Browsing by Subject "Boundary control"
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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 Boundary control of some infinite dimensional systems(IFAC, 2005) Morgül, ÖmerWe will consider the feedback stabilization of a class of infinite dimensional systems by using boundary control, i.e. control inputs are applied at the boundaries of such systems. Such systems usually possess an internal energy, and along their solutions a conservation of energy equation hold. By utilizing this relation, we will prove various stability results.We will also give an example on the application of the proposed technique to some well known passive systems. We will also present some simulation results.Item Open Access Low dimensional modelling and Dirichlét boundary controller design for Burgers equation(Taylor & Francis, 2004) Efe, M. Ö.; Özbay, HitayModelling and boundary control for the Burgers equation is studied in this paper. Modelling has been done via processing of numerical observations through proper orthogonal decomposition (POD) with Galerkin projection. This results in a set of spatial basis functions together with a set of ordinary differential equations (ODEs) describing the temporal evolution. Since the dynamics described by the Burgers equation are non-linear, the corresponding reduced-order dynamics turn out to be non-linear. The presented analysis explains how the free boundary condition appears as a control input in the ODEs and how controller design can be accomplished. The issues of control system synthesis are discussed from the point of practicality, performance and robustness. The numerical results obtained are in good compliance with the theoretical claims. A comparison of various different approaches is presented. © 2004 Taylor and Francis Ltd.Item Open Access On the boundary control of a flexible robot arm(IEEE, 2001) Morgül, ÖmerWe consider a flexible robot arm modeled as a single flexible link clamped to a rigid body. We assume that the system performs only planar motion. For this system, we pose two control problems; namely, the orientation and stabilization of the system. We propose a class of controllers to solve these problems.Item Open Access On the boundary control of Kirchhoff's nonlinear string(IFAC, 2007) Morgül, Ömer; Shahruz, S. M.In this paper we propose two new classes of controllers which stabilize Kirchhoff's nonlinear string by using boundary control techniques. We assume that the boundary displacement is the only available measurement. The classes of controllers proposed in this paper are related to the positive real controllers. One of the classes generalizes a special class of such stabilizing controllers which is already proposed in the literature and the other one is new.Item Open Access On the control of two-link flexible robot arm with nonuniform cross section(SAGE, 2010) Dogan, M.; Morgül, Ö.We consider the motion of a two-link flexible arm with nonuniform cross section. We obtain the equations of motion by using the extended Hamiltons principle. These equations consist of coupled partial differential equations and (nonlinear) ordinary differential equations with appropriate boundary conditions. Our control problem is to achieve the given desired link angles and suppress the link vibrations. To solve this problem, we propose a novel control scheme which consists of a dominant control law together with a parallel controller. We show that with the proposed controller, the control objectives are satisfied. Our stability analysis is based on the Lyapunov approach and LaSalles invariance principle extended to infinite-dimensional systems. We also present some simulation results, which indicate that large parameter uncertainties such as tip and hub mass changes are also handled effectively by the proposed controller.Item Open Access On the stabilization of a flexible beam with a tip mass(Society for Industrial and Applied Mathematics, 1998-11) Conrad, F.; Morgül, Ö.We study the stability of a flexible beam that is clamped at one end and free at the other; a mass is also attached to the free end of the beam. To stabilize this system we apply a boundary control force at the free end of the beam. We prove that the closed-loop system is well-posed and is exponentially stable. We then analyze the spectrum of the system for a special case and prove that the spectrum determines the exponential decay rate for the considered case.Item Open Access On the stabilization of the wave equation(Springer, 1993) Morgül, Ömer; Curtain, R. F.; Bensoussan, A.; Lions, J. L.Item Open Access PDE control of a rotating shear beam with boundary feedback(IEEE, 2009-08) Doğan, M.; Morgül, ÖmerWe consider a flexible structure modeled as a shear beam which is clamped to a rigid body at one end and is free at the other end. The whole structure is free to rotate on the horizontal plane. We first model the system by using Partial Differential Equations (PDE) and we propose boundary feedback laws to achieve set point regulation of the rotation angle as well as to suppress the elastic vibrations. The proposed control laws are based on PDE model, hence we do not resort to discretization of the system equations by available methods. We utilize a coordinate transformation based on an invertible integral transformation by using Volterra form and backstepping techniques. We also present some simulation results. © 2009 EUCA.Item Open Access Use of natural switching in the boundary control of DC/DC buck and boost converters(2021-08) Koç, Yunus EmreDC-DC converters are extensively used in many power electronics applications such as photovoltaic systems, wind energy systems, DC motor drives, mobile devices, electric vehicles, etc. Fundamental performance criteria in these appli-cations include tight line and load regulation, low output voltage ripple, high efficiency and fast response to load uncertainties. Also, the trade-off between high performance and component sizes must be considered. In order to meet these requirements, a boundary control method is developed for the resistive loaded buck and boost DC-DC converters. First, normalized plant models are obtained for both converters. The normalization generalizes the controller design by making it independent of the circuit parameters. Then, natural phase plane trajectories of the systems are derived in the normalized domain. Using the nat-ural trajectories of the converters as switching surfaces, special boundary control laws are defined. Switches in the systems are driven by control inputs generated according to the control laws. Via this boundary control method, the fast dy-namic response is provided by utilizing passive components that take up the most space, namely inductor and capacitor, at their theoretical limits. This allows the overall circuit size to be kept small. Finally, the control laws are altered by a small factor so that in steady state, finite and controlled frequency operation and known ripple magnitudes of system states are obtained. In this way, a common problem in boundary control applications called chattering is eliminated. It is shown via simulations that the proposed controllers manage to recover from load and start-up transients by single switching action for both converters.