Design and Analysis of Disturbance Force Observer for Milling Cutting Force Compensation

Transcription

1 International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:7 No: Design and Analysis of Disturbance Force Observer for Milling Cutting Force Compensation M. Maharof, Z. Jamaludin, M. Minhat, N. A. Anang, T. H. Chiew and J. Jamaludin Abstract Eternal disturbances acting on a drive system affect its tracking performance. In milling machine, cutting forces generated from the physical interaction between cutting tool and the workpiece eerts additional loads to the drive system and if not properly damped, could lead to significant contour error and reduced quality of the finished product. This paper focuses on design and analysis of cascade P/PI position controller and an inversemodelbased disturbance (IMBDO) for disturbance forces compensation in milling machine. The position controller was designed based on gain margin and phase margins consideration of the open loop transfer function and system bandwidth. IMBDO was addedon to the control structure for disturbance imation and compensation using difference between control input signal and signal obtained from filtered system output with the inverse of the plant model. Two control configurations were considered, namely; cascade P/PI and cascade P/PI with IMBDO. This paper presents both numerical and eperimental results of the two designed control configurations performed on an XY milling table using measured cutting force. Results showed that cascade P/PI with IMBDO produced 8.78% less tracking error compared to cascade P/PI alone. Fast Fourier Transform analysis performed on the position tracking error of cascade P/PI with IMBDO showed that at frequency 6Hz, where errors were reduced by 76.% followed at frequency.hz a reduction of 67.9% in the amplitude of the cutting force harmonics. This research was financially supported by the Ministry of Higher Education, Malaysia and the Fundamental Research Grants Scheme (FRGS) with reference number of FRGS///TK/FKP//F8. M. Maharof is with the Department of Robotics and Automation, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, 76 Melaka, Malaysia ( madihah.maharof@yahoo.com.my). Z. Jamaludin is with the Department of Robotics and Automation, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, 76 Melaka, Malaysia ( zamberi@utem.edu.my). M. Minhat, N. A. Anang, T. H.Chiew and J. Jamaludin are with the Department of Robotics and Automation, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, 76 Melaka, Malaysia ( mohamad@utem.edu.my; amiraanang@gmail.com; fosterchiew87@hotmail.com; jailani@yahoo.com). Inde Term Cascade controller, Disturbance, Cutting force, Disturbance compensation I. INTRODUCTION High speed, high accuracy and precision are crucial issues in machining processes. A study by [] stated that inaccuracy of CNC machine tool during milling process is generally the results of errors initiating from machine components and deflections from cutting force. Cutting force is the nature condition of the milling process and occurs during the cutting process in machine tool application and cannot be avoided as it is generated from interaction between the cutting tool and the workpiece. The cutting force that acts as disturbance signals must be efficiently damped to preserve tracking and positioning accuracies. Cutting force is influenced by milling parameters [] such as feed rate, depth of cut and spindle speed. In literature, an improvement of various control strategies have been developed and validated to address compensation of cutting force in milling process. Adaptive controller and algorithms were employed by [] for cutting force compensation. In [], feedforward with neural network to compensate cutting force based on changes in milling parameters were applied. State was designed in [] to compensate cutting force while [] had proposed a repetitive controller to achieve high precision positioning for a ball screw driven stage. A disturbance force was designed and validated in [6] to imate eplicitly the eternal disturbance forces in ball end milling system. In addition, the inverse model based disturbance designed by [7] was shown to be effective over different types of input disturbance signals. The authors discussed effects of inverse model based disturbance on tracking performance during milling process. Literature reviews performed have shown that disturbance is an effective method to compensate for input disturbance especially cutting force. The objective of this paper is to design and validate cascade P/PI controller with addon inverse model based disturbance for milling operation. The organizations of this paper are as follows. The following section introduces the system setup and describes the system identification performed on the 76788IJMMEIJENS October 7 IJENS

