Integral sliding mode control for flexible ball screw drives with matched and mismatched uncertainties and disturbances

Abstract

The design of servo controllers for flexible ball screw drives with matched and mismatched disturbances and uncertainties is focused to improve the tracking performance and bandwidth of ball screw drives. A two degrees of freedom mass model is established based on the axial vibration characteristics of the transport ball screw, and the controller of an adaptive integral sliding mode is proposed combining the optimal design of state feedback gain matrix K to restrain the vibration and the matched disturbances and uncertainties. Then for the counteraction of the mismatched disturbances and uncertainties, a nonlinear disturbance observer is also developed. The trajectory tracking performance experiments and bandwidth analysis were conducted on experimental setup with the proposed control method. It is proved that the adaptive integral sliding mode controller has a high tracking performance and bandwidth especially for the axial vibration characteristics model of ball screw drives. And the ball screw tracking accuracy also has a considerable improvement with the application of the proposed nonlinear disturbance observer.

Keywords

ball screw drives / matched and mismatched disturbances and uncertainties / axial vibration characteristics / adaptive integral sliding mode control / nonlinear disturbance observer

References

[1] AltintasY, VerlA, BrecherC, UriarteL, PritschowG. Machine tool feed drives [J]. CIRP Annals–Manufacturing Technology, 2011, 60(2): 779-796

[2] DongL, TangW-cheng. Hybrid modeling and analysis of structural dynamic of a ball screw feed drive system [J]. Mechanics, 2013, 19(3): 316-323

[3] VaranasiK K, NayfehS A. The dynamics of lead-screw drives: Low-order modeling and experiments [J]. Transactions-American Society of Mechanical Engineers Journal of Dynamic Systems Measurement and Control, 2004, 126(2): 388-396

[4] DongL, TangW-c, BaoD-fei. Interpolating gain-scheduled H_∞ loop shaping design for high speed ball screw feed drives [J]. ISA Transactions, 2015, 55: 219-226

[5] SepasiD, NagamuneR, SassaniF. Tracking control of flexible ball screw drives with runout effect and mass variation [J]. IEEE Transactions on Industrial Electronics, 2012, 59(2): 1248-1256

[6] AltintasY. Manufacturing automation: Metal cutting mechanics, machine tool vibrations, and CNC design [M]. New York: Cambridge University Press, 20122527

[7] ChoJ U, LeQ N, JeonJ W. An FPGA-based multiple-axis motion control chip [J]. IEEE Transactions on Industrial Electronics, 2009, 56(3): 856-870

[8] YaoB, Al-MajedM, TomizukaM. High-performance robust motion control of machine tools: An adaptive robust control approach and comparative experiments [J]. IEEE/ASME Transactions on Mechatronics, 1997, 2(2): 63-76

[9] BoucherP, DumurD, RodriguezP. Robustification of CNC controllers for machine tools motor drives [J]. CIRP Annals-Manufacturing Technology, 2003, 52(1): 293-296

[10] LeeK J, KimH M, KimJ S. Design of a chattering-free sliding mode controller with a friction compensator for motion control of a ball-screw system [J]. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2004, 218(5): 369-380

[11] AltintasY, ErkorkmazK, ZhuW H. Sliding mode controller design for high speed feed drives [J]. CIRP Annals-Manufacturing Technology, 2000, 49(1): 265-270

[12] ErkormazK, KamalzadehA. High bandwidth control of ball screw drives [J]. CIRP Annals-Manufacturing Technology, 2006, 55(1): 393-398

[13] OkwudireC, AltintasY. Minimum tracking error control of flexible ball screw drives using a discrete-time sliding mode controller [J]. Journal of Dynamic Systems, Measurement, and Control, 2009, 131(5): 051006-12

[14] GordonD J, ErkormazK. Accurate control of ball screw drives using pole-placement vibration damping and a novel trajectory prefilter [J]. Precision Engineering, 2013, 7(2): 308-322

[15] DongL, TangW-cheng. Adaptive backstepping sliding mode control of flexible ball screw drives with time-varying parametric disturbances and uncertainties [J]. ISA Transactions, 2014, 53(1): 110-116

[16] HanifzadeganM, NagamuneR. Switching gain-scheduled control design for flexible ball-screw drives [J]. Journal of Dynamic Systems, Measurement, and Control, 2014, 136(1): 014503

[17] ApkarianP, AdamsR J. Advanced gain-scheduling techniques for uncertain systems [J]. IEEE Transactions on Control Systems Technology, 1998, 6121-32

[18] LiaoY-l, ZhangM-j, WanL, LiYe. Trajectory tracking control for underactuated unmanned surface vehicles with dynamic uncertainties [J]. Journal of Central South University, 2016, 23: 370-378

[19] UtkinV, ShiJ X. Integral sliding mode in systems operating under uncertainty conditions [C]// Proceedings of the 35th IEEE Conference on Decision and Control. Lobe, Japan: IEEE, 199645914596

[20] BejaranoF J, FridmanL M, PoznyakA S. Output integral sliding mode for min-max optimization of multi-plant linear uncertain systems [J]. IEEE Transactions on Automatic Control, 2009, 54(11): 2611-2620

[21] ChenW-h, BallanceD J, GawthropP J, O’REILLYJ. A nonlinear disturbance observer for robotic manipulators [J]. IEEE Transactions on Industrial Electronics, 2000, 47(4): 932-938

[22] ChenW-hua. Nonlinear disturbance observer-enhanced dynamic inversion control of missiles [J]. Journal of Guidance, Control, and Dynamics, 2003, 26(1): 161-166

[23] YangJ, LiS-h, YuX-huo. Sliding-mode control for systems with mismatched uncertainties via a disturbance observer [J]. IEEE Transactions on Industrial Electronics, 2013, 60(1): 160-169

[24] ErkormazK, AltintasY. High speed CNC system design. Part II: modeling and identification of feed drives [J]. International Journal of Machine Tools and Manufacture, 2001, 41(10): 1487-1509