0 Introduction
A position servo system is an automatic control system. Therefore, when analyzing and designing such a system, it is necessary to use the principles of automatic control as its theoretical foundation to study the dynamic performance of the entire system, and then to study how to assemble various components into a stable control system that meets stability performance indicators. If the original system is unstable, it can be stabilized by adjusting the proportional parameters and using hysteresis compensation, and appropriate parameters can be selected to ensure the system meets design requirements. This article introduces the components and working principles of a position servo system, as well as the system design and calibration.
1. Components and working principle of a position servo system
CNC machine tool table position servo systems come in different forms, and generally consist of basic components such as a given link, a comparison link, a correction link, an actuator, a controlled object or an adjustable object, and a detection device or sensor [1]. According to the requirements of the host machine, the control power of the system is relatively small and the table stroke is relatively large, so a valve-controlled hydraulic motor system is adopted. The system block diagram is shown in Figure 1. The CNC machine tool table position servo system refers to an automatic control system that uses the movement displacement of the CNC machine tool table as the control object. As the actuator of the CNC machine tool, the position servo system integrates power electronic devices, control, drive and protection. The output displacement of the CNC machine tool table position servo system can automatically, quickly and accurately reproduce the changes in the input displacement because the output end of the table has a displacement detection device (displacement sensor) that converts the displacement signal into an electrical signal and feeds it back to the input end to form a negative feedback closed-loop control system. The feedback signal is compared with the input signal to obtain a differential pressure signal. This differential pressure signal is then converted into a current signal by a servo amplifier and sent to an electro-hydraulic servo valve (electro-hydraulic converter, power amplifier element) to be converted into a high-power hydraulic signal (flow and pressure) output. This causes the four-way spool valve of the hydraulic motor to open, resulting in pressurized oil output to the hydraulic motor. The hydraulic motor drives the reduction gear to rotate, which in turn drives the ball screw. Because the ball screw is connected to the worktable, the worktable also moves accordingly when the ball screw moves. Design requirements: Static position error (position resolution)2. Determine the parameters of the power components and select the displacement sensor and servo amplifier.
2.1 Calculate the total load force
The load force consists of three parts: cutting force, friction force, and cutting force. Friction force has a "decreasing" characteristic; for simplicity, it can be considered independent of velocity and is a constant. Taking its maximum value, and assuming the system operates under the worst load conditions (i.e., all load forces exist and acceleration is maximum), the total load force is:
2.2 Calculate the displacement of the hydraulic motor
The torque of the hydraulic motor is
If we take [value], then the displacement per revolution of the hydraulic motor is [value].
The hydraulic motor has a displacement of [missing information] per revolution.
The calculated hydraulic motor displacement needs to be standardized, and the load pressure value should then be calculated based on the selected standardized value. In this problem, the calculated hydraulic motor displacement value conforms to the standard.
2.3 Determine the servo valve specifications
The maximum speed of the hydraulic motor is
Therefore, the load flow is
At this time, the servo valve pressure drop is
Considering the impact of leakage, etc., the increase will be 15%, so we take [value missing]. According to [reference missing], referring to the manual, a valve with a rated flow rate (output flow rate when valve pressure drop is [value missing]) of 8 L/min can meet the requirements. The rated current of this valve is [value missing].
2.4 Displacement Sensor and Amplifier Gain
Amplifier gain to be determined.
3. Dynamic quality of the system
3.1 Determine the transfer function of each component.
Because the load characteristics do not have an elastic load, the transfer function between the hydraulic motor and the load is:
The moment of inertia of the worktable mass converted to the hydraulic motor shaft is:
Considering the inertia of gears, lead screws, and hydraulic motors, and taking the volume of the hydraulic motor, the natural frequency of the hydraulic system is:
Assume the damping ratio is generated solely by the valve's flow-pressure coefficient. The zero-point flow-pressure coefficient can be approximated as...
The hydraulic damping ratio is
Substituting the value into equation (2) yields
The transfer function of the servo valve can be obtained from the sample [4].
The rated flow rate of the valve at the supply pressure is 8 L/min (where is the valve pressure drop). According to the table in Chapter 2, a valve with a rated flow rate (output flow rate when the valve pressure drop is ) of 8 L/min meets the requirements.
Therefore, the rated flow gain of the valve is determined by the transfer function of the servo valve.
The transfer function between the reduction gear and the lead screw is:
Based on the transfer function determined above, the model of the CNC machine tool table position servo system can be drawn using Simulink, as shown in Figure 2.
3.2 Programmatically implement the plotting of the system's open-loop Bode plot and determine the open-loop gain based on stability.
The open-loop transfer function of the system is
Based on the open-loop transfer function of the system, the Bode plot of the system was plotted using MATLAB programming, and the result is shown in Figure 3. Through the Bode plot of Ka = 1, it was found that the phase margin and gain margin of the system are both negative, so the system is unstable [2][3] .
The MATLAB program is as follows:
Ka=1
num=Ka*4216e-6*1.25e6*9.56e-4*100
den=conv([1/600^2 2*0.5/600 1],[1/388^2 2*1.24/388 1 0])
sys=tf(num,den)
margin(sys)
4. System calibration and dynamic performance index calculation
Generally, to meet the design requirements of an electro-hydraulic servo system, the phase margin should be between 30° and 60°, and the amplitude margin should be greater than 6dB. Therefore, by shifting the zero-dB line in the diagram to make the phase margin 50°, the gain margin G = 11dB, the crossover frequency, and the open-loop gain are...
The open-loop gain is obtained from the above operations.
Therefore, the amplifier's open-loop gain
Running the model and obtaining the system output results shows that the system is stable when the input...
The dynamic performance indicators of the system were analyzed using MATLAB.
5. Calculation of System Steady-State Error and Bandwidth
The system is type-zero in terms of interference. Since startup and cutting are not in the same action phase, static friction interference can be disregarded. (Servo amplifier...)
Temperature zero drift, servo valve zero drift and hysteresis, and the insensitivity zone of the actuator are assumed to be summed. The resulting position error is:
For command input, the system is Type I, and the speed error at maximum speed is...
The system bandwidth obtained by calling the MATLAB program to calculate the system bandwidth is:
6. Conclusion
Based on the analysis of the CNC machine tool table position servo system, this paper designs and calibrates the system according to the design requirements. Dynamic and static performance analysis of the calibrated system shows that the designed CNC machine tool table position servo system has the characteristics of fast response speed, short settling time, high control accuracy, reliability, stability, and effective suppression of internal and external disturbances, thus meeting the design requirements. Address: P.O. Box 76, 2010 Graduate Student Class, School of Automation, Qingdao University of Science and Technology, No. 53 Zhengzhou Road, Qingdao, 266042, China. Contact Person: Cai Dawei. Tel: 13165012078
