Abstract: Considering the characteristics of wind turbine loads, a reverse thrust control based on a nonlinear control strategy is proposed to achieve closed-loop speed control. The designed reverse thrust control can realize speed tracking control of a permanent magnet synchronous motor, ensuring good speed tracking performance of the system. Furthermore, it improves the efficiency of wind turbine loads. Keywords: Fan load; Backstepping control; Speed ​​tracking; Permanent magnet synchronous motor Abstract: This study presents forward backstepping control based on a nonlinear control strategy as a possible way to implement close-bop speed control based on the characteristics of fan load. The newly designed backstepping control is implemented for a Pennanent Magnet Synchronous Motor (PMSM) to track speed commands. The design can provide better speed tracking performance and improve the efficiency of fan load. Key words: fans load; backstepping control; speed tracking; PMSM 1 Introduction When a constant speed motor drives a fluid load such as a fan or pump and the flow needs to be controlled, the traditional approach is to use throttling devices such as baffles or valves to adjust the flow. This method consumes a large amount of energy in the friction and heat generation of the throttling device and pipeline, resulting in very low system efficiency. Currently, most systems use asynchronous motor frequency conversion speed regulation for control, which saves energy and has better speed regulation performance, but it is relatively expensive, and it mostly uses open-loop control, without forming a closed-loop speed control. Therefore, in some experimental applications requiring precise negative pressure, variable frequency speed control is insufficient. Permanent magnet synchronous motors (PMSMs) possess advantages such as compact structure, high power density, high air gap flux, and high torque-to-inertia ratio. Thus, PMSMs offer significant advantages. This paper proposes a novel nonlinear back-stepping control strategy based on Lyapunov functions, aiming for global asymptotic stability. This strategy not only achieves complete decoupling of the PMSM system but also demonstrates excellent control performance for fan-type loads. 2. Permanent Magnet Synchronous Motor and Fan-Type Load Model A surface-mount permanent magnet synchronous motor is used. The dq model based on the synchronous rotating rotor coordinates is as follows: where u_d and u_q are the d-axis and q-axis stator voltages, respectively; i_d and i_q are the d-axis and q-axis stator currents, respectively; R is the stator resistance; L is the stator inductance; T_L is the load torque; J is the moment of inertia; B is the coefficient of viscous friction; P is the number of pole pairs; ω is the rotor mechanical angular velocity; and is the permanent magnet flux. For fan-type loads, the load is proportional to the square of the rotational speed, where K_m is a constant. 3 System Control Design 3.1 Backstepping Control Design Steps Backstepping, as an effective nonlinear control design method, has the following design steps: 1) Select a state of the system to form a subsystem, construct the Lyapunov function of the subsystem, and design the assumed control function to stabilize the subsystem; 2) Based on the assumed control in 1), design the error variable, and form a new subsystem with the error variable and the previous subsystem. Construct the Lyapunov function of the new subsystem, and design the assumed control to stabilize the new subsystem; 3) If the actual control of the system has not yet been obtained, return to 1) to continue the design. If the actual control of the system is obtained, continue the design; 4) Design the actual control of the system to ensure the stability of the entire system. From the above steps, it can be seen that the biggest advantage of backstepping is that the final control can guarantee the global stability of the entire system. 3.2 Backstepping Control Implementation For fan-type loads, the air volume is proportional to the motor speed, and the load is proportional to the square of the speed. Therefore, controlling the air volume is equivalent to controlling the motor speed. Its control objective is mainly speed tracking. The tracking error is defined as choosing e as the new state variable to form a subsystem. The system equation is to make the speed tracking error approach zero. For the subsystem (6), the following L yapunov function is constructed. Therefore, the control equation (10) is realized, and the purpose of global asymptotic speed tracking can be achieved. In order to realize the complete decoupling and speed tracking of the permanent magnet synchronous motor, the following assumption of the current function can be made. In order to realize current tracking, the q-axis current tracking error is chosen as the new state variable. A new system can be formed by e, e[sub]q[/sub]. Taking the derivative of equation (14), we can obtain equation (17), which contains the actual control uq of the system. In order to make equation (16) always satisfy V[sub]2[/sub]<0, we choose e[sub]q[/sub], e[sub]d[/sub]. A new system can be formed again. Taking the derivative of equation (20), we can obtain that for the new system, a new L yapunov function can be constructed. Taking the derivative of equation (21), we can obtain equation (22), which contains the actual control ud of the system. To ensure that equation (22) always satisfies V<0, we choose to make the Lyapunov function V₃ = 0 for any given parameter. According to the Lyapunov stability theorem, the control equations (19) and (25) can enable the permanent magnet synchronous motor system to not only achieve asymptotic speed tracking, but also current tracking, so that the system has a fast response speed. 4 System Simulation Analysis The backstepping control structure block diagram of the permanent magnet synchronous motor system under the fan load is shown in Figure 1. The parameters of the permanent magnet synchronous motor are shown in Table 1. [align=center] Fig 1 Diagram of system control [align=center] Table 1 Parameters of PM SM [align=center] Wherein, the constant of the fan load is set to Km=5*10-6 based on the actual situation, and the reference speed is assumed to be 500 r/min, that is, the air volume is kept constant. The parameters for the back-stepping control are k=30, k1=100, and k2=450. The simulation results of the back-stepping control are shown in Figure 2. The simulation results show that the back-stepping control enables the system to achieve rapid tracking while ensuring good dynamic performance. 5. Conclusion This paper applies the back-stepping control strategy to the constant wind pressure control of wind turbine loads. This design uses the Lyapunov function to ensure the global asymptotic stability of the system. It only requires adjusting three parameters, k, k1, and k2, simplifying the design method and proposing a new control strategy for wind turbine loads. MATLAB simulations show that it can track the given value well, giving wind turbine loads good stability. Furthermore, compared with traditional control methods, it saves energy and improves efficiency. References: [1]Pillay P, Krishnan R.Modeling of pemanentmagnet motot drives[J]. IEEE Trans on Industrial ElectronIcs, 1988.35(4):537-541 [2]RahmanM A, Vilathgam uwwaM, U ddinM N, et al. Nonlinear control of interior pemanent-magnet synchronous motor[J] IEEE Trans on Industrial Application, 2003, 39 (2): 408-416 [3] Kokotovic P. The joy of feedback: nonlinear and adaptive [J]. IEEE Control System Magazine, 1992, 12 (3): 7-17 [4] Wang Kaixia. Variable frequency speed of fans and pump with its application [J] Machine Tool Electricity, 2001, 28(1): 46-48 [5] Liu Guangbin, Liu Ping. Application of frequency converter in boiler fan control system [J] Electric Drive, 2001, 31(1): 63-64 [6] Peng Weifa, Zhao Jin, Yang Lu, et al. Design of a new controller for servo system [J]. Proceedings of the CSU-EPSA, 2002, 14(3): 63-66 Authors' profiles: Liu Dongliang (1977-), male, doctoral candidate, mainly engaged in the research of nonlinear control and motor servo system. Email: [email protected] Zhao Guangxiu (1946-), male, doctoral supervisor, mainly engaged in the research of nonlinear control and chaotic control. Email: [email protected]