Pith. sign in

REVIEW 5 major objections 3 minor 46 references

Design and Application of Energy-saving Sub-Optimal Sliding Mode Control

T0 review · 5 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A two-threshold sliding-mode controller can track a moving rough surface as accurately as the standard one while consuming less fuel.

desk verdict A cleanly written consolidation of prior ES-SOSMC results with a new simulation application, but a dimensional slip in the example's disturbance-to-control ratio undermines the parameterization. read the letter →

arxiv 2505.05918 v1 pith:JPDJLVIC submitted 2025-05-09 eess.SY cs.SY

Michael Ruderman This is my paper · ORCID
classification eess.SYcs.SY
keywords energy-savingsub-optimalslidingmodecontrolsecond-orderfuel-optimalcontrol-offchatteringdescribingfunctionanalysisstiffpositionmovingroughsurface
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper is trying to establish that the energy-saving sub-optimal sliding-mode controller (ES-SOSMC), a second-order sliding-mode law that inserts control-off intervals during finite-time convergence, can be tuned so that its total fuel consumption is guaranteed to be lower than that of the conventional sub-optimal sliding-mode controller (SOSMC) for the same task. The tuning is a constrained minimization of an energy-cost function over two anticipation parameters, $\beta_1$ and $\beta_2$, whose admissible values form a triangle defined by the convergence conditions (22)--(24). The paper then puts the controller to a stiff position-control application: an actuator-held tool scanning or machining a moving rough surface, with a pre-computed disturbance bound. In simulation, ES-SOSMC matches the tracking and stabilization performance of SOSMC while its fuel norm stays below the linear upper bound $U t$ and the saving grows over time. The payoff is energy saving without the usual robust-tracking performance loss.

What carries the argument

The central object is the ES-SOSMC control law $u(t)=-0.5U\,\mathrm{sign}(\sigma-\beta_1\sigma_M)-0.5U\,\mathrm{sign}(\sigma-\beta_2\sigma_M)$ for $t>t_{M1}$, with the initial phase $\bar u(t)=-U\,\mathrm{sign}(\sigma(t)-\sigma(0))$ on $[0,t_{M1}]$, where $\sigma_M$ is the most recent extremum of the sliding variable. The two thresholds $\beta_1,\beta_2$ create a three-state relay: control is positive, negative, or zero depending on where $\sigma$ sits relative to the two threshold lines, and the zero zone is the energy-saving mechanism. The parameterization is carried by the cost functions (27)--(28) and the constrained minimization (29) subject to the hard constraints (30)--(31), which select threshold pairs inside the admissible triangle (22)--(24). A separate harmonic-balance analysis, using the describing function (37) of the three-state relay against the double-integrator-plus-actuator transfer function, predicts the chattering frequency and amplitude in equations (39)--(40).

What would settle it

Measure or simulate the fuel norm $E=\int_0^{T_f}|u|\,dt$ for the scanning benchmark with a surface roughness large enough that $G+\Phi>0.00003$ N, or with intermittent tool-surface separation, and compare with the SOSMC benchmark; observing $E$ meet or exceed $U t$, or worse tracking error than SOSMC, would falsify the energy-saving guarantee (30).

Watch

Extended reading notes

Core claim

The central claim is that the ES-SOSMC defined by equations (20)--(21) and parameterized by the constrained minimization (29)--(31) is globally finite-time convergent for relative-degree-two systems with bounded matched perturbations, and that its fuel consumption is strictly lower than that of the conventional SOSMC while tracking and stabilization performance are equivalent. The control law is the parallel connection of two SOSMC terms with the same authority $0.5U$ but different anticipation factors $\beta_1>\beta_2$; when the two sign terms have opposite signs, the control output is zero, creating the energy-saving control-off phase. The paper's energy-cost functions, equations (27)--(28), express fuel consumed during convergence, and the hard constraint (30) enforces the saving. In the application, a tool in non-separating contact with a randomly rough moving surface must hold a constant scanning distance or a fixed machining position; with $\Delta/U=0.3$, the pairs $(\beta_1,\beta_2)=(0.85,0.27)$ and $(0.97,0.05)$ yield the same target-distance behavior as SOSMC while keeping the fuel norm below $U t$. The describing-function analysis adds that residual chattering caused by parasitic actuator dynamics has a larger amplitude and a lower frequency for ES-SOSMC than for SOSMC.

