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How to effectively improve the positioning accuracy of servo system

the positioning accuracy of CNC machine tools directly affects the machining accuracy of machine tools. Traditionally, the machine tool with stepper motor as the driving mechanism, due to the inherent characteristics of stepper motor, the repeated positioning accuracy of the machine tool can reach a pulse equivalent. However, the pulse equivalent of stepping motor cannot be very small, so the positioning accuracy is not high. The pulse equivalent of servo system can be much smaller than that of stepping motor system, but the positioning accuracy of servo system is difficult to reach a pulse equivalent. Since the CPU performance has been greatly improved, the positioning accuracy can be effectively improved by using software. We analyze the reasons why the conventional control algorithm leads to the large positioning accuracy error of the servo system, and propose a method of piecewise linear deceleration and accurate positioning in an open-loop manner, which has achieved good results in practice

I. causes and solutions of positioning error of servo system

generally, the control process of servo system is: speed up, constant speed, deceleration and low speed approaching the positioning point, and the whole process is position closed-loop control. The two processes of deceleration and low-speed approaching the positioning point have a very important impact on the positioning accuracy of the servo system

there are many specific implementation methods of deceleration control, including exponential law acceleration and deceleration algorithm and linear law acceleration and deceleration algorithm. The exponential law acceleration and deceleration algorithm has strong tracking ability, but its stability is poor when the speed is high, so it is generally suitable for machining with high tracking response requirements. The acceleration and deceleration algorithm of linear law has good stability and is suitable for fast positioning with a large range of speed changes

when selecting the deceleration law, we should not only consider the stability, but also consider the positioning accuracy when stopping. Theoretically, as long as the deceleration point is selected correctly, the deceleration of exponential law and linear law can be accurately located, but the difficulty is to determine the deceleration point. Generally, the determination methods of deceleration point are:

(1) if the same acceleration and deceleration law is adopted during starting and stopping, the deceleration point can be determined according to the relevant parameters and symmetry of the acceleration process

(2) calculate the deceleration point according to the relevant parameters such as feed speed, deceleration time and deceleration acceleration. Under the condition that high-speed CPU is very popular today, this is easy to realize for CNC servo system, and is more flexible than method (1)

during servo control, the software judges in each sampling cycle: if the remaining total feed is greater than the remaining feed corresponding to the deceleration point, the instantaneous feed speed remains unchanged (equal to the given value), otherwise, decelerate according to a certain law

theoretically, decelerate when the remaining total feed is exactly equal to the remaining feed corresponding to the deceleration point, and decelerate to stop at the positioning point according to the expected deceleration law. But in fact, when the servo system operates normally, the number of feedback pulses per sampling period is several, dozens, dozens or even more, so the actual deceleration point does not coincide with the theoretical deceleration point. As shown in Figure 1, the maximum error is equal to the number of pulses in the sampling period before deceleration. If the actual deceleration point is advanced, it may take a long time to reach the positioning point when the deceleration speed drops to a very low level according to the expected law. If the actual deceleration point lags behind the theoretical deceleration point, the speed when reaching the positioning point is still high, affecting the positioning accuracy and stability. Therefore, we propose that the piecewise linear reduction square spindle and its drive system are formed by a series of hardware product groups in the sheath extrusion

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Figure 1 deceleration point error press the" OK "key schematic diagram

in the process of approaching the positioning point at low speed, set the speed to V0 (mm/s), and the pulse equivalent of the servo system is δ （ μ m) , sampling period is τ (MS), then the number of pulses that should be fed back in each sampling period is: n0=v0 τ/δ。 Since the actual number of feedback pulses is an integer, there may be an error of one pulse, that is, at this time, the maximum value of speed detection error is l/n0= δ/(V0 τ)。 The smaller the sampling period and the lower the speed, the greater the speed detection error. In order to meet the requirement that the positioning accuracy is a pulse, V should be made small without reducing the physical, chemical and functional properties of raw materials, so that N0 ≤ 1. At this time, the speed detection error reaches 100% or even higher. If the position closed-loop control is still implemented at this time, it will inevitably cause great speed fluctuations and seriously affect the precise positioning of the servo mechanism. Therefore, we believe that position open-loop control should be adopted at this time to avoid speed fluctuation

II. Precise positioning of piecewise linear deceleration

1. Methods and steps

the characteristic of piecewise linear deceleration is that the deceleration point does not need to be accurately determined, and the speed curve of deceleration process is shown in Figure 2. First, the most unfavorable situation is discussed, that is, the deceleration process starts from the highest speed of the servo system. The specific deceleration steps are:

(1) the initial speed VG slows down to V2 with the acceleration A2 through the AB section, and runs T2 sampling cycles at the uniform speed V2 in the BC section. BC is used to compensate the error of the deceleration point a. The maximum error of point a is the number of pulses in a sampling period corresponding to VG ng=vg τ/δ， When the speed is V2, the number of pulses in a sampling period is n2=v2 τ/δ， As long as T2 ≥ ng/n2=vg/v2 is guaranteed, the BC time period can compensate for the error of deceleration point a

(2) the speed V2 is reduced to V1 by the acceleration A1 through the CD section, and T1 sampling cycles are run at the uniform speed of V1 in the de section. The error of deceleration point C is compensated by the time period of de. Similarly, T1 ≥ v2/v1 should be guaranteed. Since the speed V1 is low, assume that v1=5mm/s, pulse equivalent δ= one μ m. Sampling period τ= 1ms, the number of pulses that should be fed back per unit sampling period is n1=5, and the maximum speed detection error can reach 20%. Therefore, open-loop control can be adopted from the beginning of this process to avoid speed fluctuation caused by speed detection error. It is worth noting that the open-loop control algorithm should include the dead time compensation and zero drift compensation modules of the servo mechanism

(3) speed V1 decreases to V0 through EF section with acceleration A1, and t0 runs at V0 constant speed in FG section

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