The most important function of the servo system of CNC machine tools is to ensure the output speed and distance to accurately duplicate the input requirements. In order to ensure the realization of this function, the servo system of the CNC machine tool basically includes a current control loop, a speed control loop and a three-loop control system of the position control loop. The current loop ensures that the current of the servo system is optimal when it is dynamic; the speed loop and position loop ensure that the servo system accurately replicates the speed and position required by the input signal at any instant output speed and position. The evaluation servo system often starts from the static characteristics and dynamic characteristics of the system. This article evaluates the performance of the servo system from the following specific indicators.

Requirements for output characteristics

It refers to the static characteristics of the servo motor and driver being controlled. Based on this characteristic, it is judged whether there is enough output torque in the required speed range to drive the load. Is there a sufficient overload multiple to start the mechanical load. The characteristics of the motor are shown in Figure 1. General servo motor torque as the main parameter. The continuous working torque must not exceed the continuous working area. The intermittent work area must not be exceeded during braking and acceleration/deceleration. In order to work reversely and under braking, the servo system also requires four-quadrant operation.

Fig. 1 Torque characteristics of quadrant I

Analysis of system dynamic characteristics

The dynamic characteristic of the system is to describe the situation that the output of the system changes with time under the input of the system.

Speed â€‹â€‹and current control systems, both digital and analog control methods, can be analyzed using discrete and continuous mathematical methods. In order to simplify the analysis in engineering, according to Shannon's theorem, the sampling frequency f0 of the digital system is selected, and the highest frequency in the signal spectrum of the digital system is fmax. In this way, the system can be analyzed in a continuous system using the Laplace transfer function.

F0 â‰¥ fmax (1)

The sampling period T0 is the reciprocal of the sampling frequency.

That is, T0 < 1/f0, then how to determine the highest frequency in the digital system signal spectrum? Taking the current loop as an example, the current loop is composed of a current regulator, a power PWM amplifier, a motor winding current generating circuit, and current feedback when the back-EMF action is ignored; the electromagnetic time constant of the winding is generally on the order of tens to hundreds of microseconds. The corresponding sampling period orders of magnitude and the general use of power modules are shown in Table 1.

Table 1 Relationship between sampling period and power module

Two control methods often used in the speed loop

In order to analyze the speed system, the current loop is approximated as 1; Because the shaft end of the servo motor applies a load, the dynamic characteristics of the servo system are affected by the damping and the inertial load. In order to improve the dynamic performance of the system, the PID algorithm is often used in engineering. The PI and IP control methods are often used in the speed loop. In essence, both PI and IP are proportional-integrated. However, the sequence of PI control software processing is proportional and post-integration, and the emphasis is on the proportion; while the order of IP control software processing is the integration and post-proportion, and the emphasis is on integration.

lPI control: Figure 2 shows the proportional-integral control, in which K2 is the proportional gain, K1 is the integral gain, KT is the motor torque coefficient, and J is the inertia of the servo motor shaft. Structurally, PI emphasizes the relationship between proportions. Therefore, after the system receives the speed command, the torque is increased for a relatively short time. The PI control is suitable for the large machinery with low mechanical rigidity, large gap, poor response performance, and the requirement for the system to quickly keep up with the system. At this time, K2 can be increased and K1 can be reduced. If the rigid machine needs to improve the start-up characteristics, PI control can also be implemented.

Figure 2 PI control

lIP control: Figure 3 shows the integral ratio control, where K1 is the integral gain and K2 is the proportional gain. KT is the motor torque factor. Structural IP emphasizes the relationship of points. Therefore, there will be a certain delay when the machine starts to start, and the system is relatively stable to start. Therefore, IP control is mainly used in systems that require stable start-up. For example, if a certain machine is a rigid, fast-response small machine, in order to increase the damping of the disturbance and stabilize the starting, IP control can be used, and the speed loop can be increased appropriately. Gain K1.

Figure 3 IP control

From the above analysis and calculation of the relevant frequency characteristics, it can be obtained that: PI has a large high-frequency gain, thus improving the responsiveness. Phase-frequency characteristics: PI falls close to 90Â° in the frequency domain; while IP falls closer to 180Â° and thus PI control is more stable; both PI and IP have the same anti-disturbance characteristics.

Speed â€‹â€‹loop sampling time: Select the current loop sampling time 2-3 times. At present, the sampling period of the servo system is approximately as shown in Table 2:

Table 2 Sampling cycle of the servo system three rings

After analyzing the speed loop, look at the current loop again and generally adopt the structure of PI or IP. The analysis method is the same.

In addition to the structure of PI and IP, compensation is sometimes performed using the reference model PI regulator.

Load inertia

Influence on the dynamic characteristics of the servo system

The inertia on the servomotor axis includes the inertia of the motor and the load. The above analysis of the speed loop does not consider load inertia. The direct influence of the load inertia degrades the amplitude and frequency characteristics of the speed loop. In general, the greater the inertia, the worse the dynamic characteristics. From Figure 2 to Figure 3, the load inertia has an effect on the dynamic characteristics of the servo system. The general choice of load inertia is not more than 3 to 5 times the motor inertia.