Load-bearing premise

The energy-saving guarantee rests on the pre-calculated disturbance bound $G+\Phi=0.00003$ N being valid and on the tool never separating from the moving surface; if the true disturbance exceeds that bound or contact is lost, the tuning ratio $\Delta/U=0.3$ no longer holds and the promised saving is not guaranteed.

Editorial extensions

If this is right

  • The energy-saving guarantee is quantitative: for any fixed $\beta_1$ obeying the upper bound (31), the constrained minimization (29) delivers a $\beta_2$ for which the ES-SOSMC cost (27) is strictly smaller than the SOSMC cost (28).
  • In the scanning benchmark, both locally optimal pairs $(\beta_1,\beta_2)=(0.85,0.27)$ and $(0.97,0.05)$ keep the same relative-distance accuracy as SOSMC with $\beta_1=0.65$, while their fuel norms stay below the linear upper bound $U t$ and the gap widens over time.
  • The same design applies to the machining scenario because that task reduces to stabilization and the plant and control parameters scale in the same way; the chapter reports the same design procedure and similar energy-saving performance.
  • Chattering is not eliminated but is characterized: with parasitic actuator dynamics, ES-SOSMC oscillates at a lower frequency and higher amplitude than SOSMC, with $\omega_o$ and $\sigma_A$ given by (39)--(40).

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the saving accumulates with time, the method pays off most in long-duration contact operations such as scanning, grinding, and milling rather than in short transients; the paper's own examples are of the long-duration type.
  • The same two-threshold construction could in principle be layered onto other second-order sliding-mode algorithms, such as twisting or super-twisting, when a relative-degree-two sliding variable and bounded actuation are available; the paper does not analyze those variants.
  • The practical guarantee depends on the pre-set disturbance bound $G+\Phi=0.00003$ N. A natural test is to vary the surface roughness amplitude until the bound is exceeded and measure when the fuel curve touches $U t$, which would mark the limit of the energy-saving regime.
  • Since chattering amplitude is larger for ES-SOSMC, applications with tight positioning noise tolerances may need to trade some energy saving for a smaller $\beta_1-\beta_2$ separation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 3 minor

Summary. The manuscript presents the energy-saving sub-optimal sliding mode control (ES-SOSMC) introduced in [35], summarizing its control law, finite-time convergence conditions, energy-cost parameterization via a constrained minimization, and describing-function based chattering analysis. It then applies the controller to a stiff position-control problem in which a tool scans a moving rough surface, comparing tracking performance and a fuel-consumption norm against conventional SOSMC. A second machining scenario is described but not simulated in detail.

Significance. If the validation were sound, the paper would be a useful consolidation of ES-SOSMC and a relevant application to AFM-like scanning tasks. The explicit fuel metric (1), the constrained minimization (29)-(31), and the describing-function estimates (37)-(40) are concrete and potentially transferable tools. However, the paper does not provide machine-checked proofs, code, or a quantitative statistical validation, and the main application example contains a parameterization inconsistency that currently prevents the claimed energy-saving guarantee from being demonstrated.

