Browsing by Subject "Distributed parameter systems"
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Item Open Access Boundary control of a rotating shear beam with observer feedback(Sage Publications, 2012) Dog̃an, M.; Morgül, O.We consider a flexible structure modeled as a shear beam which is free to rotate on the horizontal plane. We first model the system by using partial differential equations and we propose boundary feedback laws to achieve set-point regulation of the rotation angle as well as to suppress elastic vibrations. The main advantage of the proposed design, which consists of a decoupling controller together with an observer, is that it is easy to implement. We utilize a coordinate transformation based on an invertible integral transformation by using Volterra form and backstepping techniques. We show that with the proposed controller, the control objectives are satisfied.Item Open Access Control and stabilization of a rotating flexible structure(Elsevier, 1994) Morgül, Ö.We consider a flexible beam clamped to a rigid base at one end and free at the other end. We assume that the rigid base rotates with a constant angular velocity and that the motion of the flexible beam takes place on a plane. To suppress the beam vibrations, we propose dynamic control laws for boundary control force and torque, both applied to the free end of the beam. We show that, under some conditions, one of which is the strict positive realness of the actuator transfer functions which generate the boundary control force and torque, the beam vibrations asymptotically decay to zero if the rigid base angular frequency is sufficiently small. Moreover, if the transfer functions are proper but not strictly proper, we show that the decay is exponential. We also give a bound on the constant angular velocity above which the system becomes unstable.Item Open Access Dynamic boundary control of the timoshenko beam(Pergamon Press, 1992) Morgül, Ö.We consider a clamped-free Timoshenko beam. To stabilize the beam vibrations, we propose a dynamic boundary control law applied at the free end of the beam. We prove that with the proposed control law, the beam vibrations uniformly and exponentially decay to zero. The proof uses a Lyapunov functional based on the energy of the system. © 1992.Item Open Access An exponential stability result for the wave equation(Elsevier, 2002) Morgül, Ö.We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize this system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function which consists of a strictly positive real function and some poles on the imaginary axis. We then show that under some conditions the closed-loop system is exponentially stable. © 2002 Published by Elsevier Ltd.Item Open Access On the boundary control of beam equation(IFAC, 2002) Morgül, ÖmerA flexible system described by Euler-Bernoulli beam equation is considered. The beam is clamped at one end, and is free at the other end. Boundary control force and torque inputs are applied at the free end of the beam. The transfer functions of the controllers are marginally stable and may contain some poles on the imaginary axis. Various stability results are shown and the application of the proposed control law to disturbance rejection problem is considered.Item Open Access On the strain feedback control of a flexible robot arm(IEEE, 2011) Morgül, ÖmerWe consider a flexible robot arm modeled as a rigid hub which rotates in an inertial space; a light flexible link is clamped to the rigid body at one end and is free at the other. We assume that the flexible link performs only planar motion. We assume that the strain of the flexible link at the clamped end is measurable. We show that suitable control torques applied to the rigid hub stabilizes the system and achieves orientation under certain conditions. The proposed torque contains derivative, proportional and integral terms of the strain. The stability proofs depend on the passivity of the controller transfer function.Item Open Access An operator theoretic approach to robust control of infinite dimensional systems(Applied Mathematics Scientific Research Institute, 2013) Özbay, HitayThe purpose of this paper is to give an overview of the skew Toeplitz approach to H∞ control of a class of infinite dimensional systems. Numerical steps involved in the computations of optimal and suboptimal controllers are demonstrated with different examples, including flexible beam models and systems with time delays.Item Open Access Sensitivity reduction by strongly stabilizing controllers for MIMO distributed parameter systems(Institute of Electrical and Electronics Engineers, 2011-12-09) Wakaiki, M.; Yamamoto, Y.; Özbay, HitayThis note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time-invariant multi-input multioutput distributed parameter system. The plant we consider has finitely many unstable zeros, which are simple and blocking, but can possess infinitely many unstable poles. We obtain a necessary condition and a sufficient condition for the solvability of the problem, using the matrix Nevanlinna-Pick interpolation with boundary conditions. We also develop a necessary and sufficient condition for the solvability of the interpolation problem, and show an algorithm to obtain the solutions. Our method to solve the interpolation problem is based on the Schur-Nevanlinna algorithm.Item Open Access Stabilization and disturbance rejection for the beam equation(IEEE, 2001) Morgül, ÖmerWe consider a system described by the Euler-Bernoulli beam equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. We show that with the proposed controller, the closed-loop system is asymptotically stable. Moreover, we consider the case in which the output of the controller is corrupted by disturbance.Item Open Access Stabilization and disturbance rejection for the beam equation(IEEE, 2001) Morgül, Ö.We consider a system described by the Euler-Bernoulli beam equation. For stabilization, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the controller is a marginally stable positive real function which may contain poles on the imaginary axis. We then give various asymptotical and exponential stability results. We also consider the disturbance rejection problem.Item Open Access Stabilization and disturbance rejection for the wave equation(Institute of Electrical and Electronics Engineers, 1998-01) Morgül, Ö.We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function of the complex variable s and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis, provided that the residues corresponding to these poles are nonnegative; the rest of the transfer function is required to be a strictly positive real function. We then show that depending on the location of the pole on the imaginary axis, the closed-loop system is asymptotically stable. We also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately. We also present some numerical simulation results which support this argument.Item Open Access Tangential Nevanlinna-Pick interpolation for strong stabilization of MIMO distributed parameter systems(IEEE, 2012-12) Wakaiki, M.; Yamamoto, Y.; Özbay, HitayWe study the problem of finding stable controllers that stabilize a multi-input multi-output distributed parameter system while simultaneously reducing the sensitivity of the system. The plants we consider have finitely many unstable transmission zeros, but they can possess infinitely many unstable poles. Using the tangential Nevanlinna-Pick interpolation with boundary conditions, we obtain both upper and lower bounds of the minimum sensitivity that can be achieved by stable controllers. We also derive a method to find stable controllers for sensitivity reduction. In addition, we apply the proposed method to a repetitive control system. © 2012 IEEE.