0
Research Papers

A New Parabolic Sliding Mode Filter Augmented by a Linear Low-Pass Filter and Its Application to Position Control

[+] Author and Article Information
Myo Thant Sin Aung

Department of Mechatronic Engineering,
Yangon Technological University,
Yangon 11012, Myanmar
e-mail: nayaye1@gmail.com

Zhan Shi

Department of Mechanical Engineering,
Kyushu University,
Fukuoka 819-0395, Japan

Ryo Kikuuwe

Department of Mechanical Engineering,
Kyushu University,
Fukuoka 819-0395, Japan
e-mail: kikuuwe@ieee.org

1Present address: Googol Technology (Shenzhen) Ltd., Shenzhen 518057, China.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 27, 2016; final manuscript received June 21, 2017; published online November 10, 2017. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 140(4), 041005 (Nov 10, 2017) (10 pages) Paper No: DS-16-1573; doi: 10.1115/1.4037732 History: Received November 27, 2016; Revised June 21, 2017

This paper proposes a new sliding mode filter augmented by a linear low-pass filter (LPF) for mitigating the effect of high-frequency noise. It is based on the derivation of three new variants of Jin et al.'s (2012, “Real-Time Quadratic Sliding Mode Filter for Removing Noise,” Adv. Rob., 26(8–9), pp. 877–896) parabolic sliding mode filter (J-PSMF) and investigation on their frequency-response characteristics. The new filter is developed by augmenting one of the variants of J-PSMF by a second-order linear LPF. It has better balance between the noise attenuation and signal preservation than both linear LPFs and J-PSMF. The effectiveness of the new filter is experimentally evaluated on a direct current (DC) servomotor equipped with an optical encoder. This paper also shows the application of the proposed filter to a positioning system under PDD2 (proportional, derivative, and second derivative) control, which successfully realizes the noise attenuation and the nonovershooting response simultaneously.

Copyright © 2018 by ASME
Topics: Filters , Signals
Your Session has timed out. Please sign back in to continue.