major comments (5)
  1. [§4.2, Eq. (43), Figs. 4-5] The parameterization of the simulation is inconsistent with the stated disturbance-to-control ratio. With m=0.0005 kg, G+Phi=0.00003 N and U=0.2 N, Eq. (43) gives Delta=0.06 m/s^2, while the normalized control amplitude in plant (8) is U/m=400 m/s^2, so Delta/(U/m)=1.5e-4, not 0.3. The pairs (0.85,0.27), (0.97,0.05) and the benchmark beta1=0.65 are taken from the Delta/U=0.3 panels of Figs. 4-5, so the simulated plant is not in the regime for which these parameters and the energy-saving guarantee (30) were computed. Please correct the normalization or recompute the parameterization for the actual ratio.
  2. [§4.2, Eqs. (42)-(43)] The bound G+Phi=0.00003 N is asserted without derivation, measurement, or sensitivity analysis. Since the convergence conditions (22)-(24), the cost functions (27)-(28), and the guarantee (30) all depend on Delta, an underestimate of this bound would invalidate the energy-saving claim and could also violate the finite-time convergence conditions. Provide a derivation or measurement of the bound and a sensitivity study showing the behavior for larger Delta.
  3. [§3.3, §4.2, Fig. 11] The hard constraint (30) enforces J - Jhat < 0 by construction, so the energy-saving result is not an empirical finding unless the simulated comparison is validated quantitatively. Fig. 11(b) shows only single trajectories of a stochastic excitation; no energy-saving percentage, no multiple realizations, and no error bars are reported. Please add a quantitative statistic such as the final E_ES/E_SOSMC ratio with confidence intervals, and state the number of realizations used.
  4. [§4.3] The machining scenario is described only qualitatively and the section explicitly states that a detailed presentation is omitted. Since the abstract and introduction claim a demonstration for both scanning and machining, the machining application claim is not supported by any simulation or experimental result. Either add a simulation for the machining case or restrict the claim to the scanning application.
  5. [§3.2-3.3, Eqs. (22)-(28)] The central theoretical assertions are cited to [35] and not derived in this manuscript: the convergence conditions (22)-(24), the convergence-time bound (25), the reaching and contraction factors Omega and eta, and the cost functions (27)-(28) are defined only by reference. Because the energy-saving guarantee (30) and the example parameter choices rest on these formulas, the paper would be more convincing if the derivations were reproduced in an appendix or if the manuscript explicitly framed itself as a survey whose original analysis is in [35].
minor comments (3)
  1. [§4.2, Fig. 10] The caption of Fig. 10 gives the reference distance as B=2 um, while the text states B=0.2 um; please make these consistent.
  2. [§3.4, Eq. (40)] Equation (40) appears to have a units or typographical problem: as written, the right-hand side has dimension 1/s^2 rather than the dimension of sigma_M. Please check against [35] and correct.
  3. [§4.3] In the sentence comparing parameters to the scanning case, the cross-reference 'section 4.3' should presumably read 'section 4.2'; please correct this and any similar internal cross-reference errors.

Circularity Check

1 steps flagged · score 4.0 of 10

Energy-saving 'guarantee' is inserted as constraint (30) of the parameterization optimization, so the analytical claim is by construction; the independent fuel-norm simulation limits the circularity.

  1. self definitional [Section 3.3, Eqs. (29)-(31)]
    "the following minimization problem [35] min_{β1,β2}[J(β1,β2,U,Δ) − Ĵ(β1,U,Δ)] (29) is formulated under the hard constraint J(β1,β2,U,Δ) − Ĵ(β1,U,Δ) < 0. (30) The latter condition is strictly required in order to guarantee that for any fixed β1 the ES-SOSMC consumes less energy in comparison to the conventional SOSMC."

    The inequality (30) is the feasibility condition defining which (β1,β2) are accepted by the optimization, not a property derived from the closed-loop plant. Any solution of (29)-(31) must satisfy J−Ĵ<0 by construction, so the paper's statement that the ES-SOSMC 'guarantees' lower energy consumption than the SOSMC is a restatement of the hard constraint rather than an independent result. The simulation in Fig. 11(b) computes the actual fuel norm E=∫|u|dt from the simulated control signals and does provide independent evidence, which is why the circularity is only partial; but the analytical guarantee advertised in the abstract is exactly the constraint, not a derivation.

full rationale

Score 4 reflects one partial circular step. The parameterization method in Section 3.3 defines 'energy-saving' solutions by the hard constraint (30), so the analytical guarantee that ES-SOSMC consumes less energy than SOSMC is by construction. However, the application section does not rely solely on that guarantee: it simulates the actual plant (41) and evaluates E=∫|u|dt from the real control signal, showing lower fuel curves for the ES-SOSMC configurations. That independent simulation prevents the central claim from being fully circular. The chapter also imports the convergence conditions and energy-cost expressions from the same authors' prior work [35] without derivation; this is a normal self-citation for a summary chapter, and the simulation provides partial validation. A separate numerical inconsistency—the Δ/U=0.3 ratio in Section 4.2 is not consistent with Eq. (43) and the stated m and U—is a correctness risk rather than a circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper's demonstrable new content is the application simulation; almost all mathematical machinery (control law, convergence inequalities, energy costs, describing functions, chattering estimates) is carried over from the author's previous papers [35] and [34]. The application adds several effective free parameters (beta1, beta2, U, G+Phi, surface amplitude, velocity) and relies on unverified modeling assumptions, while no code or data are shipped.