Position control dynamics

Figure 4 Simplified view of servo system position control loop

After the above analysis, the speed loop is approximately 1 when the speed gain is large; then the position control is shown in FIG. 4 . You can think of it as an integral link. The closed loop is a first-order inertial link, and the time constant is the reciprocal of the position gain Kp in FIG. The size of Kp has a great relationship with the mechanical load characteristics. The larger the Kp, the faster the response. General large machine tools Kp=20-40/s, medium and small machine tools Kp=30-60/s. With the continuous improvement of control system performance, in the high-speed and high-precision systems, the speed loop gain is improved by improving the current loop characteristics. In order to eliminate mechanical resonances and other measures, Kp can be greater than 100/s.

Figure 5 Simplified diagram of the feed servo system

Relationship between system maximum speed and position resolution

The servo system of CNC machine tools is a digital position control system. With the maximum output speed unchanged, the higher the resolution of the position, the higher the system requirements. For the convenience of analysis, let the gain of the system current loop and speed loop be large enough. Therefore, the servo system diagram can be simplified as shown in Fig. 5; Kp in Fig. 4 is the simplified position gain of the servo system diagram, and its meaning is the position system. When there is a unit error of detection, how much is the speed V of the system.

That is, Kp=V/Îµ(2)

In equation (2), when the position gain is constant and the system's error is at its maximum, its output speed is also the maximum Vmax. If the position controller has an N-bit binary error register, the maximum error is 2N-1, in order to achieve The maximum Vmax, formula (3) must be satisfied.

Kp(2N-1)â‰¥Vmax (3)

The larger the Vmax is, the larger the number of N is in the case of constant Kp; the more complicated the system is. Let 2N>>1, then:

N â‰¥ lg(Vmax/Kp)/lg2 (4)

For example, a machine tool design requires a resolution of 1nm, a maximum speed of 1m/min=109nm/min, an equivalent of 16.7x106pps, and a position gain of 100/s. According to equation (4), an error register of 18 bits or more is required to satisfy the index. Claim. If the position gain is 25/s, an error register of more than 20 bits is required to meet the index requirement. The lower the gain, the larger the required number of bits.

Electronic gear ratio

Taking into account the difference between the input and output units, the feed servo system of the CNC machine tool is simplified to Figure 5, where C, D are the ratio of the command unit to the detection unit. R2 is the minimum movement unit, M2 is the detection unit, R1 is the minimum input increment, or the command unit; M1 is the number of pulses of the encoder PC per revolution of the servo motor; set the machine movement of the servo motor to L, through C, The coefficient transformation of D can yield:

R1/C=R2(5)

L/M1Ã—D=M2(6)

Since R2=M2, C/D=R1Ã—M1/L (7)

C/D is called the electronic gear ratio; changing C, D can make the servo system get the output of different size detection unit when inputting the same minimum input increment. For example, the minimum input increment is 1 Î¼m, the detection unit is 0.1 Î¼m, C=10, L=5 mm, M1=10000 p/r, then D=5.

Servo System Improvements

Analog servo systems require a lot of extra hardware to increase performance. However, digital servo systems can easily add functionality and improve performance through software algorithms and communication interface resources. such as:

Feedforward control

Using feed-forward control is a method to effectively reduce the steady-state following error. It is essentially a compensation control. Using digital servo position feedforward control algorithms, the position loop control lag can be reduced. After the feedforward is added, the following error is changed from Equation (2) to Equation (8).

e=V/[ KP/(1-a)] (8)

Where a is the feed forward coefficient; In order to reduce the vibration at high speed, it is also possible to increase the speed feed forward control.

Inner ring structure improvement

l The current loop adds "1/2 PI" control: when the load is low current, the current loop has PI control characteristics; when the load is high current, it has the characteristics of IP control, so that the current due to large current can be compressed Overshoot to meet the need for high speed, high precision machining control;

l Dual-position loop control: Machines with large clearances are stable when working in semi-closed loops, but they may vibrate when they are closed loops. For this purpose, a dual position control method is adopted; when the transition process is performed, the system is operated in a semi-closed loop, and when positioned, the system is operated in a fully closed loop;

l Vibration Damping Control: The position closed loop system sometimes uses the encoder on the motor shaft as the speed feedback, and uses the separate encoder as the position feedback; when the acceleration and deceleration, the connection between the motor and the machinery may become bad, making the mechanical The speed is slightly different from the speed of the motor, which makes it difficult to control the machine. For this purpose, a vibration damping control link is established, which feedbacks the speed difference between the motor and the machine to the torque command to reduce the vibration of the machine.

Observer function: For example, use software to estimate the control status and establish a state observer. It can be used to estimate motor current, speed to identify unintended currents and control to eliminate mechanical oscillations.

Digital filter

In digital servo systems, digital filters are often used to remove mechanical resonances. This filter has the following types: Low-pass filters, various band-stop filters.

Nonlinear compensation

Such as pitch compensation, reverse compensation, etc.

Conclusion

Since modern CNC systems use AC digital servo technology, software algorithms can be used to improve the performance of the servo system and increase functionality. But for the basic performance of the servo system is the design of the numerical control system should first grasp. It includes static characteristics, dynamic characteristics, fast and resolution relationships, and electronic gear ratios.

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