References

Aung, M. T. S. , Shi, Z. , and Kikuuwe, R. , 2014, “ A New Noise Reduction Filter With Sliding Mode and Low-Pass Filtering,” IEEE Conference on Control Applications (CCA), Juan Les Antibes, France, Oct. 8–10, pp. 1029–1034.
Su, Y. X. , Zheng, C. H. , Mueller, P. C. , and Duan, B. Y. , 2006, “ A Simple Improved Velocity Estimation for Low-Speed Regions Based on Position Measurements Only,” IEEE Trans. Control Syst. Technol., 14(5), pp. 937–942. [CrossRef]
Willaert, B. , Corteville, B. , Reynaerts, D. , Van Brussel, H. , and Vander Poorten, E. B. , 2011, “ A Mechatronic Analysis of the Classical Position-Force Controller Based on Bounded Environment Passivity,” Int. J. Rob. Res., 30(4), pp. 444–462. [CrossRef]
Chawda, V. , and O'Malley, M. K. , 2011, “ A Lyapunov Approach for SOSM Based Velocity Estimation and Its Application to Improve Bilateral Teleoperation Performance,” ASME Paper No. DSCC2011-6181.
Chawda, V. , and O'Malley, M. K. , 2012, “ On the Performance of Passivity-Based Control of Haptic Displays Employing Levant's Differentiator for Velocity Estimation,” IEEE Haptics Symposium, Vancouver, BC, Canada, Mar. 4–7, pp. 415–419.
Chawda, V. , Celik, O. , and O'Malley, M. K. , 2014, “ A Method for Selecting Velocity Filter Cut-Off Frequency for Maximizing Impedance Width Performance in Haptic Interfaces,” ASME. J. Dyn. Syst. Meas. Control, 137(2), p. 024503. [CrossRef]
Kikuuwe, R. , Kanaoka, K. , Kumon, T. , and Yamamoto, M. , 2015, “ Phase-Lead Stabilization of Force-Projecting Master-Slave Systems With a New Sliding Mode Filter,” IEEE Trans. Control Syst. Technol., 23(6), pp. 2182–2194. [CrossRef]
Chen, F. , and Dunnigan, M. , 2002, “ Comparative Study of a Sliding-Mode Observer and Kalman Filters for Full State Estimation in an Induction Machine,” IEE Proc. Electr. Power Appl., 149(1), pp. 53–64. [CrossRef]
Alessandri, A. , 2003, “ Sliding-Mode Estimators for a Class of Non-Linear Systems Affected by Bounded Disturbances,” Int. J. Control, 76(3), pp. 226–236. [CrossRef]
Levant, A. , 1993, “ Sliding Order and Sliding Accuracy in Sliding Mode Control,” Int. J. Control, 58(6), pp. 1247–1263. [CrossRef]
Levant, A. , 2003, “ Higher-Order Sliding Modes, Differentiation and Output-Feedback Control,” Int. J. Control, 76(9–10), pp. 924–941. [CrossRef]
Levant, A. , 2007, “ Principles of 2-Sliding Mode Design,” Automatica, 43(4), pp. 576–586. [CrossRef]
Davila, J. , Fridman, L. , and Levant, A. , 2005, “ Second-Order Sliding-Mode Observer for Mechanical Systems,” IEEE Trans. Autom. Control, 50(11), pp. 1785–1789. [CrossRef]
Daly, J. , and Wang, D. , 2014, “ Time-Delayed Output Feedback Bilateral Teleoperation With Force Estimation for n-DOF Nonlinear Manipulators,” IEEE Trans. Control Syst. Technol., 22(1), pp. 299–306. [CrossRef]
M'Sirdi, N. , Rabhi, A. , Fridman, L. , Davila, J. , and Delanne, Y. , 1993, “ Second Order Sliding-Mode Observer for Estimation of Vehicle Dynamic Parameters,” Int. J. Veh. Des., 48(3–4), pp. 190–207.
Levant, A. , 1998, “ Robust Exact Differentiation Via Sliding Mode Technique,” Automatica, 34(3), pp. 379–384. [CrossRef]
Mobayen, S. , 2015, “ Fast Terminal Sliding Mode Tracking of Non-Holonomic Systems With Exponential Decay Rate,” IET Control Theory Appl., 9(8), pp. 1294–1301. [CrossRef]
Mobayen, S. , 2015, “ Finite-Time Tracking Control of Chained-Form Nonholonomic Systems With External Disturbances Based on Recursive Terminal Sliding Mode Method,” Nonlinear Dyn., 80(1), pp. 669–683. [CrossRef]
Mobayen, S. , 2015, “ An Adaptive Fast Terminal Sliding Mode Control Combined With Global Sliding Mode Scheme for Tracking Control of Uncertain Nonlinear Third-Order Systems,” Nonlinear Dyn., 82(1), pp. 599–610. [CrossRef]
Mobayen, S. , 2015, “ Fast Terminal Sliding Mode Controller Design for Nonlinear Second-Order Systems With Time-Varying Uncertainties,” Complexity, 21(2), pp. 239–244. [CrossRef]
Mobayen, S. , 2015, “ An LMI-Based Robust Controller Design Using Global Nonlinear Sliding Surfaces and Application to Chaotic Systems,” Nonlinear Dyn., 79(2), pp. 1075–1084. [CrossRef]