free parameters (5)
  • beta1, beta2 (ES-SOSMC anticipation factors) = (0.85, 0.27) and (0.97, 0.05) for Delta/U = 0.3
    Chosen by solving the constrained minimization (29)-(30) of the energy cost functions J and J_hat; these values determine the control-off intervals and therefore the claimed energy saving.
  • beta1 (SOSMC comparison) = 0.65
    Assigned as the globally optimal beta1 for the SOSMC energy cost J_hat at Delta/U = 0.3, cf. Fig. 4, to give a fair comparison.
  • Control amplitude U = 0.2 N
    Design parameter chosen so that the disturbance-to-control ratio Delta/U = 0.3, used to generate the admissible parameter triangle and the optimized pairs.
  • Disturbance bound G+Phi = 0.00003 N
    Pre-calculated upper bound for the surface-induced disturbance and actuator disturbance in (41)-(43); no derivation is given, and it fixes Delta.
  • Surface roughness amplitude and velocity = max peak-to-peak approx 0.5 um; v = 100 um/s
    The roughness coefficient S in the PSD (44) is not explicitly given; the generated x0(t) is calibrated to the stated peak-to-peak range, so the stochastic excitation is effectively fitted.
assumptions (4)
  • domain assumption The cost functions J and J_hat (Eqs. 27-28) and the convergence-time bounds (25) from [35] correctly model worst-case fuel consumption of ES-SOSMC and SOSMC.
    These formulas are used unchanged in the parameterization and in the comparison. They are not re-derived or independently verified in this chapter.
  • domain assumption For the controlled plant, the relative degree between sigma and u is two and the matched perturbations satisfy |p| <= Delta with Delta = (G+Phi)/m after assuming unity input gain.
    This grounds the application in the general ES-SOSMC framework; the gain normalization and the scalar bound are assumed rather than derived from the AFM parameters.
  • domain assumption The tool never separates from the moving rough surface, and the surface height x0(t) is a stationary Gaussian process generated by the first-order filter (46).
    This is introduced in Sections 4 and 4.1; if contact is lost or the Gaussian PSD model is inaccurate, the disturbance bound (42) and the plant model may be invalid.
  • domain assumption Chattering analysis via the describing function (37)-(40) from [35] is valid for the ES-SOSMC relay and the linear part W(jw).
    The DF and harmonic balance solution (33) are taken from [35] and used to draw conclusions about residual oscillations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Design and Application of Energy-saving Sub-Optimal Sliding Mode Control." pith.science (2026). https://pith.science/paper/JPDJLVIC

@misc{pith2026250505918,
  author       = {Pith},
  title        = {Pith review of: Design and Application of Energy-saving Sub-Optimal Sliding Mode Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JPDJLVIC}},
  note         = {Machine review of arXiv:2505.05918}
}
read the original abstract

The recently introduced energy-saving extension of the sub-optimal sliding mode control (SOSMC), which is known in the literature for the last two and half decades, incorporates a control-off mode that allows for saving energy during the finite-time convergence process. This novel energy-saving algorithm (denoted by ES-SOSMC) assumes the systems with relative degree two between the sliding variable and the switching control with a bounded magnitude, while the matched upper-bounded perturbations are not necessarily continuous. The design and practical application of the ES-SOSMC are the subject of this chapter. A method for parameterizing the ES-SOSMC through a constrained minimization of the energy cost function is recalled which guarantees the total energy consumption is lower than that of the conventional SOSMC. Also the residual steady-state oscillations (chattering), occurring when additional (actuator) dynamics are taken into account, are addressed. An application example for scanning and machining a rough surface, both of which require a stiff position control in contact with a moving surface, demonstrates practical suitability of the control. Here, ES-SOSMC is compared with SOSMC by showing an equivalent tracking and stabilization performance and evaluating the energy-saving operation with respect to a fuel consumption norm.

Figures

Figures reproduced from arXiv: 2505.05918 by the authors.

