Discretization of control law for a class of variable structure control systems

G. Golo, Arjan van der Schaft, Č. Milosavljević

Research output: Book/ReportReportOther research output

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Abstract

A new method for the discretization of a class of continuous-time variable structure control systems, based on the linear complementarity theory, is proposed. The proposed method consists two steps. In the first step, the motion projected on the sliding manifold (the fast dynamics) is discretized by means of backward Euler time-step method. In the second step, the sampled and hold control law is determined such that the trajectories of the discrete-time closed loop system projected on the sliding manifold coincide with the trajectories of discretized fast dynamics. The discrete-time closed-loop system exhibits discrete-time sliding motion. It means that the trajectories of the discrete-time closed loop system reach the sliding manifold in a finite number of steps and stay on it after that. Also, it is proved that control law is a continuous function. Therefore, the closed loop system is chattering free. The theoretically obtained results are verified on the example of the non-holonomic integrator.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 2000

Publication series

NameMemorandum / Faculty of Mathematical Sciences
PublisherDepartment of Applied Mathematics, University of Twente
No.1551
ISSN (Print)0169-2690

Keywords

  • MSC-74M05
  • MSC-90C33
  • MSC-93C55
  • IR-65738
  • MSC-93C83
  • EWI-3371
  • MSC-93C62

Cite this

Golo, G., van der Schaft, A., & Milosavljević, Č. (2000). Discretization of control law for a class of variable structure control systems. (Memorandum / Faculty of Mathematical Sciences; No. 1551). Enschede: University of Twente, Department of Applied Mathematics.
Golo, G. ; van der Schaft, Arjan ; Milosavljević, Č. / Discretization of control law for a class of variable structure control systems. Enschede : University of Twente, Department of Applied Mathematics, 2000. (Memorandum / Faculty of Mathematical Sciences; 1551).
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abstract = "A new method for the discretization of a class of continuous-time variable structure control systems, based on the linear complementarity theory, is proposed. The proposed method consists two steps. In the first step, the motion projected on the sliding manifold (the fast dynamics) is discretized by means of backward Euler time-step method. In the second step, the sampled and hold control law is determined such that the trajectories of the discrete-time closed loop system projected on the sliding manifold coincide with the trajectories of discretized fast dynamics. The discrete-time closed-loop system exhibits discrete-time sliding motion. It means that the trajectories of the discrete-time closed loop system reach the sliding manifold in a finite number of steps and stay on it after that. Also, it is proved that control law is a continuous function. Therefore, the closed loop system is chattering free. The theoretically obtained results are verified on the example of the non-holonomic integrator.",
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series = "Memorandum / Faculty of Mathematical Sciences",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1551",

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Golo, G, van der Schaft, A & Milosavljević, Č 2000, Discretization of control law for a class of variable structure control systems. Memorandum / Faculty of Mathematical Sciences, no. 1551, University of Twente, Department of Applied Mathematics, Enschede.

Discretization of control law for a class of variable structure control systems. / Golo, G.; van der Schaft, Arjan; Milosavljević, Č.

Enschede : University of Twente, Department of Applied Mathematics, 2000. (Memorandum / Faculty of Mathematical Sciences; No. 1551).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Discretization of control law for a class of variable structure control systems

AU - Golo, G.

AU - van der Schaft, Arjan

AU - Milosavljević, Č.

N1 - Imported from MEMORANDA

PY - 2000

Y1 - 2000

N2 - A new method for the discretization of a class of continuous-time variable structure control systems, based on the linear complementarity theory, is proposed. The proposed method consists two steps. In the first step, the motion projected on the sliding manifold (the fast dynamics) is discretized by means of backward Euler time-step method. In the second step, the sampled and hold control law is determined such that the trajectories of the discrete-time closed loop system projected on the sliding manifold coincide with the trajectories of discretized fast dynamics. The discrete-time closed-loop system exhibits discrete-time sliding motion. It means that the trajectories of the discrete-time closed loop system reach the sliding manifold in a finite number of steps and stay on it after that. Also, it is proved that control law is a continuous function. Therefore, the closed loop system is chattering free. The theoretically obtained results are verified on the example of the non-holonomic integrator.

AB - A new method for the discretization of a class of continuous-time variable structure control systems, based on the linear complementarity theory, is proposed. The proposed method consists two steps. In the first step, the motion projected on the sliding manifold (the fast dynamics) is discretized by means of backward Euler time-step method. In the second step, the sampled and hold control law is determined such that the trajectories of the discrete-time closed loop system projected on the sliding manifold coincide with the trajectories of discretized fast dynamics. The discrete-time closed-loop system exhibits discrete-time sliding motion. It means that the trajectories of the discrete-time closed loop system reach the sliding manifold in a finite number of steps and stay on it after that. Also, it is proved that control law is a continuous function. Therefore, the closed loop system is chattering free. The theoretically obtained results are verified on the example of the non-holonomic integrator.

KW - MSC-74M05

KW - MSC-90C33

KW - MSC-93C55

KW - IR-65738

KW - MSC-93C83

KW - EWI-3371

KW - MSC-93C62

M3 - Report

T3 - Memorandum / Faculty of Mathematical Sciences

BT - Discretization of control law for a class of variable structure control systems

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

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Golo G, van der Schaft A, Milosavljević Č. Discretization of control law for a class of variable structure control systems. Enschede: University of Twente, Department of Applied Mathematics, 2000. (Memorandum / Faculty of Mathematical Sciences; 1551).