The Experts below are selected from a list of 243 Experts worldwide ranked by ideXlab platform
Eugene M. Cliff - One of the best experts on this subject based on the ideXlab platform.
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Singular-perturbation of the time-optimal soft-constrained cheap-control problem
IEEE Transactions on Automatic Control, 1993Co-Authors: M.u. Bikdash, Ali H. Nayfeh, Eugene M. CliffAbstract:The solution of a time-optimal soft-constrained control problem with linear dynamics is considered. The cost function has no penalty on the integral of the state. The solution is formulated in terms of the Controllability Grammian and is obtained as the solution of a system of linear algebraic equations and a nonlinear scalar algebraic equation. As the state approaches the origin, or equivalently, as the control becomes cheap, the optimal final time becomes small. This introduces a highly degenerate hierarchy of amplitude scales. An approach based solely on expanding the Controllability Grammian is developed to obtain an asymptotic solution of the problem without resorting to boundary-layer theory. >
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Saturating and time-optimal feedback controls
Journal of Guidance Control and Dynamics, 1993Co-Authors: M.u. Bikdash, Eugene M. Cliff, Ali H. NayfehAbstract:The open-loop solution of the soft-constrained time-optimal control problem can be efficiently computed in terms of the Controllability Grammian matrix, but a closed-loop implementation was found to be cumbersome. This control was observed to have a saturation property strongly reminiscent of the hard-constrained time-optimal control problem. In this paper, we present a theoretical justification for the observed saturation and propose a modification of the problem statement that gives a suboptimal solution and results in a drastically simpler implementation of the feedback time-optimal soft-constrained control. Moreover, we generalize the proposed approach to generate a family of saturating control laws occupying a middle ground between linear state-feedback and hard-constrained time-optimal controls. For illustration, we consider the simultaneous slewing and vibration suppression of an undamped flexible beam that is reducible to a marginally stable linear system. As an example, we design a simple and elegant feedback control law where the regulation time and control amplitude saturate like the square root of the norm of the state vector.
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Closed-loop soft-constrained time-optimal control of flexible space structures
Journal of Guidance Control and Dynamics, 1992Co-Authors: M.u. Bikdash, Eugene M. Cliff, Ali H. NayfehAbstract:We propose numerically efficient solutions for the openand closed-loop time-optimal soft-constrained control of a linear system representing a large flexible space structure. The open-loop solution is expressed in terms of the Controllability Grammian matrix, for which we have obtained a closed-form expression for the undamped system. The qualitative dependence of the control on the initial state and the existence of many solutions satisfying the necessary conditions are shown. A nominal closed-loop control policy is subsequently formulated, but it is shown to be numerically expensive due to the nonuniqueness of extremal solutions. A continuation-based algorithm is proposed to alleviate the computational problem. Finally, the openand closedloop controls are shown to exhibit a saturation property reminiscent of the hard-constrained problem.
M.u. Bikdash - One of the best experts on this subject based on the ideXlab platform.
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Singular-perturbation of the time-optimal soft-constrained cheap-control problem
IEEE Transactions on Automatic Control, 1993Co-Authors: M.u. Bikdash, Ali H. Nayfeh, Eugene M. CliffAbstract:The solution of a time-optimal soft-constrained control problem with linear dynamics is considered. The cost function has no penalty on the integral of the state. The solution is formulated in terms of the Controllability Grammian and is obtained as the solution of a system of linear algebraic equations and a nonlinear scalar algebraic equation. As the state approaches the origin, or equivalently, as the control becomes cheap, the optimal final time becomes small. This introduces a highly degenerate hierarchy of amplitude scales. An approach based solely on expanding the Controllability Grammian is developed to obtain an asymptotic solution of the problem without resorting to boundary-layer theory. >
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Saturating and time-optimal feedback controls
Journal of Guidance Control and Dynamics, 1993Co-Authors: M.u. Bikdash, Eugene M. Cliff, Ali H. NayfehAbstract:The open-loop solution of the soft-constrained time-optimal control problem can be efficiently computed in terms of the Controllability Grammian matrix, but a closed-loop implementation was found to be cumbersome. This control was observed to have a saturation property strongly reminiscent of the hard-constrained time-optimal control problem. In this paper, we present a theoretical justification for the observed saturation and propose a modification of the problem statement that gives a suboptimal solution and results in a drastically simpler implementation of the feedback time-optimal soft-constrained control. Moreover, we generalize the proposed approach to generate a family of saturating control laws occupying a middle ground between linear state-feedback and hard-constrained time-optimal controls. For illustration, we consider the simultaneous slewing and vibration suppression of an undamped flexible beam that is reducible to a marginally stable linear system. As an example, we design a simple and elegant feedback control law where the regulation time and control amplitude saturate like the square root of the norm of the state vector.
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Closed-loop soft-constrained time-optimal control of flexible space structures
Journal of Guidance Control and Dynamics, 1992Co-Authors: M.u. Bikdash, Eugene M. Cliff, Ali H. NayfehAbstract:We propose numerically efficient solutions for the openand closed-loop time-optimal soft-constrained control of a linear system representing a large flexible space structure. The open-loop solution is expressed in terms of the Controllability Grammian matrix, for which we have obtained a closed-form expression for the undamped system. The qualitative dependence of the control on the initial state and the existence of many solutions satisfying the necessary conditions are shown. A nominal closed-loop control policy is subsequently formulated, but it is shown to be numerically expensive due to the nonuniqueness of extremal solutions. A continuation-based algorithm is proposed to alleviate the computational problem. Finally, the openand closedloop controls are shown to exhibit a saturation property reminiscent of the hard-constrained problem.
Pagavathigounder Balasubramaniam - One of the best experts on this subject based on the ideXlab platform.
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Null Controllability of Nonlinear Fractional Stochastic Large-Scale Neutral Systems
Differential Equations and Dynamical Systems, 2019Co-Authors: T. Sathiyaraj, Pagavathigounder BalasubramaniamAbstract:This paper is concerned with the problem of null Controllability of the newly constructed nonlinear fractional stochastic large-scale neutral systems in the finite dimensional space. In particular, a new set of sufficient conditions are derived based on the concepts of null Controllability and under the proved result of the corresponding linear system is null controllable. The results are established by means of the Controllability Grammian matrix which is defined by Mittag-Leffler matrix function, Schauder fixed point theorem and the stochastic analysis approach. Finally, an example is provided to illustrate the obtained theoretical result with numerical simulation.
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Fractional order stochastic dynamical systems with distributed delayed control and Poisson jumps
The European Physical Journal Special Topics, 2016Co-Authors: T. Sathiyaraj, Pagavathigounder BalasubramaniamAbstract:In this paper, we study the Controllability results for nonlinear fractional order stochastic dynamical systems with distributed delayed control and Poisson jumps in finite dimensional space. New set of sufficient conditions are derived based on Schauder’s fixed point theorem and the Controllability Grammian matrix is defined by Mittag-Leffler matrix function. Finally, a numerical example has been given to validate the efficiency of the proposed theoretical results.
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Fractional order stochastic dynamical systems with distributed delayed control and Poisson jumps
The European Physical Journal Special Topics, 2016Co-Authors: T. Sathiyaraj, Pagavathigounder BalasubramaniamAbstract:In this paper, we study the Controllability results for nonlinear fractional order stochastic dynamical systems with distributed delayed control and Poisson jumps in finite dimensional space. New set of sufficient conditions are derived based on Schauder’s fixed point theorem and the Controllability Grammian matrix is defined by Mittag-Leffler matrix function. Finally, a numerical example has been given to validate the efficiency of the proposed theoretical results.