Figure 7
Figure 7. The negative reciprocal of (35) is a straight line lyi [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 7
Figure 7. Following to that, can directly conclude that the cor [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [35]

    Energy-saving sub-optimal sliding mode control with bounded actuation

    Michael Ruderman, Alessandro Pisano, and Elio Usai. Ene rgy-saving sub-optimal sliding mode control with bounded actuation. arXiv preprint arXiv:2305.07891, 2023

    work page Pith review arXiv 2023

  2. [34]

    Experimental benchmarking of energy -saving sub-optimal sliding mode control

    Michael Ruderman. Experimental benchmarking of energy -saving sub-optimal sliding mode control. In IEEE 17th International Workshop on Variable Structure Sys tems (VSS) , pages 208–213, 2024

    work page 2024

  3. [1]

    Analysis of stability an d performance of a cascaded PI sliding-mode control DC–DC boost converter via LPRS

    Ayman Al Zawaideh and Igor Boiko. Analysis of stability an d performance of a cascaded PI sliding-mode control DC–DC boost converter via LPRS. IEEE Transactions on Power Electronics, 37(9):10455–10465, 2022

    work page 2022

  4. [2]

    Chatter stability of met al cutting and grinding

    Yusuf Altintas and Manfred Weck. Chatter stability of met al cutting and grinding. CIRP annals, 53(2):619–642, 2004

    work page 2004

  5. [3]

    Minimum-fuel feedback control systems: second-order case

    Michael Athans. Minimum-fuel feedback control systems: second-order case. IEEE Transac- tions on Applications and Industry , 82(65):8–17, 1963

    work page 1963

  6. [4]

    Fuel-optimal control of a double integra l plant with response time constraints

    Michael Athans. Fuel-optimal control of a double integra l plant with response time constraints. IEEE Transactions on Applications and Industry , 83(73):240–246, 1964

    work page 1964

  7. [5]

    Nonlinear Control Engineering - Describing Function Analy sis and Design

    Derek Atherton. Nonlinear Control Engineering - Describing Function Analy sis and Design . Workingam Beks, 1975

    work page 1975

  8. [6]

    Modelling and simulation of process: machine interaction in grinding

    Jan Aurich, Dirk Biermann, Heribert Blum, Christian Brec her, Carsten Carstensen, Berend Denkena, Fritz Klocke, Matthias Kr ¨oger, Paul Steinmann, and Klaus Weinert. Modelling and simulation of process: machine interaction in grinding. Production Engineering, 3:111–120, 2009

    work page 2009

Show all 46 references
  1. [7]

    Out put tracking control of uncertain nonlinear second-order systems

    Giorgio Bartolini, Antonella Ferrara, and Elio Usai. Out put tracking control of uncertain nonlinear second-order systems. Automatica, 33(12):2203–2212, 1997

    1997

  2. [8]

    Cha ttering avoidance by second-order sliding mode control

    Giorgio Bartolini, Antonella Ferrara, and Elio Usai. Cha ttering avoidance by second-order sliding mode control. IEEE Transactions on Automatic Control, 43(2):241–246, 1998

    1998

  3. [9]

    A survey of applications of second-order sliding mode control to mechanical systems

    Giorgio Bartolini, Alessandro Pisano, Elisabetta Punta , and Elio Usai. A survey of applications of second-order sliding mode control to mechanical systems. International Journal of Control, 76(9–10):875–892, 2003

    2003

  4. [10]

    Discontinuous control systems: frequency-domain analysi s and design

    Igor Boiko. Discontinuous control systems: frequency-domain analysi s and design . Birkhaeuser, 2009

    2009

  5. [11]

    Parameter tuning of second-order sliding mode controllers for linear plants with dynamic actuators

    Igor Boiko, Leonid Fridman, Rafael Iriarte, Alessandro Pisano, and Elio Usai. Parameter tuning of second-order sliding mode controllers for linear plants with dynamic actuators. Automatica, 42(5):833–839, 2006

    2006

  6. [12]

    Analysis of chattering in sys- tems with second-order sliding modes.IEEE Transactions on Automatic Control, 52(11):2085– 2102, 2007

    Igor Boiko, Leonid Fridman, Alessandro Pisano, and Elio Usai. Analysis of chattering in sys- tems with second-order sliding modes.IEEE Transactions on Automatic Control, 52(11):2085– 2102, 2007

    2007

  7. [13]

    An activ e tool holder and robust lpv control design for practical vibration suppression in internal tur ning

    Ziv Brand, Matthew Cole, and Nikolay Razoronov. An activ e tool holder and robust lpv control design for practical vibration suppression in internal tur ning. Control Engineering Practice , 156:106215, 2025

    2025

  8. [14]

    Calibratio n of AFM cantilever stiffness: a microfabricated array of reflective springs

