Performance Robustness and Stiffness Analysis on a Machine Tool Servo

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PERFORMANCE ROBUSTNESS AND STIFFNESS ANALYSIS ON A MACHINE TOOL SERVO Jia-Yush Yen Hui-Man Chang Professor Graduate Student I Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617 e-mail : jycl1((I(ccms.ntu.cdu.tw Keywords: Machine tool servo, motion control, servo stiffuess, PDFF (Younkin, 1989, Alter and Tsao, 1994, Choi, et. al. , 1999, Cuttino, et. al., 1999, Arakawa and Miyata, 1996, Xiao, 1996, Liu, et. al., 1998). Some of the results have tried to add machine intelligence to improve servo performance (Fomaro and Dow, 1988, Wang and Kwok, 1994, Wu and Huang, 1997, Lin and Chen, 1997, lshigami, et. al., 1994, Wang and Yen, 1999, Tesar and Drzik, 1995, Ulyanov, et. al., 1995, McGookin, et. al., 2000, Wu and Liu, 1995, Tamg, et. al., 1999). Very few results have directly addressed the problem of the most suitable underlying control algorithm. This paper would like to examine the behavior of the most commonly used controllers such as the PID controller, the PDF controller (Ohm, 1994, Nagy and Bradshaw, 1998) and the Model Based Compensators (Koichi, et. al., 1991, Gawthrop and MacCallum, 1992), and probably to offer a reasonable comparison based on the machine tool servo considerations. Because the tests will be conducted on a programmable controller with a commercial EDM machine, the study should be practical and should offer better insight to the interested readers.

Abstract The machine tool servo design is very different from the traditional high performance servo systems. The machine tool servo systems seldom use the common control synthesis process . In stead, most high performance machine tool systems still use the classic PlO or PDF controllers in conjunction with complicate friction and temperature compensation algorithms. This paper would like to explore the reason, and have studied the different designs based on a house designed servo control board. The performance robustness was tested both numerically and experimentally. The numerical tests conducted with PlO, PDF, and LQG controllers showed that the PlO controller is the easiest to achieve good performance, but the PDF controller contains the best performance robust margin. Experimental results also indicated that the PDF controller provides the most robust stiffuess margin. Copyright © 2002 IFA C

1. Introduction The CNC machine tool servo uses very different design philosophy to formulate its control algorithm. The machine tool servo design do not stress on a precise system model. Instead, the servo system tries to achieve very high performance with very good robustness properties. It is quite understandable in the machine tool servo design the precise model is not emphasized. Usually, machine dynamics often contributed relatively little amount of effect during cutting. The system experiences mainly the cutting force and the material removing action. It would not be practical for the servo system design to base on any particular cutting process, and a robust universally high performance system is desirable.

2. System Description The experiment is based on a PC based CNC controller implemented on a small-hole EDM machine (Figure. I). The CNC controller is the result of a project between the NTU Precision System Control Laboratory with the Chanceux Co. Taiwan.

Looking more closely into the design, one notices that even though many modem control design techniques are now available, most machine tool servo designs still based on the well-known PDF control architecture. More delicate processes are then added to eliminate the effect of backlash, axis spikes, friction, etc. The previous researches have discussed machine servo problems in some specific domains like stiction, axes spikes, etc

Figure I. The EDM machine and the CNC controller interface

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The CNC controller is composed of an Industrial PC with a house designed motion card. The IPC runs windows CE for user interface and task coordination. It allows trajectory programming, speed specification, s-curve motion, etc. The motion card is based on a TMS320F243 microconrroller [24,25 ,26) with an FPGA to decode the optical encoder and to communicate with the IPC . The motion card in equipped with four channel I2-bit DIA for multi-axes servo control. The encoder on the EDM machine has a resolution of 5f!m, and with three 180w DC servo motor to drive the different axes. The tachometer sensitivity on the servomotor is 7VlKrmp.

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The controller setup basically allows for not only the change of the control parameters, but also allows for the reprogramming of the controller structure. Therefore different servo control algorithms can be implemented on thc test machine. This paper examined the popular PlO controller, the PDF controller, and the more advanced Model Based Compensator (MBC) derived from the LQG.

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Figure 3. The LFT ' 6tructure for PlO control system As shown in figure 3, the LFT expression for the PlO control system can thus be described as

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3. Robustness AnalYSis The system identification result for the y-axis motion table on the EDM machine is shown in figure 2. The servo controller is then designed based on the identification result. ,.,~

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3.2 PDF control: The PDF controller uses both the output position and the positioning error for its input, therefore, the controller variations for the proportional gain and the differential gain are treated separately.

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This paper examined the popular PlO controller, the PDF controller, and the more advanced Model Based Compensator (M BC) derived from the LQG. According to the machine setup for parameter tuning, the system uncertainties due to controller parameter can be represented as follows :

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The PlO controller takes the output position error from the worktable and computes the control effort. It is intuitive to treat the controller as a single block . Thus it is reasonable to treat the controller variation

Figure 4. The LFT structure for the PDF control system As shown in figure 4, the PDF control system can be described by

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Q33 =(/ +GKTLfIGKTL With the LFT for the different types of control algorithm, we can perturb the parameters with 20%, 40%, 60010, 80% and 100010 of their nominal values. The robust performance margin can be calculated with MATLAB. If the computed robust performance margin is greater than I, the system performance is robust the specified control gain variations.

