Robust State Feedback Regulator Design for General Linear Heterodirectional Hyperbolic Systems

Deutscher, Joachim; Gabriel, Jakob

doi:10.1109/tac.2018.2791524

Cited by 25 publications

(19 citation statements)

References 12 publications

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“…On the other hand, there is still a huge gap between abstract theory and PDEs, because abstract theory gives little insight in control design for PDEs, and in many cases, the involved unbounded operators should be extended to meet the regularity of the abstract framework but this is very difficult task for PDEs 3 . In the last few years, several researchers have developed some direct PDE approaches under the guidance of the internal model principle 5,6 . In a recent paper, 7 we proposed an observer based approach for a SISO heat equation, which is similar to that of Reference 8 for ODEs.…”

Section: Introductionmentioning

confidence: 99%

Robust output regulation for Timoshenko beam equation with two inputs and two outputs

Guo

Meng

2020

Intl J Robust & Nonlinear

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In this article, we consider two‐dimensional robust output tracking for a Timoshenko beam equation where the disturbances and references are produced by a finite‐dimensional exosystem. This requires at least two controls from basic output regulation theory of linear systems. The observer‐based error feedback control approach is adopted in investigation through the following steps: (a) for the plant with no systematic uncertainties, choose a set of disturbances and references to obtain a nominal system; (b) for the nominal system, design an observer to realize 2‐copy of the exosystem; (c) find a feedforward control for nominal system; and (d) allocate proportionally the states in feedforward control by those of the observer to obtain an observer based error feedback control also for nominal system. Since the control contains a 2‐copy of the exo‐system and the states of the observer are proportionally allocated in control, the problem is significantly different from SISO cases. The error feedback control is then proved to be bounded and also robust to systematic uncertainties and all disturbances and references produced from the exo‐system. The numerical simulations validate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Robust output regulation for Timoshenko beam equation with two inputs and two outputs

Guo

Meng

2020

Intl J Robust & Nonlinear

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“…Although excellent theoretical results were developed in the field of output regulation, very few works have applied these theories to practical processes 20 . Moreover, existing literature 21‐27 based on internal model principle (IMP) provides robust periodic reference tracking control design. Motivated by this fact, this article develops novel robust error feedback regulator design for the column froth flotation process, which is a rather complex system described by coupled conservative transport hyperbolic PDEs–ordinary differential equations (ODEs) with transport time delay.…”

Section: Introductionmentioning

confidence: 99%

Robust tracking control of column froth flotation process with an unknown disturbance

Dubljević

2021

AIChE Journal

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This manuscript develops a robust output regulator for the column froth flotation process in the presence of unknown disturbance. In particular, motivated by relevant physical modeling setting, all information (including magnitude, phase, bias, and frequency) of the disturbance is unavailable. The system considered is consisting of froth and collection zones and is governed by a set of conservative heterodirectional transport hyperbolic partial differential equations (PDEs). Moreover, the transport related time delay between the froth and the collection region is considered, and is associated with the boundary conditions of the PDEs. The velocity of the feed is considered the input and the concentration of the solid particle with air phase at the top of froth region as the output. We propose a disturbance frequency identifier and formulate a robust controller according to the internal model principle such that the output tracks the desired concentration despite the model uncertainties and unknown disturbance.

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“…The recent monographs [19], [38] demonstrate that cooperative output regulation is still a very active research area for linear finite-dimensional MAS, where also a more detailed literature overview can be found. Recent advances in the backstepping-based solution of the output regulation problem for distributed-parameter systems (see, e. g., [13], [12] for parabolic systems and [2], [10], [11] for hyperbolic systems as well as the references in these works) suggest to generalize these results to networks of parabolic PDEs, in order to solve the cooperative robust output regulation problem also for distributed-parameter MAS.…”

Section: Introductionmentioning

confidence: 99%

Robust Cooperative Output Regulation for a Network of Parabolic PDE Systems

Deutscher¹

2020

Preprint

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This paper considers the robust cooperative output regulation for a network of parabolic PDE systems. The solution of this problem is obtained by extending the cooperative internal model principle from finite to infinite dimensions. For a time-invariant digraph describing the communication topology, a two-step backstepping approach is presented to systematically design cooperative state feedback regulators. They allow to solve both the leader-follower and the leaderless output synchronization problem in the presence of disturbances and model uncertainty for a finite-dimensional leader. Solvability conditions of the robust cooperative output regulation problem are presented in terms of the communication graph and the agent transfer behaviour. The results of the paper are demonstrated for a MAS consisting of four uncertain parabolic agents with and without a finite-dimensional leader in the presence of disturbances.

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Robust State Feedback Regulator Design for General Linear Heterodirectional Hyperbolic Systems

Cited by 25 publications

References 12 publications

Robust output regulation for Timoshenko beam equation with two inputs and two outputs

Robust output regulation for Timoshenko beam equation with two inputs and two outputs

Robust tracking control of column froth flotation process with an unknown disturbance

Robust Cooperative Output Regulation for a Network of Parabolic PDE Systems

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