    Peter Cumpson, Peter Zhdan, and John Hedley. Calibratio n of AFM cantilever stiffness: a microfabricated array of reflective springs. Ultramicroscopy, 100(3-4):241–251, 2004

    2004

  9. [15]

    Fast and accurate: high- speed metrological large-range AFM for surface and nanomet rology

    Gaoliang Dai, Ludger Koenders, Jens Fluegge, and Matthias Hemmleb. Fast and accurate: high- speed metrological large-range AFM for surface and nanomet rology. Measurement Science and Technology, 29(5):054012, 2018

    2018

  10. [16]

    Sliding mode control: theory and applications

    Christopher Edwards and Sarah Spurgeon. Sliding mode control: theory and applications . CRC Press, 1998

    1998

  11. [17]

    Calculation of the power sp ectral density from surface profile data

    Merle Elson and Jean Bennett. Calculation of the power sp ectral density from surface profile data. Applied optics, 34(1):201–208, 1995

    1995

  12. [18]

    Hydraulic actuator control based on continuous higher order sliding modes

    Manuel Estrada, Michael Ruderman, Oscar Texis-Loaiza, and Leonid Fridman. Hydraulic actuator control based on continuous higher order sliding modes. Control Engineering Practice, 156:106218, 2025. 22 Energy-saving Sub-Optimal SMC (submitted chapter manuscript)

    2025

  13. [19]

    Higher order sliding mod es

    Leonid Fridman and Arie Levant. Higher order sliding mod es. In Wilfrid Peruquetti and Jean-Pierre Barbot, editors, Sliding mode control in engineering . Marcel Dekker, 2002

    2002

  14. [20]

    A.T. Fuller. Relay control systems optimized for variou s performance criteria. IFAC Proceed- ings Volumes, 1(1):520–529, 1960

    1960

  15. [21]

    Surface roughness measurements using power spectrum density analysis with enhanced spatia l correlation length

    Yuxuan Gong, Scott Misture, Peng Gao, and Nathan Mellott . Surface roughness measurements using power spectrum density analysis with enhanced spatia l correlation length. The Journal of Physical Chemistry C , 120(39):22358–22364, 2016

    2016

  16. [22]

    Survey of advanced suspension developmen ts and related optimal control applications

    Davor Hrovat. Survey of advanced suspension developmen ts and related optimal control applications. Automatica, 33(10):1781–1817, 1997

    1997

  17. [23]

    Atomic force microscopy c apable of vibration isolation with low-stiffness z-axis actuation

    Shingo Ito and Georg Schitter. Atomic force microscopy c apable of vibration isolation with low-stiffness z-axis actuation. Ultramicroscopy, 186:9–17, 2018

    2018

  18. [24]

    Sliding mode control of a distributed-parameter wafer spin clean process

    Stefan Koch, Martin Kleindienst, Jaime Moreno, and Mart in Horn. Sliding mode control of a distributed-parameter wafer spin clean process. IEEE Transactions on Control Systems Technology, 29(5):2271–2278, 2020

    2020

  19. [25]

    Chattering suppression method s in sliding mode control systems

    Hoon Lee and Vadim Utkin. Chattering suppression method s in sliding mode control systems. Annual Reviews in Control, 31(2):179–188, 2007

    2007

  20. [26]

    Sliding order and sliding accuracy in slidi ng mode control

    Arie Levant. Sliding order and sliding accuracy in slidi ng mode control. International journal of control, 58(6):1247–1263, 1993

    1993

  21. [27]

    Machining process monitoring and control: the state-of-the-art

    Steven Liang, Rogelio Hecker, and Robert Landers. Machining process monitoring and control: the state-of-the-art. J. of Manufacturing Science and Engineering , 126(2):297–310, 2004

    2004

  22. [28]

    Random process model of rough surfaces

    Ranganath Nayak. Random process model of rough surfaces . ASME Journal of Lubrication Technology, 93(3):398–407, 1971

    1971

  23. [29]

    Contact mechanics for randomly rough surfac es

    Bo Persson. Contact mechanics for randomly rough surfac es. Surface science reports , 61(4):201–227, 2006

    2006

  24. [30]

    Pontryagin, V .G

    L.S. Pontryagin, V .G. Boltyanskii, R.V . Gamkrelidze, and E. Mishchenko. The mathematical theory of optimal processes. Interscience Publishers, 1962

    1962

  25. [31]

    Adaptive super-twisting control ler design for accurate trajectory tracking performance of unmanned aerial vehicles

    Venkateswara Rao, Hamed Habibi, Jose Luis Sanchez-Lope z, Prathyush Menon, Christopher Edwards, and Holger Voos. Adaptive super-twisting control ler design for accurate trajectory tracking performance of unmanned aerial vehicles. IEEE Transactions on Control Systems Technology...

