Stabilization of time delay systems with saturations via PDE predictor boundary control design

Selvaraj, Palanisamy; Kwon, Oh‐Min; Lee, Seung-Hoon; Sakthivel, R.

doi:10.1016/j.jfranklin.2021.09.011

Cited by 6 publications

(3 citation statements)

References 40 publications

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“…In order to calculate f d (k − 1), a Lyapunov functional is defned based on equation (10), and by negating its increment in the direction of discrete-time subjected to system dynamics, a convex inequality of equation ( 11) is obtained.…”

Section: Trajectory Planning For the Moving Support Based On Dynamic ...mentioning

confidence: 99%

“…By placing the 􏽢 f d (k − 1) in the dynamic equation of the actuator, the value of f C (k − 1) is calculated. Since the dynamic equation of the actuator is discretized according to equation ( 16) and is a second-order dynamic similar to that expressed in equations ( 8)- (10), in order to prevent the repetition of the explanations, the command control signal f C (k − 1) is calculated based on equation (17). Corresponding to the predictive error of the force generated by the actuator according to equation (17), the appropriate proximity coefcients are determined so as to specify the control signal f C (k − 1).…”

Section: Constrained Actuator Output Planning Based On Outputmentioning

confidence: 99%

“…Among the most important methods of mathematical modeling and control of fexible systems, modal methods, the method of assume modes, the linear or nonlinear fnite elements method, the method of lines, and variable separation methods, can be mentioned [7,8]. Another technique of mechanical systems' control with fexible arms is the boundary control method, in which the dynamic equations of the system that are in the form of PDE are used directly by methods such as functional analysis, operators' techniques, and the semigroup theory, and the diferential geometry calculus is included in the design of the control system [9,10]. Te subject of controlling systems with fexible components, in the presence of nonlinear efects of stifness and damping in the system confguration, is acutely more difcult than in the case where the mathematical model is considered as linear operators.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Tracking Control Algorithm for Dynamical Output Systems Manipulated by the Hardly Constrained Oscillatory Actuator

Homaeinezhad

Mostaghim

2023

Structural Control and Health Monitoring

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In this article, a nonlinear control algorithm has been presented, in order to reduce vibrational movements of a flexible beam cantilevered in a cart supported by nonlinear stiffness, actuated by a hardly constrained second-order dynamic system. In the presented control algorithm, the interactive model of the solid body and a flexible beam has been extracted and utilized to design an algorithm, based on which the nonlinear vibrations of the tip point of the beam whose function is smooth and nonoscillatory tracking of the predefined desired trajectory are diminished. To design a nonlinear vibration control system of the beam, it has been assumed that the feedback system includes three modules: a vibrational beam cantilevered on a base, a base affected by nonlinear stiffness and actuator’s control force, and a force imposing system with constraints of bandwidth frequency limitation and actuation saturation boundary. In order to design this control system, the generalized tracking error function has been defined to nonlinearly amplify the vibrationally induced error and its rate, which by properly adjusting them, a new quantity can be extracted that satisfies the control system design constraints. To design a tracking control system for a nonlinear vibrating beam for the aforementioned three-modulus system, first, the generalized tracking error for the three modules is separately defined and parametrized, and then, by simultaneously adjusting all the defined parameters systematically, the predominant system presence in Lyapunov stability conditions is guaranteed. To illustrate the multimodule imitative (MMI) controller design algorithm, a moving support connected to a nonlinear spring and damper is considered, which carries a flexible cantilevered beam. The applied actuation system has second-order linear dynamics with the presence of command control saturation boundaries. For each of the abovementioned modules, a generalized tracking error is defined, and then, it is explained to how simultaneously adjust the parameters based on the stability and actuation constraints. The MMI controller is applied to the mentioned mechanical system modeled in the ANSYS® Mechanical APDL environment, and then, the necessary conclusions are discussed about the performance of the control system in eliminating the vibrations of the flexible arm, considering the actuation constraints while possessing the dominant Lyapunov stability.

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Section: Trajectory Planning For the Moving Support Based On Dynamic ...mentioning

confidence: 99%