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Controllability of fractional order stochastic differential inclusions with fractional Brownian motion in finite dimensional space
IEEE CAA Journal of Automatica Sinica, 2016Co-Authors: T. Sathiyaraj, Pagavathigounder BalasubramaniamAbstract:In this paper, sufficient conditions are formulated for Controllability of fractional order stochastic differential inclusions with fractional Brownian motion U+0028 fBm U+0029 via fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler fixed point theorem for the nonconvex case. The Controllability Grammian matrix is defined by using Mittag-Leffler matrix function. Finally, a numerical example is presented to illustrate the efficiency of the obtained theoretical results.
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Controllability of Nonlinear Fractional Neutral Stochastic Dynamical Systems with Poisson Jumps
Mathematical Analysis and its Applications, 2015Co-Authors: T. Sathiyaraj, Pagavathigounder BalasubramaniamAbstract:This paper is concerned with the Controllability of fractional neutral stochastic dynamical systems with Poisson jumps in the finite dimensional space. Sufficient conditions for Controllability results are obtained by using Krasnoselskii’s fixed point theorem. The Controllability Grammian matrix is defined by Mittag-Leffler matrix function.
Ali H. Nayfeh - One of the best experts on this subject based on the ideXlab platform.
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Singular-perturbation of the time-optimal soft-constrained cheap-control problem
IEEE Transactions on Automatic Control, 1993Co-Authors: M.u. Bikdash, Ali H. Nayfeh, Eugene M. CliffAbstract:The solution of a time-optimal soft-constrained control problem with linear dynamics is considered. The cost function has no penalty on the integral of the state. The solution is formulated in terms of the Controllability Grammian and is obtained as the solution of a system of linear algebraic equations and a nonlinear scalar algebraic equation. As the state approaches the origin, or equivalently, as the control becomes cheap, the optimal final time becomes small. This introduces a highly degenerate hierarchy of amplitude scales. An approach based solely on expanding the Controllability Grammian is developed to obtain an asymptotic solution of the problem without resorting to boundary-layer theory. >
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Saturating and time-optimal feedback controls
Journal of Guidance Control and Dynamics, 1993Co-Authors: M.u. Bikdash, Eugene M. Cliff, Ali H. NayfehAbstract:The open-loop solution of the soft-constrained time-optimal control problem can be efficiently computed in terms of the Controllability Grammian matrix, but a closed-loop implementation was found to be cumbersome. This control was observed to have a saturation property strongly reminiscent of the hard-constrained time-optimal control problem. In this paper, we present a theoretical justification for the observed saturation and propose a modification of the problem statement that gives a suboptimal solution and results in a drastically simpler implementation of the feedback time-optimal soft-constrained control. Moreover, we generalize the proposed approach to generate a family of saturating control laws occupying a middle ground between linear state-feedback and hard-constrained time-optimal controls. For illustration, we consider the simultaneous slewing and vibration suppression of an undamped flexible beam that is reducible to a marginally stable linear system. As an example, we design a simple and elegant feedback control law where the regulation time and control amplitude saturate like the square root of the norm of the state vector.
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Closed-loop soft-constrained time-optimal control of flexible space structures
Journal of Guidance Control and Dynamics, 1992Co-Authors: M.u. Bikdash, Eugene M. Cliff, Ali H. NayfehAbstract:We propose numerically efficient solutions for the openand closed-loop time-optimal soft-constrained control of a linear system representing a large flexible space structure. The open-loop solution is expressed in terms of the Controllability Grammian matrix, for which we have obtained a closed-form expression for the undamped system. The qualitative dependence of the control on the initial state and the existence of many solutions satisfying the necessary conditions are shown. A nominal closed-loop control policy is subsequently formulated, but it is shown to be numerically expensive due to the nonuniqueness of extremal solutions. A continuation-based algorithm is proposed to alleviate the computational problem. Finally, the openand closedloop controls are shown to exhibit a saturation property reminiscent of the hard-constrained problem.
Mehrdad R. Kermani - One of the best experts on this subject based on the ideXlab platform.
