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Biswa Nath Datta - One of the best experts on this subject based on the ideXlab platform.

  • Numerical Methods for Linear Control Systems - CHAPTER 11 – NUMERICAL METHODS AND CONDITIONING OF THE Eigenvalue Assignment PROBLEMS
    Numerical Methods for Linear Control Systems, 2020
    Co-Authors: Biswa Nath Datta
    Abstract:

    This chapter discusses numerical methods and the perturbation analysis for the Eigenvalue Assignment (EVA) problem. There are many methods for the EVA problem. A few of these methods include: a single-input recursive algorithm and its RQ implementation, a multi-input generalization of the single-input recursive algorithm, a multi-input explicit QR algorithm, a multi-input Schur algorithm, and a Sylvester equation algorithm for partial Eigenvalue Assignment. A single-input recursive algorithm and a multi-input explicit QR algorithm are the fastest algorithms, respectively, for the single input and the multi-input Eigenvalue Assignment problems. Unfortunately, the numerical stability of these algorithms is not guaranteed. The multi-input explicit QR algorithm is also numerically stable. However, it might give a complex feedback in some cases. The Schur algorithm, based on the real Schur decomposition of the matrix “A,” is the most expensive, but it has a distinguished feature that it can be used as a partial-pole placement algorithm in the sense that it lets the user reassign only a part of the spectrum leaving the rest unchanged. The algorithm is also believed to be numerically stable. Besides the above-mentioned algorithms, an algorithm for robust Eigenvalue Assignment (REVA) that not only assigns a desired set of Eigenvalues but also a set of well-conditioned eigenvectors as well, is also included in this chapter. The REVA is important because the conditioning of the closed-loop eigenvector matrix greatly influences the sensitivity of the closed-loop Eigenvalues.

  • robust partial quadratic Eigenvalue Assignment with time delay using the receptance and the system matrices
    Journal of Sound and Vibration, 2016
    Co-Authors: Jinku Yang, Biswa Nath Datta
    Abstract:

    Abstract In this paper, we consider the robust partial quadratic Eigenvalue Assignment problem in vibration by active feedback control. Based on the receptance measurements and the system matrices, we propose an optimization method for the robust and minimum norm partial quadratic Eigenvalue Assignment problem. We provide a new cost function and the closed-loop Eigenvalue sensitivity and the feedback norms can be minimized simultaneously. Our method is also extended to the case of time delay between measurements of state and actuation of control. Numerical tests demonstrate the effectiveness of our method.

  • Optimization methods for partial quadratic Eigenvalue Assignment in vibrations
    2011 International Conference on Communications Computing and Control Applications (CCCA), 2011
    Co-Authors: Biswa Nath Datta
    Abstract:

    Vibrating structures, e.g., buildings, bridges, highways, and others, sometime experience dangerous vibrations when acted upon by external forces. A smart way to control such vibrations is to apply active vibration control. The most important aspect of an active vibration control strategy is to effectively compute the feedback control force to absorb these vibrations. For practical applications, the feedback control force must be computed in a numerically robust way. It is, therefore, desired that these computed feedback matrices have small norms and the closed-loop condition number is as small as possible. These considerations give rise to some beautiful but extremely difficult (usually nonconvex) nonlinear optimization problems. In this paper, we survey some of the recent developments on numerical solutions of the optimization problems arising in partial Eigenvalue Assignment for second-order control systems.

  • quadratic partial Eigenvalue Assignment problem with time delay for active vibration control
    Journal of Physics: Conference Series, 2009
    Co-Authors: Jesse M Pratt, Kumar Vikram Singh, Biswa Nath Datta
    Abstract:

    Partial pole Assignment in active vibration control refers to reassigning a small set of unwanted Eigenvalues of the quadratic Eigenvalue problem (QEP) associated with the second order system of a vibrating structure, by using feedback control force, to suitably chosen location without altering the remaining large number of Eigenvalues and eigenvectors. There are several challenges of solving this quadratic partial Eigenvalue Assignment problem (QPEVAP) in a computational setting which the traditional pole-placement problems for first-order control systems do not have to deal with. In order to these challenges, there has been some work in recent years to solve QPEVAP in a computationally viable way. However, these works do not take into account of the practical phenomenon of the time-delay effect in the system. In this paper, a new direct and partial modal approach of the quadratic partial Eigenvalue Assignment problem with time-delay is proposed. The approach works directly in the quadratic system without requiring transformation to a standard state-space system and requires the knowledge of only a small number of Eigenvalues and eigenvectors that can be computed or measured in practice. Two illustrative examples are presented in the context of active vibration control with constant time-delay to illustrate the success of our proposed approach. Future work includes generalization of this approach to a more practical complex time-delay system and extension of this work to the multi-input problem.

