Abstract: A dual-mode control method for a precision machine tool servo system is proposed, and a novel closed-loop position control system based on this method is developed. This method effectively compensates for the influence of nonlinearity in the actuator's dead zone caused by dynamic and static friction without altering the original controller structure, making it relatively simple to implement. Experiments show that the maximum tracking error is less than ±0.1 μm in low-speed tracking. Keywords : Ultra -precision machine tool, dual-mode control, dead zone, nonlinearity Keywords : precision machine tool; dual-mode control; near dead zone. Under normal operating conditions, the feed speed of the worktable in an ultra-precision machine tool is only 5 mm/min, requiring the servo system to have excellent low-speed characteristics. However, due to the frictional forces in the support and transmission components, especially the difference in dynamic and static friction torques between contact surfaces, a dead zone exists in the actuator, resulting in uneven system motion and significant steady-state tracking errors. Therefore, to solve these problems, this paper proposes a variable-mode control method. Outside the range of the nonlinear dead zone, conventional control methods are used; within the nonlinear influence, a control term is added to the original controller for compensation. This allows the system to effectively correct displacement deviations caused by nonlinear factors, thereby ensuring good low-speed performance of the CNC machine tool. 1. System Composition and Conventional Controller Design The ultra-precision machine tool servo feed system uses an AC servo motor and ball screw to achieve position servo feed, and a dual-frequency laser interferometer for position detection. An air-static pressure guide rail and an air-bearing worktable are used to reduce the influence of friction during transmission. The system structure is shown in Figure 1. For the AC servo drive unit used in this paper, a closed-loop speed regulation structure is adopted, and a P-type regulator is used in the speed loop. Kτ in the speed loop represents the torque constant. The dynamic model of the position servo system is shown in Figure 2. In the figure, D(s) is the position controller, and Tυ is the system's disturbance torque, which is mainly caused by friction torque and the torque fluctuation of the motor itself. The torque constant Tυ is 16 N (ra/v), the tachometer proportional coefficient Cε is 0.796 V/Rad/s, and the speed regulator proportional coefficient Kτ is 32 s~. The ball screw transmission coefficient Kτ is 0.8 ram/rod. Kd represents the circuit amplification factor of the laser interferometer. Due to the high frequency response of the laser interferometer's measurement circuit, it is treated as a proportional element, and Kτ is 1. R is the input signal, representing the output position of the worktable. In the modeling, the high-frequency oscillation modes that may exist in the worktable are treated as unmodeled dynamic characteristics. In order to obtain the measured model of the system, the frequency method is used to identify the system. A sinusoidal sweep frequency signal is input from the speed loop input terminal of the motor servo drive unit, and the output displacement is read by the laser interferometer. The open-loop transfer function of the system shown in Figure 2 is identified as follows: From the identified open-loop transfer function, the load rotational inertia J = 2.32 kg·m². This system is a type I system. The design of this type of control system generally boils down to how to design the system as a wide bandwidth, high stiffness servo system to ensure fast response speed and strong anti-interference capability. In this paper, D(s) adopts a controller of the form k(Tδ+1)/s. Since D(s) contains a pure integral element, the static servo stiffness of the system is infinite, so the system can effectively suppress the influence of the step disturbance torque on the motor shaft. The system's good damping characteristics can be obtained by adjusting the parameters. Considering the system's response speed, noise error and the influence of unmodeled dynamic characteristics, this paper designs the system bandwidth to 10Hz. Finally, the controller can be determined as follows: 2. Design of Dead Zone Compensation Controller Due to the existence of static friction torque, the actuator has a dead zone nonlinear effect during the process from stationary to moving. Let φ be the dead zone voltage of the power amplifier corresponding to the maximum static friction torque, K be the proportional coefficient in D(s), and φ be the position deviation. The effective range of the dead zone can be determined by the following formula: The design idea of ​​dual-mode control to compensate for friction torque is to use a conventional controller, D(s), outside the dead zone range, and a dead zone compensation controller when approaching the dead zone. The switching action is executed by the decision-making mechanism. The schematic diagram of the dual-mode controller is shown in Figure 3. The dead zone compensation controller is based on the conventional controller with an additional compensation term M(e) for compensation. Let the control voltage generated by the conventional controller be ε. M[sub]0[/sub](e), then the control algorithm to achieve dead zone compensation is: ε>0, which is a small selected quantity. In this way, the additional control term M[sub]c[/sub](e) works in the range close to the dead zone, eτ≤e≤eπ. The selection of e can make the generated control torque exceed the static friction torque, so that the system reaches the desired equilibrium state. 3. Experimental Results To verify the effectiveness of the proposed dual-mode control method, it was digitally implemented and applied to the servo system of the HCM-1 ultra-precision machine tool. This machine tool uses a Parker DM1050A AC torque servo motor and an L-Im-20B dual-frequency laser interferometer manufactured by Tokyo Seimitsu Corporation, Japan, with a detection resolution of 5nm. The measured dead-zone voltage of the power amplifier was 0.4V, so e_L = 0.0014mm and e_H = 0.0014mm. Taking s = 0.0001mm, using a ramp signal as input, and a tracking speed of 5mm/min, the measured tracking error curve is shown as curve 1 in Figure 4. Curve 2 in Figure 4 is the tracking error curve when only a conventional controller is added without a dead-zone compensation controller. It can be seen from the figure that the dual-mode control method can largely eliminate the steady-state tracking error of the system, achieving smooth and error-free tracking at low speeds. The dual-mode control method can ensure that the maximum steady-state tracking error does not exceed ±0.1µm when the actuator has a dead zone. 4 Conclusion The dead zone nonlinear effect of the actuator caused by the difference between static and dynamic friction torque in the ultra-precision machine tool servo system is the main factor affecting the system accuracy. This paper first experimentally measured the system model and designed a conventional controller; then, by analyzing the characteristics of the dead zone effect, a dead zone compensation control algorithm was introduced; finally, the effectiveness of the dual-mode control method designed in this paper was verified by experiments. [References] [1] Y. S. Tarng+ and HECheng+. An Investigation of Stick-sHp Friction on the Contouring Accuracy of CNC Machine Tools. Int J Mach. Tools Manufaet. Vol. 35. No. 4. 1999: [2] Wu Guangyu. System Identification and Adaptive Control. Harbin Institute of Technology Press, 1987 [3] Wang Guangxiong. Control System Design Aerospace Press, 1992 Click here to download the original text