2 International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:7 No: XY milling table ball screw driven system. This section is followed by section on methodology relating to cutting force identification and analysis. Section introduces designs of the positioning controller and disturbance. Results and discussion are shown in section while section 6 concludes the finding of this paper. II. EXPERIMENTAL SETUP A. System setup Fig. shows the equipment used in this research. System identification was performed based on measured frequency response function (FRF) generated from the measurement of output position signal and the corresponding input voltage to the drive system. The XY milling table applied consists of three positioning aes and each ais is driven by Panasonic MSMD GIU A.C. servo motors. Incremental encoder with resolution of.mm/pulse is located at each near end of all the aes. zais data collection and analysis purposes. From the singleinput singleoutput (SISO) signal, FRF of each drive system was imated using H imator [8]. A model was fitted on the measured FRF for the system transfer function using Fdident toolbo in MATLAB Simulink software [9]. Equation () shows a second order transfer function for a single ais of the ballscrew driven system; Z G U s A e Bs C std where U is the input voltage in volt (v), is the time delay in second (s) and Z is the table position in millimetre (mm). The system parameters identified are; A=78 mm/vs, B =6s, C=9.s and T d=.s. Personal computer (PC) with MATLAB and ControlDesk Digital signal Tracking condition Td DS (Digital Signal Processor) Digital encoder signal Analog signal () Signal to drive motor Encoder yais ais XY milling table Analog encoder signal Drives Amplifier Fig.. Schematic diagram of system setup Limit switch Fig.. GoogolTech XY milling table ball screw driven system B. System identification Fig. illustrates the schematic diagram of the eperimental setup. The setup consists of four main components, namely; a personal computer with MATLAB/Simulink and ControlDesk software, dspace DS Digital Signal Processing (DSP) board, an amplifier and a XY milling table ball screw driven unit. The host computer with ControlDesk software is integrated with the dspace DS digital signal processing (DSP) board. The DSP board is linked to the servo amplifier of the plant (XY milling table) for signal conversions and data gathering. The host computer acts as a central control processing unit providing necessary inputs to the plant and monitoring essential feedbacks for effective control of the positioning table. The DSP board is a data acquisition unit for III. CUTTING FORCE MEASUREMENT The workpiece used is aluminum and it is attached on Kistler Dynamometer []. Fig. shows a straight line milling cutting process was performed onto an aluminum block using HSS cutter of diameter mm with four flute cutter edges. Cuts were performed at spindle speeds of rpm, rpm and rpm. The cutting force was etracted using Kistler Dynamometer. Frequency analysis of the cutting force were obtained using Fast Fourier Transform (FFT) method []. Fig. shows the FFT analysis for different spindle speeds. The identified harmonic frequencies are 6Hz, 9Hz and.hz. The analysis showed different peaks of the force harmonics. In order to improve tracking performance, these peaks must be efficiently damped. Position controller provides for good tracking performance while the disturbance provides for good disturbance rejection IJMMEIJENS October 7 IJENS

3 International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:7 No: Workpiece (Aluminum) Tool Bit Kistler Dynamometer The cascade controller consists of two control loops.the first control loop is a velocity loop. The second control loop is a position loop and it encircles the velocity control loop. First, a velocity loop with proportionalintegral (PI) control was designed as shown in (); PI ki k p () s Net, the velocity open loop transfer function in () and closed loop transfer function in () are analysed. The velocity open and closed loop transfer functions are: V ol () Fig.. Aluminum block during milling process V cl () rpm rpm rpm Finally, the sensitivity function of the velocity loop is; Spectral Analysis of Cutting Force at rpm 6 Fig.. FFT cutting forces analysis at rpm rpm and (c) rpm spindle speed rotation IV. CONTROLLER AND OBSERVER DESIGN A. Design of position controller Fig. shows schematic diagram of a cascade controller. Reference Position, Zref (t) X: 6 Y: 7.97 ep (t) Position Loop Spectral Analysis of Cutting Force at rpm X: 9 Y:.9 6 Fig.. Schematic diagram of the cascade P/PI controller for a ball screw driven system Spectral Analysis of Cutting Force at rpm X:. Y:.9 6 (c) ev (t) u(t) P PI G(s) ˆ. Z V(s) Disturbance Forces, d(t) /k f Velocity Loop Output Position, Zout (t) Sv The velocity loop PI control parameters were selected based on gain margin and phase margin consideration of the velocity open loop transfer function. A reasonable value of gain margin and phase margin ensures stability and good transient response characteristics []. The PI parameters obtained for and are.66vs/mm and.7 Vs /mm respectively. Second, the position loop was designed around the velocity loop. The position open loop and closed loop characteristics are eamined for a proportional gain controller as in (6): k v s k v k p () (6) According to Fig., the position open loop transfer function in (7) and closed loop transfer function in (8) are: P PI Gˆ Pol PI Gˆ P PI Gˆ Pcl (8) P PI Gˆ The sensitivity function of position loop equals: S p (9) PI Gˆ P PI Gˆ Table I lists the gain margin and phase margin obtained for the velocity and position open loop transfer functions. Meanwhile, (7) ki 76788IJMMEIJENS October 7 IJENS

