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Lyapunov stability based sliding mode observer for sensorless control of permanent magnet synchronous motor

Navaneethan Soundirarajan, Kanthalakshmi Srinivasan, Aandrew Baggio S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 2

art. no. e140353

EN

In recent years there has been an increasing demand for electric vehicles due to their attractive features including low pollution and increase in efficiency. Electric vehicles use electric motors as primary motion elements and permanent magnet machines found a proven record of use in electric vehicles. Permanent magnet synchronous motor (PMSM) as electric propulsion in electric vehicles supersedes the performance compared to other motor types. However, in order to eliminate the cumbersome mechanical sensors used for feedback, sensorless control of motors has been proposed. This paper proposes the design of sliding mode observer (SMO) based on Lyapunov stability for sensorless control of PMSM. The designed observer is modeled with a simulated PMSM model to evaluate the tracking efficiency of the observer. Further, the SMO is coded using MATLAB/Xilinx block models to investigate the performance at real-time.

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Trajectory tracking control of a mobile manipulator with an external force compensation

Galicki Mirosław

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 5

art. no. e137943

EN

This paper considers the problem of the accurate task space finite-time control susceptible to both undesirable disturbance forces exerted on the end-effector and unknown friction forces coming from joints directly driven by the actuators as well as unstructured forces resulting from the kinematic singularities appearing on the mechanism trajectory. We obtain a class of estimated extended transposed Jacobian controllers which seem to successfully counteract the external disturbance forces on the basis of a suitably defined task-space non-singular terminal sliding manifold (TSM) and the Lyapunov stability theory. Moreover, in order to overcome (or to minimise) the undesirable chattering effects, the proposed robust control law involves the second-order sliding technique. The numerical simulations (closely related to an experiment) ran for a mobile manipulator consisting of a non-holononic platform of (2;0) type and a holonomic manipulator of two revolute kinematic pairs show the performance of the proposed controllers and make a comparison with other well-known control schemes.

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An analytical method for well-formed workflow/Petri net verification of classical soundness

Clempner J.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

931--939

EN

In this paper we consider workflow nets as dynamical systems governed by ordinary difference equations described by a particular class of Petri nets. Workflow nets are a formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems necessary to require the soundness of workflow nets, there exist business processes with conditional behavior that will not necessarily satisfy the soundness property. In this sense, we propose an analytical method for showing that a workflow net satisfies the classical soundness property using a Petri net. To present our statement, we use Lyapunov stability theory to tackle the classical soundness verification problem for a class of dynamical systems described by Petri nets. This class of Petri nets allows a dynamical model representation that can be expressed in terms of difference equations. As a result, by applying Lyapunov theory, the classical soundness property for workflow nets is solved proving that the Petri net representation is stable. We show that a finite and non-blocking workflow net satisfies the sound property if and only if its corresponding PN is stable, i.e., given the incidence matrix A of the corresponding PN, there exists a Φ strictly positive m vector such that AΦ ≤ 0. The key contribution of the paper is the analytical method itself that satisfies part of the definition of the classical soundness requirements. The method is designed for practical applications, guarantees that anomalies can be detected without domain knowledge, and can be easily implemented into existing commercial systems that do not support the verification of workflows. The validity of the proposed method is successfully demonstrated by application examples.

4

Stability of a class of adaptive nonlinear systems

Dzieliński A.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 4

455-462

EN

This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology.