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.

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.

Design of Experiments for the Controller of Rotor Systems With a Magnetic Bearing

1997 ◽  
Vol 119 (2) ◽  
pp. 200-207 ◽  
Author(s):  
G. J. Sheu ◽  
S. M. Yang ◽  
C. D. Yang
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Magnetic Bearing ◽  
Control Technique ◽  
Design Parameters ◽  
Control Engineering ◽  
Rotor Systems ◽  
Experimental Design Method ◽  
Loss Index ◽  
And Performance

A new design methodology for the vibration control of rotor systems with a magnetic bearing is developed in this paper. The methodology combines the experimental design method in quality control engineering and the conventional PD control technique such that their advantages in implementation feasibility and performance-robustness can be integrated together. A quality loss index defined by the summation of the infinity norm of unbalanced vibration is used to characterize the system dynamics. By using the location of the magnetic bearing and PD feedback gains as design parameters, the controller can be determined by a small number of matrix experiments to achieve the best system performance. In addition, it is robust to the vibration modes within a desired speed range. A rotor system consisting of 4 rigid disks, 3 isotropic bearings, and 1 magnetic bearing is applied to illustrate the feasibility and effectiveness of the experiment-aided controller design.

Vibration Control of Rotor Systems With Noncollocated Sensor/Actuator by Experimental Design

1997 ◽  
Vol 119 (3) ◽  
pp. 420-427 ◽  
Author(s):  
S. M. Yang ◽  
G. J. Sheu ◽  
C. D. Yang
Keyword(s):  
Experimental Design ◽  
Vibration Suppression ◽  
Controller Design ◽  
Design Method ◽  
Control Technique ◽  
Design Parameters ◽  
Rotor Systems ◽  
Sensor Actuator ◽  
Operation Speed ◽  
And Performance

This paper presents a controller design methodology for vibration suppression of rotor systems in noncollocated sensor/actuator configuration. The methodology combines the experimental design method of quality engineering and the active damping control technique such that their advantages in implementation feasibility and performance-robustness can be integrated together. By using the locations of sensor/actuator and the feedback gains as design parameters, the controller design is shown to achieve a near optimal performance within the two-sigma confidence among all possible parameter combinations. Compared with LQ-based designs, the controller order is smaller and it is applicable to systems in an operation speed range. In addition, neither preselected sensor/actuator location(s) nor state measurement/ estimation is needed.

scholarly journals Control of systems on spatial domains with moving boundaries: 3D printing and traffic

2019 ◽  
Vol 32 (4) ◽  
pp. 503-512
Author(s):  
Miroslav Krstic
Keyword(s):  
3D Printing ◽  
Differential Equations ◽  
Moving Boundary ◽  
Freeway Traffic ◽  
Control Laws ◽  
Infinite Dimensional ◽  
Spatial Domains ◽  
And Performance ◽  
Solid Liquid ◽  
Year 2000

Until roughly the year 2000, control algorithms (of the kind that can be physically implemented and provided guarantees of stability and performance) were mostly available only for systems modeled by ordinary differential equations. In other words, while controllers were available for finite-dimensional systems, such as robotic manipulators of vehicles, they were not available for systems like fluid flows. With the emergence of the ?backstepping? approach, it became possible to design control laws for systems modeled by partial differential equations (PDEs), i.e., for infinite dimensional systems, and with inputs at the boundaries of spatial domains. But, until recently, such backstepping controllers for PDEs were available only for systems evolving on fixed spatial PDE domains, not for systems whose boundaries are also dynamical and move, such as in systems undergoing transition of phase of matter (like the solid-liquid transition, i.e., melting or crystallization). In this invited article we review new control designs for moving-boundary PDEs of both parabolic and hyperbolic types and illustrate them by applications, respectively, in additive manufacturing (3D printing) and freeway traffic.

Feedback Control Via Eigenvalue Assignment for Time Delayed Systems Using the Lambert W Function

2007 ◽  
Author(s):  
Sun Yi ◽  
Patrick W. Nelson ◽  
A. Galip Ulsoy
Keyword(s):  
Differential Equations ◽  
Controller Design ◽  
Analytical Form ◽  
Lambert W Function ◽  
Feedback Controllers ◽  
Delayed Systems ◽  
Linear Delay ◽  
The Matrix ◽  
Delay Differential ◽  
Eigenvalue Assignment

In this paper, we consider the problem of feedback controller design via eigenvalue assignment for systems of linear delay differential equations (DDEs). Unlike ordinary differential equations (ODEs), DDEs have an infinite eigenspectrum and it is not feasible to assign all closed-loop eigenvalues. However, we can assign a critical subset of them using a solution to linear DDEs in terms of the matrix Lambert W function. The solution has an analytical form expressed in terms of the parameters of the DDE, and is similar to the state transition matrix in linear ODEs. Hence, one can extend controller design methods developed based upon the solution form of ODEs to systems of DDEs, including the design of feedback controllers via eigenvalue assignment. We present such an approach here, illustrate using some examples, and compare with other existing methods.

A Unified Framework for the Study of Periodic Solutions of Nonlinear Delay Differential Equations

2001 ◽  
Author(s):  
M. S. Fofana
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Dimensional Space ◽  
Multiple Time ◽  
Unified Framework ◽  
Center Manifold Theorem ◽  
Infinite Dimensional ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential

Abstract Periodic solutions of delay differential equations (DDEs) splitting into stable and unstable branches are examined in an infinite-dimensional space for fixed and multiple time delays. The center manifold theorem and the classical Hopf bifurcation theorem for the study of periodic solutions of ordinary differential equations (ODEs) are employed to reduce the infinite-dimensional character of the DDEs to finite-dimensional ODEs. Using integral averaging method, the vector field of the ODEs is converted and averaged into amplitude a and phase φ relations. From these relations bifurcation equations of the form ℑ(a, φ) = 0 for the solution branches are derived.

scholarly journals Computation of double Hopf points for delay differential equations

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Yingxiang Xu ◽  
Tingting Shi
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Delay Systems ◽  
System Of Equations ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Defining System ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Branch Switching

AbstractRelating to the crucial problem of branch switching, the calculation of codimension 2 bifurcation points is one of the major issues in numerical bifurcation analysis. In this paper, we focus on the double Hopf points for delay differential equations and analyze in detail the corresponding eigenspace, which enable us to obtain the finite dimensional defining system of equations of such points, instead of an infinite dimensional one that happens naturally for delay systems. We show that the double Hopf point, together with the corresponding eigenvalues, eigenvectors and the critical values of the bifurcation parameters, is a regular solution of the finite dimensional defining system of equations, and thus can be obtained numerically through applying the classical iterative methods. We show our theoretical findings by a numerical example.

scholarly journals Experiment-Aided Controller Design of Rotor Systems With a Magnetic Bearing

1995 ◽  
Author(s):  
G. J. Sheu ◽  
C. D. Yang ◽  
S. M. Yang
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Magnetic Bearing ◽  
Control Technique ◽  
Design Parameters ◽  
Control Engineering ◽  
Rotor Systems ◽  
Loss Index ◽  
And Performance ◽  
Aided Design

A new design methodology for the vibration control of rotor systems with a magnetic bearing is developed in this paper. The methodology combines the experimental design method in quality control engineering and the conventional PD control technique such that their advantages in implementation feasibility and performance-robustness can be integrated together. A quality loss index defined by the summation of the infinity norm of unbalanced vibration is used to characterize the system dynamics. By using the location of the magnetic bearing and PD feedback gains as design parameters, the controller of experiment-aided design achieves the best system performance. In addition, it is robust to operating speed variations. A rotor system consisting of 4 rigid disks, 3 isotropic bearings, and 1 magnetic bearing is applied to illustrate the feasibility and effectiveness of the experiment-aided controller design.

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