4 International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:7 No: 6 Fig.6 and showed the Nyquist stability criterion and sensitivity function for both loops respectively. Table I Gain margin and phase margin of velocity open loop and position open loop transfer function Imaginary Ais Magnitude (db) Gain margin Phase margin Velocity loop 9. db 6.7 deg Position loop. db 7.7 deg 6 7 Nyquist Diagram Bode Diagram System: S_p Frequency (Hz): 8. 8 Frequency (Hz) System: S_v Frequency (Hz): 6. V_ol P_ol Real Ais S_v S_p Fig. 6. Nyquist plots and Sensitivity function for the velocity open loop and position open loop transfer functions The disturbance is applied to the cascade P/PI controller for cutting force compensation. According to Fig. 7, Z ref is the reference signal for the system. Z is the actual output position signal in [mm].g P is the position controller of (6) and G PI is the velocity loop controller of (). G is the system model transfer function. k f is the force constant that converts disturbance signal from [N] to [V]. The disturbance design freedom is rricted to the selection of the inverse model G n and characteristics of the Qfilter. A low pass filter, known as the Qfilter [], was added to preserve stability. Structure for the Qfilter was sugged in []. The Qfilter applied was as follow; Q s where; m i qis i () s c n q i s are the filter numerator coefficients, c is the cutoff frequency and m and n are the order of the numerator and the order of the denominator respectively, with n > m. Design of IMBDO was analysed using frequency response approach to determine gain margin and phase margin of the controlled system. Table lists the gain margin and the phase margin of velocity open loop and position open loop transfer functions respectively. Fig. 8 and Fig. 9 illustrated the influenced of the disturbance on velocity open loop and position open loop transfer functions. Table II Gain margin and phase margin of velocity open loop and position open loop for system with and without Gain Margin Phase Margin No With No With Velocity loop 9. db 6.6 db 6.7 deg. deg Position loop. db 6.8 db 7.7 deg 7. deg B. Design of IMBDO Fig. 7 shows schematic diagram of the control scheme that consists of cascade position controller and IMBDO. Disturbance Forces, d /kf Reference Position, Zref ep(t) up ev(t) upi u GP GPI System, G. Z Low Pass Filter Position Velocity Controller Controller Q Gn V(s) Inverse Model Disturbance Observer Output Position, Z Position Loop Velocity Loop Fig.7. Schematic diagram of cascade P/PI with IMBDO 76788IJMMEIJENS October 7 IJENS

5 International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:7 No: 7 Imaginary Ais Nyquist Diagram Based on the presented Bode and Nyquist diagram of the position open loop transfer function, the disturbance increase the bandwidth of position loop by.7hz. The updated bandwidth is 9.9Hz. Meanwhile, Nyquist diagram of position open loop transfer function that confirm the loop stability and robustness. Magnitude (db) Magnitude (db) Real Ais Bode Diagram Fig. 8. Nyquist plots and Sensitivity function for the velocity open loop transfer function of the system with and without. Imaginary Ais System: Frequency (Hz): 9. Frequency (Hz) Nyquist Diagram Bode Diagram System: Frequency (Hz): 8. System: Frequency (Hz): Real Ais System: Frequency (Hz): 9.9 V. RESULT AND DISCUSSION The designed controller and were validated on the XY milling table. Eperiments were conducted by eerting the system with the measured cutting force. Input signal of amplitude mm and frequency.hz was applied to the system and the position errors were measured and analysed accordingly. The first harmonic frequencies for each measured cutting forces were 6Hz, 9Hz and.hz. Two analyses were performed, namely; Root Mean Square of Error (RMSE) and FFT analyses. Results showed that cascade P/PI with IMBDO produced 8.78% error reduction compared to cascade P/PI controller. Fig. shows RMSE for cascade P/PI controller and cascade/pi with IMBDO. Net, Fig. shows FFT results of the position error for cascade P/PI controller and cascade P/PI with IMBDO. Measured Cutting Force Tracking Error. RMSE=.6 mm. Fig.. RMSE of position tracking for Cascade P/PI controller and Cascade P/PI with IMBDO Measured Cutting Force Tracking Error. RMSE=.6 mm. 8 Frequency (Hz) Fig.9. Nyquist plots and Sensitivity function for the position open loop transfer function of the system with and without 76788IJMMEIJENS October 7 IJENS

6 International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:7 No: 8 X: 6 X: 6 X: 6 X: 6..e.89 Y:.89 Y:.89 Y:.e Y:.e Fig.. FFT position error for Cascade P/PI controller and Cascade P/PI with IMBDO X: 9 X: 9 X: 9 X: 9. X: 9 Y:.9 Y:.9 X: 9 Y:. Y:. Y:.9 Y: FFT Tracking Error. X:. X:. X:. X:. X:. Y:.9 Y:.9 X:. Y:.6e Y:.6e Y:.9 Y:.6e Table summarizes the values of the FFT position tracking error and percentage error reduction. Results showed significant reduction at all single harmonic frequencies of cascade P/PI with IMBDO compared to cascade P/PI controller. IMBDO was able to compensate disturbance forces acting on the system. However, two phenomenon were observed, namely; waterbed effect [] and ripple [6]. These are shown in Fig. and Fig. respectively. Due to waterbed effect, an increase in performance at some harmonic frequencies will yielded degradation of performance at other frequencies. The result showed that at 6Hz, errors were reduced by 76.% followed at.hz that shows a reduction of 67.9%. However, there was increase about % at frequency 9Hz. However, the magnitude of error at this frequency was really low at µm and the positioning performance was not affected much by this increment. Ripples are potentially caused by current measurement error due to current sensor offset and low input voltage during real cutting. Table III Results of FFT position tracking error for cascade P/PI controller and cascade P/PI with IMBDO Eperimental Analysis Results [mm] Frequency [Hz] Cascade P/PI Cascade P/PI with IMBDO Percentage Error Reduction [%] Fig.. Waterbed effect phenomenon observed for Cascade P/PI controller and Cascade P/PI with IMBDO Fig.. Ripple phenomenon during eperimental validation 76788IJMMEIJENS October 7 IJENS

