Control of Delay-ODE, Delay-PDE, and PDE-ODE Cascades
نویسنده
چکیده
I. INTRODUCTION Delay systems occupy a special place within the field of distributed parameter systems. Certain problems for this class of distributed parameter systems lend themselves to more elegant, or even explicit solutions. An enormous wealth of knowledge and research results exists for control of systems with state delays and input delays. Problems with long input delays, for unstable plants, represent a particular challenge. It has been known for about three decades now [1], [2] that the system
منابع مشابه
THE USE OF A RUNGE-KUTTA SCHEME FOR AN ODE-PDE MODEL OF SUPPLY CHAINS
Integrating various suppliers to satisfy market demand is of great importance for e ective supply chain management. In this paper, we consider the ODE-PDE model of supply chain and apply a classical explicit fourth-order Runge-Kutta scheme for the related ODE model of suppliers. Also, the convergence of the proposed method is proved. Finally a numerical example is studied to demonstrate the acc...
متن کاملCompensating actuator and sensor dynamics governed by diffusion PDEs
For (possibly unstable) ODE systems with actuator delay, predictor-based infinite-dimensional feedback can compensate for actuator delay of arbitrary length and achieve stabilization.We extend this concept to another class of PDE-ODE cascades, where the infinite-dimensional part of the plant is of diffusive, rather than convective type. We derive predictor-like feedback laws and observers, with...
متن کاملCompensation of actuator dynamics governed by quasilinear hyperbolic PDEs
We present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by a certain class of, quasilinear, first-order hyperbolic PDEs. Since for such PDE–ODE cascades the speed of propagation depends on the PDE state itself (which implies that the prediction horizon cannot be a priori known analytically), the key design challenge is the determination of the pre...
متن کاملPDE based observer design for nonlinear systems with large output delay
In this paper, we develop a new observer design method for nonlinear systems with large transport delays. The new observer design is a generalization of the PDE-based backstepping-like observer design approach. First developed for delayed linear systems, this approach relies on a modelling of the output time-delay by a 1st order hyperbolic equation, leading to an ODE–PDE representation of the s...
متن کاملNonlinear stabilization through wave PDE dynamics with a moving uncontrolled boundary
In deep oil drilling, the length of the domain overwhich thewave equationmodels the torsional dynamics of the drill string keeps changing with time, and it also depends on the drill bit speed. Moreover, the drill bit speed cannot be controlled directly. In this context, we consider predictor-based design for the cascade system of a nonlinear ODE and a wave PDE with a moving uncontrolled boundar...
متن کامل