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.

References

1.
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
.
2.
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
.
3.
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
.
4.
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.
5.
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
.
6.
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
.
7.
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
.
8.
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
.
9.
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
.
10.
Levant
,
A.
,
1993
, “
Sliding Order and Sliding Accuracy in Sliding Mode Control
,”
Int. J. Control
,
58
(
6
), pp.
1247
1263
.
11.
Levant
,
A.
,
2003
, “
Higher-Order Sliding Modes, Differentiation and Output-Feedback Control
,”
Int. J. Control
,
76
(
9–10
), pp.
924
941
.
12.
Levant
,
A.
,
2007
, “
Principles of 2-Sliding Mode Design
,”
Automatica
,
43
(
4
), pp.
576
586
.
13.
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
.
14.
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
.
15.
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
.
16.
Levant
,
A.
,
1998
, “
Robust Exact Differentiation Via Sliding Mode Technique
,”
Automatica
,
34
(
3
), pp.
379
384
.
17.
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
.
18.
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
.
19.
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
.
20.
Mobayen
,
S.
,
2015
, “
Fast Terminal Sliding Mode Controller Design for Nonlinear Second-Order Systems With Time-Varying Uncertainties
,”
Complexity
,
21
(
2
), pp.
239
244
.
21.
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
.
22.
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
.
23.
Madani
,
T.
,
Daachi
,
B.
, and
Djouani
,
K.
,
2016
, “
Non-Singular Terminal Sliding Mode Controller: Application to an Actuated Exoskeleton
,”
Mechatronics
,
33
, pp.
136
145
.
24.
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
.
25.
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.
26.
Eker
,
İ.
,
2006
, “
Sliding Mode Control With PID Sliding Surface and Experimental Application to an Electromechanical Plant
,”
ISA Trans.
,
45
(
1
), pp.
109
118
.
27.
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
.
28.
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
29.
Perruquetti
,
W.
, and
Barbot
,
J.
,
2007
,
Sliding Mode Control in Engineering
,
Marcel Dekker
,
New York
.
30.
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
31.
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
.
32.
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
.
33.
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
.
34.
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
.
35.
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
.
36.
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
.
37.
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
.
38.
Smirnov
,
G. V.
,
2002
,
Introduction to the Theory of Differential Inclusions
,
American Mathematical Society
,
Providence, RI
.
39.
Cortés
,
J.
,
2008
, “
Discontinuous Dynamical Systems
,”
IEEE Control Syst. Mag.
,
28
(
3
), pp.
36
73
.
40.
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
.
41.
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
.
42.
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
.
43.
Dieulot
,
J.-Y.
, and
Colas
,
F.
,
2009
, “
Robust PID Control of a Linear Mechanical Axis: A Case Study
,”
Mechatronics
,
19
(
2
), pp.
269
273
.
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