Mobayen, S. , 2015, “ An Adaptive Chattering-Free PID Sliding Mode Control Based on Dynamic Sliding Manifolds for a Class of Uncertain Nonlinear Systems,” Nonlinear Dyn., 82(1), pp. 53–60. [CrossRef]
Madani, T. , Daachi, B. , and Djouani, K. , 2016, “ Non-Singular Terminal Sliding Mode Controller: Application to an Actuated Exoskeleton,” Mechatronics, 33, pp. 136–145. [CrossRef]
Madani, T. , Daachi, B. , and Djouani, K. , 2016, “ Modular-Controller-Design-Based Fast Terminal Sliding Mode for Articulated Exoskeleton Systems,” IEEE Trans. Control Syst. Technol., 25(3), pp. 1133–1140. [CrossRef]
Zhu, S. , Jin, X. , Yao, B. , Chen, Q. , Pei, X. , and Pan, Z. , 2016, “ Non-Linear Sliding Mode Control of the Lower Extremity Exoskeleton Based on Human-Robot Cooperation,” Int. J. Adv. Rob. Syst., 13(5), pp. 1–10.
Eker, İ. , 2006, “ Sliding Mode Control With PID Sliding Surface and Experimental Application to an Electromechanical Plant,” ISA Trans., 45(1), pp. 109–118. [CrossRef] [PubMed]
Emaru, T. , and Tsuchiya, T. , 2003, “ Research on Estimating Smoothed Value and Differential Value by Using Sliding Mode System,” IEEE Trans. Rob., 19(3), pp. 391–402. [CrossRef]
Han, J. , and Wang, W. , 1994, “ Nonlinear Tracking-Differentiator,” J. Syst. Sci. Math. Sci., 14(2), pp. 177–183 (in Chinese). http://caod.oriprobe.com/articles/1385655/fei_xian_xing_gen_zong___wei_fen_qi_.htm
Perruquetti, W. , and Barbot, J. , 2007, Sliding Mode Control in Engineering, Marcel Dekker, New York.
Jin, S. , Kikuuwe, R. , and Yamamoto, M. , 2012, “ Real-Time Quadratic Sliding Mode Filter for Removing Noise,” Adv. Rob., 26(8–9), pp. 877–896. http://www.tandfonline.com/doi/abs/10.1163/156855312X633011
Jin, S. , Kikuuwe, R. , and Yamamoto, M. , 2012, “ Parameter Selection Guidelines for a Parabolic Sliding Mode Filter Based on Frequency and Time Domain Characteristics,” J. Control Sci. Eng., 2012, p. 923679.
Kikuuwe, R. , 2014, “ A Sliding-Mode-Like Position Controller for Admittance Control With Bounded Actuator Force,” IEEE/ASME Trans. Mechatronics, 19(5), pp. 1489–1500. [CrossRef]
Acary, V. , and Brogliato, B. , 2010, “ Implicit Euler Numerical Scheme and Chattering-Free Implementation of Sliding Mode Systems,” Syst. Control Lett., 59(5), pp. 284–293. [CrossRef]
Acary, V. , Brogliato, B. , and Orlov, Y. V. , 2012, “ Chattering-Free Digital Sliding-Mode Control With State Observer and Disturbance Rejection,” IEEE Trans. Autom. Control, 57(5), pp. 1087–1101. [CrossRef]
Wang, B. , Brogliato, B. , Acary, V. , Boubakir, A. , and Plestan, F. , 2015, “ Experimental Comparisons Between Implicit and Explicit Implementations of Discrete-Time Sliding Mode Controllers: Toward Input and Output Chattering Suppression,” IEEE Trans. Control Syst. Technol., 23(5), pp. 2071–2075. [CrossRef]
Huber, O. , Acary, V. , and Brogliato, B. , 2015, “ Lyapunov Stability and Performance Analysis of the Implicit Discrete Sliding Mode Control,” IEEE Trans. Autom. Control, 61(10), pp. 3016–3030. [CrossRef]
Huber, O. , Acary, V. , Brogliato, B. , and Plestan, F. , 2016, “ Implicit Discrete-Time Twisting Controller Without Numerical Chattering: Analysis and Experimental Results,” Control Eng. Pract., 46, pp. 129–141. [CrossRef]
Smirnov, G. V. , 2002, Introduction to the Theory of Differential Inclusions, American Mathematical Society, Providence, RI.
Cortés, J. , 2008, “ Discontinuous Dynamical Systems,” IEEE Control Syst. Mag., 28(3), pp. 36–73. [CrossRef]
Jin, S. , Kikuuwe, R. , and Yamamoto, M. , 2014, “ Improving Velocity Feedback for Position Control by Using a Discrete-Time Sliding Mode Filtering With Adaptive Windowing,” Adv. Rob., 28(14), pp. 943–953. [CrossRef]
Cheng, G. , and Hu, J.-G. , 2014, “ An Observer-Based Mode Switching Control Scheme for Improved Position Regulation in Servomotors,” IEEE Trans. Control Syst. Technol., 22(5), pp. 1883–1891. [CrossRef]
Alagoz, B. B. , Ates, A. , and Yeroglu, C. , 2013, “ Auto-Tuning of PID Controller According to Fractional-Order Reference Model Approximation for DC Rotor Control,” Mechatronics, 23(7), pp. 789–797. [CrossRef]
Dieulot, J.-Y. , and Colas, F. , 2009, “ Robust PID Control of a Linear Mechanical Axis: A Case Study,” Mechatronics, 19(2), pp. 269–273. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

