Implicit Discretization of a PID-Like Sliding-Mode Controller for Double Integrator Systems

Martin Zapf; Benedikt Andritsch; Stefan Koch; Leonid Fridman; Martin Horn

doi:10.1109/CDC57313.2025.11312954

Implicit Discretization of a PID-Like Sliding-Mode Controller for Double Integrator Systems

Martin Zapf
, Benedikt Andritsch
, Stefan Koch
, Leonid Fridman
, Martin Horn

Institute of Automation and Control (4430)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

This paper presents the fully implicit (backward-Euler) discretization of a PID-like sliding-mode controller for undisturbed double-integrator systems. The method inherits the third-order sliding accuracy of the continuous-time PID-like controller while eliminating discretization chattering. The controller is compared in simulation studies to an explicit Euler discretization and a cascaded implementation with a super-twisting controller in the inner loop. The results reveal unique strengths and weaknesses of each approach. It is finally applied to patient positioning of a real-world magnetic resonance imaging system, demonstrating its practical applicability.

Original language	English
Title of host publication	2025 IEEE 64rd Conference on Decision and Control (CDC)
Publisher	IEEE Xplore
Number of pages	6
ISBN (Electronic)	979-8-3315-2627-6
ISBN (Print)	979-8-3315-2628-3
DOIs	https://doi.org/10.1109/CDC57313.2025.11312954
Publication status	Published - 12 Jan 2026
Event	64th IEEE Conference on Decision and Control, CDC 2025 - Windsor Convention Center, Rio de Janeiro, Brazil Duration: 10 Dec 2025 → 12 Dec 2025 https://cdc2025.ieeecss.org/

Publication series

Name	IEEE Conference on Decision and Control (CDC)
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	64th IEEE Conference on Decision and Control, CDC 2025
Country/Territory	Brazil
City	Rio de Janeiro
Period	10/12/25 → 12/12/25
Internet address	https://cdc2025.ieeecss.org/

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1109/CDC57313.2025.11312954

Cite this

Implicit Discretization of a PID-Like Sliding-Mode Controller for Double Integrator Systems. / Zapf, Martin; Andritsch, Benedikt ; Koch, Stefan et al.
2025 IEEE 64rd Conference on Decision and Control (CDC). IEEE Xplore, 2026. (IEEE Conference on Decision and Control (CDC)).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Zapf, M, Andritsch, B , Koch, S, Fridman, L & Horn, M 2026, Implicit Discretization of a PID-Like Sliding-Mode Controller for Double Integrator Systems. in 2025 IEEE 64rd Conference on Decision and Control (CDC). IEEE Conference on Decision and Control (CDC), IEEE Xplore, 64th IEEE Conference on Decision and Control, CDC 2025, Rio de Janeiro, Brazil, 10/12/25. https://doi.org/10.1109/CDC57313.2025.11312954

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abstract = "This paper presents the fully implicit (backward-Euler) discretization of a PID-like sliding-mode controller for undisturbed double-integrator systems. The method inherits the third-order sliding accuracy of the continuous-time PID-like controller while eliminating discretization chattering. The controller is compared in simulation studies to an explicit Euler discretization and a cascaded implementation with a super-twisting controller in the inner loop. The results reveal unique strengths and weaknesses of each approach. It is finally applied to patient positioning of a real-world magnetic resonance imaging system, demonstrating its practical applicability. ",

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T1 - Implicit Discretization of a PID-Like Sliding-Mode Controller for Double Integrator Systems

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AU - Koch, Stefan

AU - Fridman, Leonid

AU - Horn, Martin

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N2 - This paper presents the fully implicit (backward-Euler) discretization of a PID-like sliding-mode controller for undisturbed double-integrator systems. The method inherits the third-order sliding accuracy of the continuous-time PID-like controller while eliminating discretization chattering. The controller is compared in simulation studies to an explicit Euler discretization and a cascaded implementation with a super-twisting controller in the inner loop. The results reveal unique strengths and weaknesses of each approach. It is finally applied to patient positioning of a real-world magnetic resonance imaging system, demonstrating its practical applicability.

AB - This paper presents the fully implicit (backward-Euler) discretization of a PID-like sliding-mode controller for undisturbed double-integrator systems. The method inherits the third-order sliding accuracy of the continuous-time PID-like controller while eliminating discretization chattering. The controller is compared in simulation studies to an explicit Euler discretization and a cascaded implementation with a super-twisting controller in the inner loop. The results reveal unique strengths and weaknesses of each approach. It is finally applied to patient positioning of a real-world magnetic resonance imaging system, demonstrating its practical applicability.

U2 - 10.1109/CDC57313.2025.11312954

DO - 10.1109/CDC57313.2025.11312954

M3 - Conference paper

SN - 979-8-3315-2628-3

T3 - IEEE Conference on Decision and Control (CDC)

BT - 2025 IEEE 64rd Conference on Decision and Control (CDC)

PB - IEEE Xplore

T2 - 64th IEEE Conference on Decision and Control, CDC 2025

Y2 - 10 December 2025 through 12 December 2025

ER -

Implicit Discretization of a PID-Like Sliding-Mode Controller for Double Integrator Systems

Abstract

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Conference

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Cite this