  • robust and minimum norm partial quadratic Eigenvalue Assignment problems theory and computations
    2006
    Co-Authors: Biswa Nath Datta, Sanjoy Kumar Brahma
    Abstract:

    The partial Eigenvalue Assignment problem for a second-order control system, called the partial quadratic Eigenvalue Assignment problem (PQEVAP), is one of reassigning a few "troublesome" Eigenvalues by using feedback while leaving the remaining large number of Eigenvalues unchanged. The problem naturally arises in controlling dangerous vibrations, such as resonance in vibrating structures modeled by multi-input second-order control systems and in stabilizing control systems. One way to solve this problem is to transform the problem to a standard first-order state-space system and then apply one of the methods currently available for partial Eigenvalue Assignment in the first-order system. However, this approach has some computational drawbacks. To overcome these drawbacks the problems are solved using numerical algorithms that work directly with the second-order model without requiring transformation to a first-order system, which are implementable using the knowledge of a small number of Eigenvalues and eigenvectors of the associated quadratic matrix pencil and which do not require model reduction. These features make the algorithms practically applicable to even very large real-life structures. Now, since the Eigenvalues of a matrix may be highly sensitive to small perturbations, it is not enough to find the feedback matrices only. Attention must be given to finding them in such a way that they have minimum norms and the conditioning of the closed Eigenvalues is as good as possible. The latter variation of the PQEVAP is known as the robust partial quadratic Eigenvalue Assignment problem (RPQEVAP); the former is called the minimum norm partial quadratic Eigenvalue Assignment problem (MNPQEVAP). This dissertation is devoted to the study of these problems. Three new algorithms, one for solving the MNPQEVAP, one for solving the RPQEVAP, and one for simultaneously reducing the magnitude of the feedback norms and improving the conditioning of the closed-loop Eigenvalues, have been developed and numerically tested.

Galip A. Ulsoy - One of the best experts on this subject based on the ideXlab platform.

  • Time-delayed vision-based DC motor control via rightmost Eigenvalue Assignment
    2014 American Control Conference, 2014
    Co-Authors: Sun Yi, Galip A. Ulsoy
    Abstract:

    A design method for time-delayed vision-based DC motor control is presented and experimentally validated. Both proportional-velocity (PV) and proportional-integral-velocity (PIV) feedback controllers are considered. When vision is used to measure the angular displacement of the motor shaft time delays arise due to image processing. Such delays must be considered in the controller design or can lead to poor performance and even instability. In this research we use rightmost Eigenvalue Assignment, based on the Lambert W function method, to design PV and PIV controllers. Experimental results validate previous theoretical and simulation studies [19], [20].

  • robust control and time domain specifications for systems of delay differential equations via Eigenvalue Assignment
    Journal of Dynamic Systems Measurement and Control-transactions of The Asme, 2010
    Co-Authors: Sun Yi, Patrick W. Nelson, Galip A. Ulsoy
    Abstract:

    An approach to Eigenvalue Assignment for systems of linear time-invariant (LTI) delay differential equations (DDEs), based upon the solution in terms of the matrix Lambert W function, is applied to the problem of robust control design for perturbed LTI systems of DDEs, and to the problem of time-domain response specifications. Robust stability of the closed-loop system can be achieved through Eigenvalue Assignment combined with the real stability radius concept. For a LTI system of DDEs with a single delay, which has an infinite number of Eigenvalues, the recently developed Lambert W function-based approach is used to assign a dominant subset of them, which has not been previously feasible. Also, an approach to time-domain specifications for the transient response of systems of DDEs is developed in a way similar to systems of ordinary differential equations using the Lambert W function-based approach.

  • Robust control and time-domain specifications for systems of delay differential equations via Eigenvalue Assignment
    2008 American Control Conference, 2008
    Co-Authors: Sun Yi, Patrick W. Nelson, Galip A. Ulsoy
    Abstract:

    An approach for Eigenvalue Assignment for systems of delay differential equations (DDEs), based upon the Lambert W function, is applied to the problem of robust control design for perturbed systems of DDEs, and to the problem of time-domain specifications. The real stability radius, which measures the ability of a system to preserve its stability under a certain class of real perturbations, can be computed from known nominal coefficients of the DDE representing the system. In this paper, considering the stability radius, the real part of the Eigenvalues is assigned. Also, time-domain specifications for the transient response of systems of DDEs are improved in a way similar to systems of ordinary differential equations using the Eigenvalue Assignment approach.

  • feedback control via Eigenvalue Assignment for time delayed systems using the lambert w function
    ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2007
    Co-Authors: Sun Yi, Patrick W. Nelson, Galip A. Ulsoy
    Abstract:

    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.

