This paper presents a method for designing a backstepping tracking controller for a class of continuous-time linear systems with actuator delay subject to a reference signal. The actuator delay can be modeled by a first-order hyperbolic PDE, and then a PDE-ODE coupled system is obtained. By applying the backstepping transformation to the coupled system, a feedback controller that includes the state of the system, the integral of the input control, and the integral of the tracking error is derived. We show that the closed-loop system is asymptotically stable at the equilibrium point and achieves complete regulation under the stabilizability assumption. The designs in this paper are illustrated with numerical simulations.
This paper presents a method for designing a type one servomechanism for a discrete-time linear system with input delay subject to a previewable desired output and a nonmeasurable constant disturbance. The tracking problem of a delay system is transformed into a regulation problem of a delay-free system via constructing an augmented error system and a variable substitution. A controller is obtained with delay compensation and preview compensation based on preview control theory and the predictor method. When the state vector is not directly measurable, a full-dimensional observer is offered. The effectiveness of the design method is demonstrated by numerical simulations.
This paper presents a design method for preview controller of discrete-time linear systems with multiple input delays based on the discrete lifting technology for single input delay plants. The design approach is featured by the infinite dimensionality of the actuator dynamics and the discrete-time feature of the delay-accumulation feedback operator. Specifically, an augmented error system was constructed to transform the tracking problem into a regulation problem, and the delays were eliminated by a new discrete lifting technique. On this basis, a controller with preview compensation and delay compensation was developed based on the preview control technology. The proposed controller was proved through a case study as suitable for multiple input delays system like robot trajectory control. RÉSUMÉ. Cet article pré sente une mé thode de conception pour le contrôleur de pré visualisation de systèmes linéaires à temps discret avec des retards d'entrée multiples basés sur la technologie de levage discret pour des installations à retard d'entrée unique. L'approche de conception est caracté risé e par la dimension infinie de la dynamique de l'actionneur et la caracté ristique de temps discret de l'opé rateur de ré troaction d'accumulation de retard. Spé cifiquement, un systè me d'erreur amé lioré a é té construit pour transformer le problè me de suivi en problè me de ré gulation, et les retards ont é té é liminé s par une nouvelle technique de levage discret. Sur cette base, un contrôleur avec compensation de pré visualisation et compensation de retard a é té dé veloppé sur la base de la technologie de contrôle de pré visualisation. Une é tude de cas a prouvé que le contrôleur proposé convenait à un systè me à retards d'entrée multiples comme le contrôle de trajectoire de robot.
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