7 International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:7 No: 9 VI. CONCLUSION As conclusion, cascade P/PI controller with IMBDO was successfully designed and eperimentally validated. The proposed control structure was superior in disturbance rejection when compared to conventional positioning controller. In addition, cascade P/PI with IMBDO was able to reduce significantly the position tracking error. However, the performance of IMBDO was limited by the bandwidth of the applied Qfilter, waterbed effect and ripple effect. As for future study, other approaches in solving waterbed effect and ripple needs to be addressed and implemented in the system thus further improving the performance of the controlled system. [] J. R. Ryoo, T. Y. Doh, M. J. Chung, Robust disturbance for the trackfollowing control system of an optical disk drive, Control Engineering Practice, vol., pp. 77 8,. [] S. Skogad, and I. Postlethwaite, Multivariable feedback control: Analysis and design, Vol., 7, New York: Wiley. [] T. T. Phuong, K. Ohishi, Y. Yokokura, C. Mitsantisuk, FPGAbased high performance force control system with frictionfree and noisefree force observation, IEEE Transactions on Industrial Electronics, vol. 6, no., pp. 99 8,. [6] N. Miyamoto, and K. Ohishi, Online tuning method for current measurement offsets and gain deviations for SPMSM, In: IEEE Association, IECON 8th Annual Conference on IEEE Industrial Electronics Society, Montreal, QC, 8 Oct., pp. 9 9,. VII. ACKNOWLEDGEMENT The authors would like to thank the Ministry of Higher Education for the funding of this research with the reference number FRGS///TK/FKP//F8.The authors would also like to thank Faculty of Manufacturing Engineering, Universiti Teknikal Malaysia Melaka (UTeM) for the facilities provided. REFERENCES [] J. Ni, CMC machine accuracy enhancement through realtime error compensation, Journal of Manufacturing Science and Engineering, 9 (November), 997, pp [] S. Kalpakjian and S. Schmid, Manufacturing Engineering and Technology. Singapore: Pearson Prentice Hall, 6, ch.. [] U. Zuperl, F. Cus and M. Reibenschuh, Neural control strategy of constant cutting force system in end milling, Robotics and Computer Integrated Manufacturing, vol. 7, no., pp. 8 9,. [] S. Huang, K. K. Tan, G. S. Hong and Y. S. Wong, Cutting force control of milling machine, Mechatronics, vol. 7, no., pp., 7. [] H. Fujimoto, and T. Takemura, Highprecision control of ballscrewdriven stage based on repetitive control using ntimes learning filter, IEEE Transactions on Industrial Electronics, vol. 6, no. 7, pp. 69 7,. [6] J. G. Njiiri, B. W. Ikua, and G. N. Nyakoe, Cutting force control for ball end milling of sculptured surfaces using fuzzy logic controller, Scientific Conference Proceedings,. [7] O. Kouhei, and T. Murakami, Advanced motion control in robotics, In Industrial Electronics Society, IECON 989 th Annual Conference of IEEE, pp. 6 9, 989. [8] R. Pintelon, and J. Schoukens, System identification: A frequency domain approach, John Wiley & Sons,. [9] L. Abdullah, Z. Jamaludin, T. H. Chiew, N. A. Rafan, and M. S. Mohamed, System identification of y table ballscrew drive using parametric and nonparametric frequency domain imation via deterministic approach, Procedia Engineering, vol., pp. 67 7,. [] Z. Jamaludin, J. Jamaludin, T. H. Chiew, L. Abdullah, N. A. Rafan, & M. Maharof, Sustainable cutting process for milling operation using disturbance, Procedia CIRP, vol. pp. 86 9, 6. [] P. Boucher, D. Dumur & K. F. Rahmani, Generalized predictive cascade control (GPCC) for machine tools drives, CIRP AnnalsManufacturing Technology, vol. 9, pp. 7 6, 99. [] C. J. Kempf, S. Kobayashi, Disturbance and feedforward design for a highspeed direct drive positioning table, IEEE Trans, on Control System Tech, vol. 7, no., pp. 6, IJMMEIJENS October 7 IJENS