    2024

  26. [32]

    Slid- ing mode observer-based finite time control scheme for frequ ency regulation and economic dispatch in power grids

    Gianmario Rinaldi, Prathyush Menon, Christopher Edwar ds, and Antonella Ferrara. Slid- ing mode observer-based finite time control scheme for frequ ency regulation and economic dispatch in power grids. IEEE Tran. on Control Systems Technology, 30(3):1296–1303, 2021

    2021

  27. [33]

    Analysis and compensation of kinetic friction in robotic an d mechatronic control systems

    Michael Ruderman. Analysis and compensation of kinetic friction in robotic an d mechatronic control systems. CRC Press, 2023

    2023

  28. [36]

    Sliding mode control and observation

    Yuri Shtessel, Christopher Edwards, Leonid Fridman, an d Arie Levant. Sliding mode control and observation. Springer, 2014

    2014

  29. [37]

    Characterization and optimization of scan speed for tapping-mode atomic force mi croscopy

    Todd Sulchek, Goksen Y aralioglu, Calvin Quate, and Step hen Minne. Characterization and optimization of scan speed for tapping-mode atomic force mi croscopy. Review of Scientific Instruments, 73(8):2928–2936, 2002

    2002

  30. [38]

    Mod- eling and field-experiments identification of vertical dyna mics of vehicle with active anti-roll bar

    Rafael Tavares, Michael Ruderman, Daan Menjoie, Joan Mo lina, and Miguel Dhaens. Mod- eling and field-experiments identification of vertical dyna mics of vehicle with active anti-roll bar. In IEEE 16th International Workshop on Advanced Motion Control, pages 161–167, 2020

    2020

  31. [39]

    State of the art survey: active and semi-active suspension control

    Hongtei Erik Tseng and Davor Hrovat. State of the art survey: active and semi-active suspension control. Vehicle System Dynamics, 53(7):1034–1062, 2015

    2015

  32. [40]

    Sliding modes in control and optimization

    Vadim Utkin. Sliding modes in control and optimization . Springer, 1992

    1992

  33. [41]

    Discussion aspects of high-order sliding m ode control

    Vadim Utkin. Discussion aspects of high-order sliding m ode control. IEEE Transactions on Automatic Control, 61(3):829–833, 2015

    2015

  34. [42]

    Road map for sliding mode control design

    Vadim Utkin, Alex Poznyak, Yury Orlov, and Andrey Polyak ov. Road map for sliding mode control design. Springer, 2020. Design and Application of Energy-saving Sub-Optimal Slidi ng Mode Control 23

    2020

  35. [43]

    Advancing the applicat ion of atomic force microscopy (AFM) to the characterization and quantification of geologi cal material properties

    Ke Wang, Kevin Taylor, and Lin Ma. Advancing the applicat ion of atomic force microscopy (AFM) to the characterization and quantification of geologi cal material properties. Interna- tional Journal of Coal Geology , 247:103852, 2021

    2021

  36. [44]

    I nvited review article: High- speed flexure-guided nanopositioning: Mechanical design a nd control issues

    Yuen Y ong, Reza Moheimani, Brian Kenton, and Kam Leang. I nvited review article: High- speed flexure-guided nanopositioning: Mechanical design a nd control issues. Review of scien- tific instruments , 83(12), 2012

    2012

  37. [45]

    Design of an inertially counterbalanced Z-nanopositioner for high-speed atomic force microscopy

    Yuen Y ong and Reza Mohemani. Design of an inertially counterbalanced Z-nanopositioner for high-speed atomic force microscopy. IEEE Trans. on Nanotechnology, 12(2):137–145, 2012

    2012

  38. [46]

    Structured H2 optimization of vehicle suspensions based on multi-wheel models

    Lei Zuo and Samir A Nayfeh. Structured H2 optimization of vehicle suspensions based on multi-wheel models. Vehicle System Dynamics, 40(5):351–371, 2003

    2003

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.