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Figure 6 shows the robust performance margin for the PlO and PDF control system. One observes better performance robustness with the PDF contro\1er. The PlO control maintains performance robustness until around 35% of gain variation. The PDF controller, on the other hand, maintained performance robustness until close to 50% gain variation.

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The MBC control system derived from the LQG design procedure requires separate computation of a state feedback gain and an estimator gain. It is thus reasonable to separately treat the variations for the state feedback gain, K, and the observer gain, L. The LFT representation can then be written as:

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Figure 6. Robust performance margin for PlO and PDF control systems

Figure 5. The LFT structure for MBC control system

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These margins are illustrated by actual1y implementing them on the test machine. The experimental results show the response of the machine making a I .25 nun step move. Figure 7 shows the experimental result of the effect of gain variation on the system performance with PlO controller. One easily sees that the rise time for the system sustained 1000/. gain variation and maintained stability; however, vibration starts appearing when the variation exceeds 40%. Figure 8 shows the effect of gain variation on the PDF controller. System stability is still maintained throughout. The vibration does not appear until there is 60% gain variation. The situations for the model-based compensator arc shown in figure 9. We didn't show the robustness margin curve for the model-based compensator because it is extremely sensitive to parameter variation. The experimental results agree with the calculation. The machine starts vibrating seriously with only very small changes in the state feedback gain or the observer gain. It is clear that some form of loop recovery is necessary in this case. Basically,

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Q32 Q33 r Let T=(S/ -A-BK +LC)-I Then QII =(LCTL - L )Q31 - LCT QI2 =(LCTL-L)Q32 -LCTB QI3 =L-LCTL+(LCTL-L)Q33 Q21 =KT - KTLQ31 Q22 =KTB - KTLQ32 Q23 =KTL - KYLQ33

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all three situations agree with the calculation closely. Both the numerical results and the experimental results showed that the PDF controller maintains performance robustness against up to 50% of gain perturbation; while the PID controller only sustained performance robustness up to 35%.

Cuttino, J.F., A.C. Miller, Jr., D.E. Schinstock, "Performance optimization of a fast tool servo for single-point diamond turning On machines, IEEElASME Trans. Mechatronics, Vol.4, No.2, June 1999, pp. 169-179. Dal

5. Conclusions The paper investigated some of the rationales behind the machine tool servo design. The basic idea is to try to analyze the effect of different servo designs and to experimentally verify the results. For this purpose, a PC based controller on a commercial EDM machine was setup. The PC based controller is configured so that the different types of control can be implemented. The robustness properties of some popular controllers were than analyzed. It is found out that even though the traditional PID controller seems to achieve a equally good performance, the PDF controller do exhibit more robust property against parameter vanaltons. The model-based compensator also attains fairly good servo performance; however, it is very sensitive to any change in it gains with some form of loop recovery. The results from the analysis are then verified by implementing the controllers on the EDM machine.

Y.Ohm, "Analysis of PID and PDF for motion control compensators systems",IEEE,1994

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6. Acknowledgement: This project is supported in part by the Industrial Technology Research Institute, R.O.C. under project number 893K5IAQ2, which is a subcontract from the Ministry of Economic Affairs, R.O.C., and in part by the National Science Council under project number NSC 89-TPC-7-002-008

Liu, Jiancheng, K. Yamazaki, Y. Yokoyama, "Dynamic gain motion control with multi-axis trajectory monitoring for machine tool systems," Proceedings of the 1998 International Workshop on Advanced Motion Control, AMC'98, 1998, P 316-321

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TMS320F2431F2411C242 DSP Controllers System and Peripherals Reference Guide, 2000 TMS320ClxlC2x1C2xx1C5x Assembly Language Tools User's Guide,1995 Ulyanov, S.V.; Yamafuji, K.; Miyagawa, K.; Tanaka, T.; Fukuda, T., "Intelligent fuzzy motioni control of mobile robot for service use," Proceedings of the 1995 IEEElRSJ International Conference on Intelligent Robots and Systems, Part 3 (of 3) Aug 5-9 1995 v3 Pittsburgh, PA, USA, 1995 P 486-489 Wang, Liang; Yen, John, "Extracting fuzzy rules for system modeling using a hybrid of genetic algorithms and Kalman filter," Fuzzy Sets and Systems, Volume: 101, Issue: 3, February I, 1999, pp. 353-362

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Wang, P.; Kwok, D.P.; "Optimal design of PlO process controllers based on genetic algorithms," Control Engineering Practice, v 2 n 4 Aug 1994 p 641-648 Wu; T. S., Liu, J. C., "Fuzzy control of rider-motorcycle system using genetic algorithm and auto-tuning," Mechatronics, Volume: 5, Issue: 4, June, 1995, pp. 441-455 Wu, Chia-Ju ; Huang, Ching-Huo , 'A Hybrid Method for Parameter Tuning of PlO Controllers," Journal of the Franklin Institute, Volume: 334, Issue: 4, July, 1997, pp. 547-562 Xiao, Ben-Xian, ' 'TIle main control mode and fuzzy control strategy of CNC system for gear hobbing and grinding machine," Proceedings of the IEEE International Conference on Industrial Technology, 1996, pp. 643-646. Younkin, G ., "Modeling machine tool feed servo drives using simulation techniques to predict performance," Conference Record of the Industry Applications Society Annual Meeting, vol.2, 1989, 1989, Page(s): 1699 -1706

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