Proportional plus integral control of ladder circuits modeled in the form of two-dimensional (2D) systems

Sulikowski, Bartłomiej; Gałkowski, Krzysztof; Kummert, Anton

doi:10.1007/s11045-013-0256-1

Cited by 24 publications

(11 citation statements)

References 23 publications

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“…Hence, the stability analysis and controller synthesis of the interconnected systems will be performed next based on the discrete repetitive process model (29).…”

Section: Control Law Designmentioning

confidence: 99%

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PD-Type Iterative Learning Control for Uncertain Spatially Interconnected Systems

et al. 2020

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This paper puts forward a PD-type iterative learning control algorithm for a class of discrete spatially interconnected systems with unstructured uncertainty. By lifting and changing the variable of discrete space model, the uncertain spatially interconnected systems is converted into equivalent singular system, and the general state space model is derived in view of singular system theory. Then, the state error and output error information are used to design the iterative learning control law, transforming the controlled system into an equivalent repetitive process model. Based on the stability theory of repetitive process, sufficient condition for the stability of the system along the trial is given in the form of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed algorithm is verified by the simulation of ladder circuits.

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“…Hence, the stability analysis and controller synthesis of the interconnected systems will be performed next based on the discrete repetitive process model (29).…”

Section: Control Law Designmentioning

confidence: 99%

“…Lemma 3. A discrete repetitive process described by (29) is stable along the trial if there exists matrix S > 0 such that [28] Φ T SΦ − S < 0 (30)…”

Section: Lmi-based Designmentioning

confidence: 99%

PD-Type Iterative Learning Control for Uncertain Spatially Interconnected Systems

et al. 2020

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“…Applying Kirchhoff's laws, the dynamics of ladder circuits, see Fig. 2 for the configuration and layout, can be written in the form of a 2-D differential-discrete linear systems state-space model, see Sulikowski et al (2015), where the independent variables are time and the node numbers p = 0, 1, . .…”

Section: Ladder Circuitsmentioning

confidence: 99%

“…Hence, for analysis, there is the option to embed the spatial dynamics into the system variables using a form of lifting based on the discrete (finite) spatial variable and obtain a system where time is the independent variable, referred to as a 1D system in some of the 2-D systems literature, see, e.g. Sulikowski et al (2015). One drawback of this approach, for systems composed of a large number of cells, is the need to compute with matrices that have very large dimensions and hence possible computational issues.…”

Section: Introductionmentioning

confidence: 99%

Characterization of a class of spatially interconnected systems (ladder circuits) using two-dimensional systems theory

Boudellioua

Gałkowski

Rogers

2019

Multidim Syst Sign Process

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This paper considers a class of spatially interconnected systems formed by ladder circuits using two-dimensional systems theory. The individual circuits in this class are described by hybrid (continuous/discrete) linear differential/difference equations in time (continuous) and spatial (discrete) variables and therefore have a two-dimensional systems structure. This paper shows that a ladder circuit model and models for 2-D dynamics have a well defined equivalence property and hence analysis tools can be transferred between them. Also the mechanism for transforming one to the other is established.

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“…The class of n-D systems includes, e. g., repetitive processes [25,27], spatially invariant systems [10,11], positive n-D systems [20], or n-D systems of the fractional order [21], and iterative learning control [10,11,12]. The n-D systems approach is applied in control of ladder circuits [32,31], and in modelling of complex systems [5,6]. Methods for identification of n-D systems are also developed in, for instance, [1,26].…”

Section: Introductionmentioning

confidence: 99%

A fast numerical test of multivariate polynomial positiveness with applications

Augusta¹,

Augustová²

2018

Kybernetika

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A fast numerical test of multivariate polynomial positiveness with applications Kybernetika, Vol. 54 (2018) A FAST NUMERICAL TEST OF MULTIVARIATE POLYNOMIAL POSITIVENESS WITH APPLICATIONS Petr Augusta and Petra AugustováThe paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.

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Proportional plus integral control of ladder circuits modeled in the form of two-dimensional (2D) systems

Cited by 24 publications

References 23 publications

PD-Type Iterative Learning Control for Uncertain Spatially Interconnected Systems

PD-Type Iterative Learning Control for Uncertain Spatially Interconnected Systems

Characterization of a class of spatially interconnected systems (ladder circuits) using two-dimensional systems theory

A fast numerical test of multivariate polynomial positiveness with applications

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