Sun Yi - One of the best experts on this subject based on the ideXlab platform.

  • Time-delayed vision-based DC motor control via rightmost Eigenvalue Assignment
    2014 American Control Conference, 2014
    Co-Authors: Sun Yi, Galip A. Ulsoy
    Abstract:

    A design method for time-delayed vision-based DC motor control is presented and experimentally validated. Both proportional-velocity (PV) and proportional-integral-velocity (PIV) feedback controllers are considered. When vision is used to measure the angular displacement of the motor shaft time delays arise due to image processing. Such delays must be considered in the controller design or can lead to poor performance and even instability. In this research we use rightmost Eigenvalue Assignment, based on the Lambert W function method, to design PV and PIV controllers. Experimental results validate previous theoretical and simulation studies [19], [20].

  • Eigenvalue Assignment via the lambert w function for control of time delay systems
    Journal of Vibration and Control, 2010
    Co-Authors: Sun Yi, Patrick W. Nelson, A G Ulsoy
    Abstract:

    In this paper, we consider the problem of feedback controller design via Eigenvalue Assignment for linear time-invariant systems of linear delay differential equations (DDEs) with a single delay. 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 systems of 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 systems of ODEs to systems of DDEs, including the design of feedback controllers via Eigenvalue Assignment. We present such an approach here, illustrate it using some examples, and compare with other existing methods.

  • robust control and time domain specifications for systems of delay differential equations via Eigenvalue Assignment
    Journal of Dynamic Systems Measurement and Control-transactions of The Asme, 2010
    Co-Authors: Sun Yi, Patrick W. Nelson, Galip A. Ulsoy
    Abstract:

    An approach to Eigenvalue Assignment for systems of linear time-invariant (LTI) delay differential equations (DDEs), based upon the solution in terms of the matrix Lambert W function, is applied to the problem of robust control design for perturbed LTI systems of DDEs, and to the problem of time-domain response specifications. Robust stability of the closed-loop system can be achieved through Eigenvalue Assignment combined with the real stability radius concept. For a LTI system of DDEs with a single delay, which has an infinite number of Eigenvalues, the recently developed Lambert W function-based approach is used to assign a dominant subset of them, which has not been previously feasible. Also, an approach to time-domain specifications for the transient response of systems of DDEs is developed in a way similar to systems of ordinary differential equations using the Lambert W function-based approach.

  • Robust control and time-domain specifications for systems of delay differential equations via Eigenvalue Assignment
    2008 American Control Conference, 2008
    Co-Authors: Sun Yi, Patrick W. Nelson, Galip A. Ulsoy
    Abstract:

    An approach for Eigenvalue Assignment for systems of delay differential equations (DDEs), based upon the Lambert W function, is applied to the problem of robust control design for perturbed systems of DDEs, and to the problem of time-domain specifications. The real stability radius, which measures the ability of a system to preserve its stability under a certain class of real perturbations, can be computed from known nominal coefficients of the DDE representing the system. In this paper, considering the stability radius, the real part of the Eigenvalues is assigned. Also, time-domain specifications for the transient response of systems of DDEs are improved in a way similar to systems of ordinary differential equations using the Eigenvalue Assignment approach.

  • feedback control via Eigenvalue Assignment for time delayed systems using the lambert w function
    ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2007
    Co-Authors: Sun Yi, Patrick W. Nelson, Galip A. Ulsoy
    Abstract:

    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.

C.h. Fang - One of the best experts on this subject based on the ideXlab platform.

  • Eigenvalue Assignment inside a disk for generalized state-space systems
    Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
    Co-Authors: Chun-lin Lu, Lin Hong, C.h. Fang
    Abstract:

    The problem of Eigenvalue Assignment inside a disk for generalized state-space systems is investigated. A necessary and sufficient condition, formulated in the linear matrix inequality form, for Eigenvalue clustering inside a specified disk is derived. Then, based on the condition, a state feedback gain is synthesized to ensure not only the closed-loop system is regular and impulse-free but all its finite Eigenvalues lie in a specified open disk. For standard state-space systems, the above same problems are dealt with by solving the Lyapunov equation and the Riccati equation whose solutions are positive definite. However, we indicate that for generalized state-space systems the corresponding solutions are not positive definite any more.

  • A new application of infinite Eigenvalue Assignment in generalized state-space systems
    [1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1991
    Co-Authors: C.h. Fang
    Abstract:

    The author proposes a new application of infinite Eigenvalue Assignment of generalized state-space systems to linear system design. The ideas of infinite Eigenvalue Assignment in generalized state-space systems are applied to develop some useful formulas for system transform and compensator synthesis. Two kinds of control law that lead to two interesting results are discussed.

Lei Zhang - One of the best experts on this subject based on the ideXlab platform.