Fuzzy PID Control In conventional control, PID control is the simplest and most practical control method. It can be designed analytically using a mathematical model, or it can be determined by experience and trial and error without relying on a model. However, in the servo system discussed in this paper, the factor of friction is considered, which increases the control difficulty. The traditional PID algorithm alone cannot achieve satisfactory control results. Compared with traditional PID control, fuzzy PID control utilizes the control experience of human experts and shows the advantages of good robustness and high control performance for nonlinear and complex control. Of course, fuzzy control is essentially a type of nonlinear PD control. Extensive theoretical analysis and experiments have shown that using only fuzzy controllers for system control often fails to meet all the performance indicators of the controlled object. Therefore, this paper connects a fuzzy PID controller in series with a conventional PID controller to form a complete fuzzy control system. [IMG=Figure 2. Control Block Diagram of Servo System under Friction Conditions]/uploadpic/THESIS/2007/11/20071116111748439591T.jpg[/IMG] Figure 2. Control Block Diagram of Servo System under Friction Conditions [IMG=Figure 3. Simulink Simulation Diagram of PID Control]/uploadpic/THESIS/2007/11/2007111611180460488F.jpg[/IMG] Figure 3. Simulink Simulation Diagram of PID Control [IMG=Figure 4. Input and Output Membership Functions of Fuzzy Controller]/uploadpic/THESIS/2007/11/20071116111852822156.jpg[/IMG] Figure 4. Input and Output Membership Functions of Fuzzy Controller [IMG=Table 1] [Fuzzy Control Rule Table]/uploadpic/THESIS/2007/11/2007111611193761802U.jpg[/IMG] Table 1 Fuzzy Control Rule Table [IMG=Figure 5 Fuzzy Control Rule Surface Diagram]/uploadpic/THESIS/2007/11/200711161120037550806.jpg[/IMG] Figure 5 Fuzzy Control Rule Surface Diagram 3 Simulation Example To illustrate the advantages of the fuzzy PID algorithm based on the Stribeck friction model, a flight simulator servo system simplified to a linear second-order element is used as an example for Matlab simulation. At low speeds, there is a strong friction phenomenon. At this time, the controlled object becomes nonlinear, making it difficult to achieve high-precision control using traditional control methods. This simulation system uses a DC motor, neglecting armature inductance, and the current loop and speed loop are open loops, as shown in Figure 2. Where: XXX is the PWM power amplifier amplification factor, R is the armature resistance, XXX is the motor torque factor, ce is the voltage feedback factor, J is the moment of inertia of the frame, θ(t) is the rotational speed, r(t) is the command signal, and u(t) is the control input. Based on the structure of the servo system, the position state equation of the flight simulation turntable can be described as follows: Where: X1(t) = θ(t) is the rotation angle, and X2(t) = (t) is the rotational speed. Suppose the parameters of a turntable servo system are as follows: R=7.77Ω, λ = 6Nm/A, Ce=1.2V/(rad/s), j=kgm2, λ = 11V/V, Fc=15Nm, Fm=20Nm, λ = 2.0Nms/rad, α1=1.0, α=0.01. The low-speed sinusoidal tracking signal command is r(t) = 0.10sin(2πt). When using traditional PID control, u(t) = 200*e + 40*e. The Simulink simulation diagram of the corresponding PID control system in Matlab is shown in Figure 3. When using fuzzy PID and conventional PID controller in series, the membership functions of the controller input and output are shown in Figure 4. The corresponding fuzzy control table is shown in Table 1. For clarity, we can see that the control surface diagram formed by the control rule is shown in Figure 5. u(t) = 200*u(t) + 40*u(t) and PD control is used in conjunction with fuzzy control. The Matlab control diagram of the corresponding system at this time is shown in Figure 6. [IMG=Figure 6 Simulink simulation diagram of fuzzy and PID series control]/uploadpic/THESIS/2007/11/20071116112120227291L.jpg[/IMG] Figure 6 Simulink simulation diagram of fuzzy and PID series control [IMG=Figure 7 Position simulation result]/uploadpic/THESIS/2007/11/20071116112136394566.jpg[/IMG] Figure 7 Position simulation result [IMG=Figure 8 Velocity simulation result]/uploadpic/THESIS/2007/11/20071116112146247405.jpg[/IMG] Figure 8 Velocity simulation result Simulation result curve 1 The position simulation comparison curves obtained by using the traditional PID algorithm with friction and the fuzzy PID and conventional PID controller series algorithm with friction are shown in Figure 7. As can be seen from the comparison, the traditional PID control exhibits a significant flat-top phenomenon, while the flat-top phenomenon is reduced or even eliminated when fuzzy control is used. Figure 8 shows the speed simulation comparison curves obtained by using the traditional PID algorithm with friction and the fuzzy PID controller connected in series with a conventional PID controller with friction. The comparison curves show that although there is jitter when using fuzzy control, its dead-zone time is short, the displacement deviation is small, no flat-top phenomenon is observed, and the accuracy is high. 4. Conclusion Through the comparison of the above simulation curves, it can be seen that: if the influence of friction is not considered, the traditional PID control algorithm can achieve good control results; if the friction element is considered, the position tracking exhibits a "flat-top" phenomenon, and the speed tracking exhibits a "dead-zone" phenomenon. It is evident that using the traditional PID algorithm at this time results in poor control robustness and cannot achieve high-precision tracking. The third set of simulation curves shows that after adopting the fuzzy PID algorithm, the fuzzy control system composed of the fuzzy PID and the conventional PID controller connected in series can effectively eliminate adverse effects such as "flat-top" and "dead-zone," improve the control effect, and basically meet the control accuracy requirements. (Proceedings of the 2nd Servo and Motion Control Forum, Proceedings of the 3rd Servo and Motion Control Forum)