Extremum Seeking Feedback With Wave Partial Differential Equation Compensation

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Tiago Roux Oliveira ◽  
Miroslav Krstic
Keyword(s):  
Wave Equations ◽  
Small Neighborhood ◽  
Extremum Seeking ◽  
Distributed Parameter ◽  
Infinite Dimensions ◽  
Partial Differential ◽  
Actuator Dynamics ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Practical Convergence

Abstract This paper addresses the compensation of wave actuator dynamics in scalar extremum seeking (ES) for static maps. Infinite-dimensional systems described by partial differential equations (PDEs) of wave type have not been considered so far in the literature of ES. A distributed-parameter-based control law using back-stepping approach and Neumann actuation is initially proposed. Local exponential stability as well as practical convergence to an arbitrarily small neighborhood of the unknown extremum point is guaranteed by employing Lyapunov–Krasovskii functionals and averaging theory in infinite dimensions. Thereafter, the extension for wave equations with Dirichlet actuation, antistable wave PDEs as well as the design for the delay-wave PDE cascade are also discussed. Numerical simulations illustrate the theoretical results.

The Description of a Distributed Parameter Process through a Finite Discrete Dimensional System

2014 ◽  
Vol 657 ◽  
pp. 874-878
Author(s):  
Sever Şerban ◽  
Doina Corina Şerban
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Industrial Process ◽  
Time Discretization ◽  
Distributed Parameter ◽  
Geometrical Parameters ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Distributed Parameters

This article analyses the process of warming a metal by using a walking beam furnace. This process is meant to offer the technologist objective information that may allow him to produce eventual modifications of the temperature references from the furnaces zones. Thus making the metals temperature at the furnaces exit to have an imposed distribution, within precise limits, according to the technological requests. This industrial process has a geometrical parameters distribution, more precisely it can be described through a partial differential equation, by being attached to dynamic infinite dimensional systems (or with distributed parameters). Using a procedure called geometric-time discretization (in the condition of the solutions convergence), we have managed to obtain a representation under the form of a finite discrete dimensional linear system for a process with distributed parameters.

Modeling and control of flexible link manipulators for unmodeled dynamics effect

2018 ◽  
Vol 233 (3) ◽  
pp. 245-263 ◽  
Author(s):  
Berk Altıner ◽  
Akın Delibaşı ◽  
Bilal Erol
Keyword(s):  
Controller Design ◽  
Flexible Structures ◽  
Lumped Parameter Model ◽  
Unmodeled Dynamics ◽  
Experimental Setup ◽  
Flexible Link ◽  
Linear Quadratic ◽  
Partial Differential ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems

Flexible link manipulators are mostly prefered in applications where energy consumption and faster operation are critically important. Since distributed nature of flexibility makes the system depend on not only time variable but also a spatial variable, the dynamics of flexible structures are expressed by partial differential equations. In the virtue of this kind of modeling, the designers encounter with infinite dimensional systems which means that the system has an infinite number of degrees of freedom. To cope with infinite dimensional systems, one of the most relevant techniques is to truncate the model into a definite order. However, this may yield the unmodeled dynamics that cause performance degradation and even instability. In this paper, the main motivation is to propose control techniques to compensate unwanted effects of unmodeled dynamics which may occur in truncation process. In order to achieve this goal, the linear quadratic Gaussian and the weighted [Formula: see text] controller design are adopted. The performances of the designed controllers are demonstrated on the experimental setup. Besides this motivation, traditional lumped parameter model of the flexible link manipulator which is widely seen in the literature is considered and the superiority of the partial differential equation model is shown on the experimental setup.

scholarly journals Twenty years of distributed port-Hamiltonian systems: a literature review

2020 ◽  
Vol 37 (4) ◽  
pp. 1400-1422 ◽  
Author(s):  
Ramy Rashad ◽  
Federico Califano ◽  
Arjan J van der Schaft ◽  
Stefano Stramigioli
Keyword(s):  
Literature Review ◽  
Complex Systems ◽  
Systems Theory ◽  
Hamiltonian Systems ◽  
Distributed Parameter ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
The Past ◽  
Finite Dimensional ◽  
Theoretical Foundations

Abstract The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups.

scholarly journals REGIONAL EXPONENTIAL REDUCED OBSERVABILITY IN DISTRIBUTED PARAMETER SYSTEMS

2015 ◽  
Vol 11 (4) ◽  
pp. 5058-5074 ◽  
Author(s):  
Shahad AL-MULLAH ◽  
Raheam Al-Saphory
Keyword(s):  
Sufficient Conditions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Usual Sense ◽  
Two Phase ◽  
Linear Dynamical Systems ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
New Concepts ◽  
Necessary And Sufficient

The regional exponential reduced observability concept in the presence for linear dynamical systems is addressed for a class of distributed parameter systems governed by strongly continuous semi group in Hilbert space. Thus, the existence of necessary and sufficient conditions is established for regional exponential reduced estimator in parabolic infinite dimensional systems. More precisely, the introduced approach is developed by using the decomposed system and reduced system in connection with various new concepts of (stability, detectability, estimator, observability and strategic sensors). Finally, we also show that there exists a dynamical system for two-phase exchange system described by the coupled parabolic equations is not exponentially reduced observable in usual sense, but it may be regionally exponentially reduced observable.

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