Asymptotic behavior of Timoshenko beam with dissipative boundary feedback

Stabilization of string system with linear boundary feedback

The initial boundary value problem for linear elastodynamic system for viscoporous materials is considered. Exponential decay of solutions via the linear boundary feedback is established. Existence of solutions is obtained through the method of c0‐semigroups. Exponential stabilization is derived via a proper collection of ideas of observability inequality, energy identity and c0‐semigroup of contractions. Copyright © 2008 John Wiley & Sons, Ltd.

This paper investigates the generalized exponential stabilization (GES) of a class of semilinear parabolic equations, which is a generalization of the result of exponential stabilization and has the character of accelerating decay process locally. From the point of admissibility of unbounded input operators of view, the well‐posedness of the open‐loop system is analyzed. Then, under some sufficient conditions expressed by linear matrix inequality, a linear boundary output feedback controller only using boundary measurement is proposed such that the closed‐loop system satisfies GES in absence of external disturbance and satisfies an H∞ performance index when disturbance exists. The well‐posedness of the resulting closed‐loop system is also given via semi‐group theory. Finally, we give numerical examples to verify the performance of the designed boundary controller.

In this article, a robust linear output feedback control scheme is proposed for the efficient regulation, and trajectory tracking tasks, in the nonlinear, multivariable, quad-rotor system model. The proposed linear feedback scheme is based on the use of a classical linear feedback controllers and suitably extended, high gain, linear Generalized Proportional Integral (GPI) observers; aiding the linear feedback controllers in two important tasks: 1) accurate estimation of the input-output system model nonlinearities, 2) accurate estimation of the unmeasured phase variables associated with the flat, or linearizing, output variables. These two key pieces of information are used in the proposed feedback controller in a) approximate, yet close, cancelation, as a lumped unstructured time-varying term, of the influence of the highly coupled nonlinearities and b) devising proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers.

A linear feedback control is designed regardless of dissipativity of the system for the stabilization of a flexible beam with a tip rigid body. The Riesz basis approach is adopted in the investigation. It is shown that the closed loop system is a Riesz spectral system and as consequences, the exponential stability, the observability and the controllability of the system are concluded. Finally, some numerical results are also presented.

Conical magnetic bearings with radial and thrust (axial) control using the input-output feedback linearization method are considered. By suitable selection of nine output variables, the nonlinear magnetic bearing system is transformed to nine linear decoupled subsystems with no internal dynamics using feedback linearization control. Furthermore, a hybrid approach integrating feedback linearization and fuzzy control is proposed for improving the transient performance and robustness of the nonlinear magnetic bearings. Computer simulations are shown to illustrate the effectiveness of the proposed control strategy for simultaneous rotor-shaft speed tracking control and gap deviations regulation.

In this paper, we consider the system modeled by an axially moving string and a mass-damper-spring (MDS) controller, applied at the right-hand side (RHS) boundary of the string. We are concerned with the nonlinear string and the effect of the control mechanism. We stabilize the system through a proposed boundary velocity feedback control law. Linear and nonlinear control laws through this controller are proposed. In this paper, we find that a linear boundary feedback caused the total mechanical energy of the system to decay an asymptotically, but it fails for an exponential decay. However, a nonlinear boundary feedback controller can stabilize the system exponentially. The asymptotic and exponential stability are verified.

Based on the finite-time control technique, the position control problem of permanent magnet synchronous motor(PMSM) servo system is studied. Using backing-stepping method, a control scheme based on feedback linearization and finite-time control technique is proposed for position loop. Rigorous mathematical analysis is given for the close loop system performance in the presence of disturbances. The results show that, compared with the conventional control scheme based on PD and feedback linearization, this method not only makes the position tracking error of the closed loop system with a faster convergence rate, but also makes the boundary of steady-state error smaller by regulating the controller parameters, which means the closed loop system has stronger disturbance rejection property. The simulation results validate the efficiency of this method.

Locally exponential stabilization for the Burgers–Fisher system is addressed by boundary control in this paper. For the nonlinear partial differential equation, a linear boundary feedback control law is applied to control the Burgers–Fisher system. Locally exponential stabilization of the closed loop system is established based on the relationship between operator theories and relations of different norms. Finally, the theory is validated through numerical simulations.

In this article we propose a robust linear output feedback control scheme for the regulation and trajectory tracking tasks of the load angle variable in a widely used, nonlinear, single synchronous generator model. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and a suitably extended high gain linear observer; aiding the linear feedback controller, in two important tasks: 1) accurate estimation of the input-output system model nonlinearities, 2) accurate estimation of the unmeasured phase variables associated with the load angle variable (shaft angular speed deviation, and shaft angular acceleration). These two key pieces of information are used in the proposed feedback controller to a) cancel, as a lumped unstructured time-varying term, the influence of the nonlinearities and b) devise a proper linear output feedback based on the approximate estimates of the phase variables. The robustness of the scheme is tested against a three phase short circuit of significant duration. The proposed, observer-based, feedback controller requires knowledge of only two constant parameters of the model. The closed loop responses are shown to be robust with respect to reasonable deviations of these parameters from their nominal values.

Exponential Stabilization of an Overhead Crane with Flexible Cable Via the Cascade Approach 1

Neural Adaptive based on feedback linearization is used in this study to control the velocity and recognition of an electro hydraulic servo system (EHSS) in the presence of flow nonlinearities as well as internal friction and noise.This controller consists of four parts: PID controller, feedback linearization controller, neural network controller and the neural network identifier.The feedback linearization controller is used to prevent the system state in a region where the neural network can be accurately trained to achieve optimal control.The combination of controllers produces a stable system which adapts to optimize performance.This technique, as shown, can be prosperously used to stabilize any selected operating point of the system with noise and without interference.All consequences achieved are validated by computer simulation of a nonlinear mathematical model of the system.The fore mentioned controllers have a vast range to control the system.We compare Neural Adaptive based on feedback linearization controller results with feedback linearization, back stepping and PID controller.

This paper investigates the problem of stabilizing a single input uncertain linear system using linear state feedback control. The uncertain system is described by a linear state equation which contains uncertain parameters which are unknown but bounded. A quadratic Lyapunov function is used to establish the stability of the closed loop system.

It is shown that the energy of a thermoelastic bar and plate decays exponentially fast. The energy method, combined with a multiplier technique and compactness property, is used.

The feedback stabilization problem of a nonuniform Timoshenko beam system with rotor inertia at the tip of the beam is studied. First, as a special kind of linear boundary force feedback and moment control is applied to the beam' s tip, the strict mathematical treatment,a suitable state Hilbert space is chosen, and the well-poseness of the corresponding closed loop system is proved by using the semigroup theory of bounded linear operators. Then the energy corresponding to the closed loop system is shown to be exponentially stable. Finally, in the special case of uniform beam,some sufficient and necessary conditions for the corresponding closed loop system to be asymptotically stable are derived.