State trajectories of parabolic sliding mode filters: (a) J-PSMF (1), (b) M1-PSMF (7), (c) M2-PSMF (8), and (d) M3-PSMF (10). The magnitude of x˙2 is F in the white regions and HF in the gray regions.

Grahic Jump Location
Fig. 2

Frequency responses of PSMFs. The input amplitude is Au = 10 and the timestep size is T = 0.001 s. Note the use of different values of F between M3- and other PSMFs.

Grahic Jump Location
Fig. 3

Frequency response of M2-PSMF and other PSMFs. The input amplitude is Au = 10 and the timestep size is T = 0.001 s. The F values are F = 340 s−2 for M3-PSMF while F = 20,000 s−2 for other PSMFs.

Grahic Jump Location
Fig. 4

Time-domain response of J-PSMF and M2-PSMF (T = 0.001 s, F = 20,000 s−2): (a) Noiseless sinusoidal input signal (u(t) = Ausin(2πfut), Au = 10, fu = 10 Hz) and outputs. The results of M2-PSMF with H = 3 and H = 100 are overlapping. (b) Noisy input signal and outputs. (Note the use of different H-values between J-PSMF and M2-PSMF.)

Grahic Jump Location
Fig. 5

Block diagram of the new filter

Grahic Jump Location
Fig. 6

Frequency response of the new filter (cutoff frequency fc = 1 Hz, F = 20,000 s−2). The input amplitude is Au = 10 and the timestep size is T = 0.001 s.

Grahic Jump Location
Fig. 7

Frequency response of J-PSMF, M2-PSMF (F = 20,000 s−2), new filter (F = 20,000 s−2, fc = 1 Hz), and LPFs (fc = 25 Hz). The input amplitude is Au = 10 and the timestep size is T = 0.001 s.

Grahic Jump Location
Fig. 8

Time-domain response of filters to a common input signal u(t)

Grahic Jump Location
Fig. 9

Comparison of the implementation of 2-LPF using bilinear transform (2-LPF-BLT) and Euler's method (2-LPF-BE). The timestep size is T = 0.001 s. (a) Comparison in a low frequency range and (b) comparison in a high frequency range.

Grahic Jump Location
Fig. 10

Experimental setup

Grahic Jump Location
Fig. 11

Effects of fc and F: (a) effects of fc on high-frequency components, (b) effects of fc on the AE, and (c) effects of fc (2-LPF and the new filter) and effects of F (J-PSMF and the new filter) on the tradeoff between IHFC and AE

Grahic Jump Location
Fig. 12

Results of open-loop experiments: 2-LPF versus new filter. Note that the red and blue lines are overlapping in the bottommost figure.

Grahic Jump Location
Fig. 13

Results of open-loop experiments: J-PSMF versus new filter. Note that the red and blue lines are overlapping in the bottommost figure.

Grahic Jump Location
Fig. 14

Block diagram of the closed-loop position control system

Grahic Jump Location
Fig. 15

Results of set-point control for 10 deg input: (a) comparison of results obtained under PD, PDD2 without a filter, and PDD2 with the new filter, (b) comparison of the new filter and 2-LPF under PDD2, and (c) comparison of the new filter and J-PSMF under PDD2. Here, it was set as H = 3 in PSMFs.

Grahic Jump Location
Fig. 16

Results of trajectory-tracking control: (a) desired trajectory. (b) Comparison of position error obtained under PD, PDD2 without a filter, and PDD2 with the new filter. (c) Comparison of position error obtained under PDD2 with the new filter and 2-LPF. (d) Comparison of position error obtained under PDD2 with the new filter and J-PSMF. (e) Actuator torques for each control scheme in (b)–(d). Here, it was set as H = 3 in PSMFs. The gray circles in the graph of J-PSMF highlight the points where noisy sound occurred in the actuator.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In