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Study of system parameters and control design for a flexible manipulator using piezoelectric transducers
Smart Materials and Structures, 2005Co-Authors: Mehrdad R. Kermani, Mehrdad Moallem, Rajni V. PatelAbstract:In this paper, a nonlinear control scheme is presented to achieve small tracking errors in a flexible manipulator with two degrees of freedom. A secondary actuation mechanism using piezoelectric materials is added to the system for suppressing residual vibrations at the end point of the flexible link. A small piece of piezo-ceramic is also used, as a sensor, in order to obtain the modal states of the system. The effects of changing physical parameters such as relative thickness of the piezo-ceramic with respect to the flexible link, the optimum location and the length of the actuator are studied based on the singular value decomposition of the Controllability Grammian of the system. A partial feedback linearization technique based on output redefinition is utilized to obtain an appropriate control output for each joint and the piezoelectric actuator. A model for friction is obtained and included in the control law. Experimental results show that applying the suggested control scheme results in smooth and precise motion of the flexible manipulator without exciting unwanted vibration modes. Comparisons are made when a linear control scheme is used for the tracking problem.
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parameter selection and control design for vibration suppression using piezoelectric transducers
Control Engineering Practice, 2004Co-Authors: Mehrdad R. Kermani, M. Moallem, R.v. PatelAbstract:Abstract In this paper a selection process for piezoelectric transducers (PZT) used as actuators for suppressing vibrations in a flexible beam system is presented. The effects of changing physical parameters such as relative thickness of the piezoelectric ceramic with respect to the beam, Young's modulus of elasticity, the optimum location and the length of the actuator are studied based on the singular value decomposition of the Controllability Grammian of the system. It is shown that for each of the aforementioned parameters, an optimum value can be found which maximizes the singular value associated with one vibrating mode. For the thickness ratio of the beam with respect to the PZT actuator, it is shown that an optimum value can be found that maximizes all singular values, simultaneously. However, in other cases, e.g., the location of the actuator, there is no such unique solution for all singular values. A nonlinear control scheme for an actuated rotating flexible link is developed based on partial feedback linearization. Simulation results are given for the case of a cantilevered beam and comparisons are made between different configurations and locations of the actuator. Experimental evaluations show that applying the control scheme to the optimized system results in considerable vibration attenuation of the dominant modes without spill-over into uncontrolled modes.
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Real-Time Active Control of Vibrations in a Flexible Beam Using Piezoelectric Transducers
IFAC Proceedings Volumes, 2002Co-Authors: Mehrdad R. Kermani, Mehrdad Moallem, Rajni V. PatelAbstract:Abstract This paper discusses the selection process for piezoelectric transducers (PZT) used as actuator elements for suppressing vibrations in a flexible beam system. A model for a clamped-free cantilevered beam is developed. The effects of changing physical parameters such as thickness of the piezoelectric ceramic, the optimum location of the PZT actuator, and the length of the PZT are studied based on the singular value decomposition of the Controllability Grammian of the resulting system. A real-time experiment using the beam system with an active damping controller is implemented under the QNX real-time operating system. Simulation and experimental results show that applying a conventional controller to the system results in considerable vibration attenuation of the dominant modes.
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ICRA - Optimizing the performance of piezoelectric actuators for active vibration control
Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292), 1Co-Authors: Mehrdad R. Kermani, Mehrdad Moallem, Rajni V. PatelAbstract:This paper discusses the selection process for piezoelectric transducers (PZT) used as actuator elements for suppressing vibrations in a flexible beam system. The effects of changing physical parameters such as the relative thickness of the piezoelectric ceramic with respect to the beam, the optimum location of the PZT actuator, and the length of the PZT are studied based on the singular value decomposition of the Controllability Grammian of the resulting system. A model for a clamped-mass cantilevered beam is developed and its frequency response is compared with that obtained experimentally. Simulation results are given to illustrate how this method can be used to determine physical properties and location of the PZT actuator. Further experimental studies are currently being performed.