Design of Dynamical Controllers for Linear Hamiltonian Systems

1999 ◽  
Author(s):  
Werner Haas ◽  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Hamiltonian Systems ◽  
Controller Design ◽  
Time Derivative ◽  
Design Parameters ◽  
Internal Dynamics ◽  
Design Algorithm ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Linear Hamiltonian Systems ◽  
Frequency Domain Approach

Abstract Linear Hamiltonian control systems with collocation of sensor and actuator are considered. Based on a frequency domain approach a controller design algorithm is stated. The design leads to a controller with internal dynamics which uses the output of the system and its first time derivative. The presence of internal dynamics in the controller is an extension of the usual PD–control law and a main result of the work. The design is based on the special properties of the proposed class of systems. In particular, these Hamiltonian systems are passive. It is shown that the design leads to strictly passive controllers for a certain choice of the design parameters. This is another significant result and offers a way for robust ℒ2–stabilization even in the case of infinite dimensional systems. Some features of the controller design are discussed with respect to an application, the control of a composite circular plate.

scholarly journals Boundary Control for a Certain Class of Reaction-Advection-Diffusion System

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1854
Author(s):  
Eduardo Cruz-Quintero ◽  
Francisco Jurado
Keyword(s):  
Boundary Conditions ◽  
Boundary Control ◽  
Distribution Systems ◽  
Controller Design ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional ◽  
Advection Diffusion

There are physical phenomena, involving diffusion and structural vibrations, modeled by partial differential equations (PDEs) whose solution reflects their spatial distribution. Systems whose dynamics evolve on an infinite-dimensional Hilbert space, i.e., infinite-dimensional systems, are modeled by PDEs. The aim when designing a controller for infinite-dimensional systems is similar to that for finite-dimensional systems, i.e., the control system must be stable. Another common goal is to design the controller in such a way that the response of the system does not be affected by external disturbances. The controller design for finite-dimensional systems is not an easy task, so, the controller design for infinite-dimensional systems is even more challenging. The backstepping control approach is a dominant methodology for boundary feedback design. In this work, we try with the backstepping design for the boundary control of a reaction-advection-diffusion (R-A-D) equation, namely, a type parabolic PDE, but with constant coefficients and Neumann boundary conditions, with actuation in one of these latter. The heat equation with Neumann boundary conditions is considered as the target system. Dynamics of the open- and closed-loop solution of the PDE system are validated via numerical simulation. The MATLAB®-based numerical algorithm related with the implementation of the control scheme is here included.

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.

Performance level and stability margins of an optimal ℋ∞ flow controller

2011 ◽  
Vol 34 (7) ◽  
pp. 914-924 ◽  
Author(s):  
Hakki Ulaş Ünal ◽  
Altuğ İftar
Keyword(s):  
Differential Equations ◽  
Controller Design ◽  
Performance Level ◽  
Design Parameters ◽  
Stability Margins ◽  
Infinite Dimensional ◽  
Flow Controller ◽  
And Performance ◽  
Uncertain Time ◽  
Delay Differential

Flow controllers are needed to avoid congestion in different types of networks. The dynamics of such networks, however, can usually be represented by infinite-dimensional models, which are either based on partial-differential equations or delay-differential equations. An optimal ℋ∞ flow controller design approach has recently been proposed for networks whose dynamics involve multiple and uncertain time-varying time delays. In the present paper, performance level and stability margins of controllers designed by this approach are analyzed. It is shown that, by choosing certain controller design parameters large, stability margins can be improved; while choosing them small improves performance levels. Therefore, there is a clear trade-off between robustness and performance.

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