This paper studies linear model predictive control of real matrix-valued single delay systems. The delay system is written as an abstract inflnite-dimensional control system which is then mapped into an infinite-dimen...
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ISBN:
(数字)9781538682661
ISBN:
(纸本)9781538682678
This paper studies linear model predictive control of real matrix-valued single delay systems. The delay system is written as an abstract inflnite-dimensional control system which is then mapped into an infinite-dimensional discrete-time control system using Cayley-Tustin discretization. A constrained model predictive control (MPC) problem is formulated for the discrete-time system where a terminal penalty function is utilized to cast the infinite-horizon optimization problem into a finite-horizon one. The proposed MPC design is demonstrated on an example of constrained stabilization of a 2 × 2 system. We will demonstrate that the proposed discrete-time MPC law not only stabilizes the discrete-time system but can be utilized in stabilizing the original continuoustime system as well, which is due to several favorable properties of the Cayley-Tustin discretization.
This paper presents a model reference adaptive control of a class of distributed parameter systems described by linear, n-dimensional, parabolic partial differential equations. Unknown parameters appearing in the syst...
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This paper presents a model reference adaptive control of a class of distributed parameter systems described by linear, n-dimensional, parabolic partial differential equations. Unknown parameters appearing in the system equation are either constant or spatially-varying. distributed sensing and actuation are assumed to be available. Adaptation laws are obtained by the Lyapunov redesign method. It is shown that the concept of persistency of excitation, which guarantees the parameter error convergence to zero in finite dimensional adaptive systems, in infinite dimensional adaptive systems should be investigated in relation to time variable, spatial variable, and also boundary conditions. Unlike finite dimensional case, in infinite dimensional adaptive systems even a constant input is shown to be persistently exciting in the sense that it guarantees the convergence of parameter errors to zero. Averaging theorems for two-time scale systems which involve a finite dimensional slow system and an infinite dimensional fast system are developed. The exponential stability of the adaptive system, which is critical in finite dimensional adaptive control in terms of tolerating disturbances and unmodeled dynamics, is shown by applying averaging. A numerical example which demonstrates an averaged system, and computer simulations are provided.< >
In this paper, we propose a hierarchical modeling of the systems described by conservation laws. A conservation law on a hierarchically parted domain can be considered as a subsystem which interacts with neighbor elem...
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In this paper, we propose a hierarchical modeling of the systems described by conservation laws. A conservation law on a hierarchically parted domain can be considered as a subsystem which interacts with neighbor elements through fluxes. Therefore, we regard the system as a networked system of each subsystem. The important idea is to weaken the interconnection in the sense of a rank. For detailed analysis of our method, we apply the proposed method to a diffusion equation. The hierarchical model is described by a non-circulant block Toeplitz matrix. Because the resulting system is symmetrically-networked system, we can show that the eigenvalues of the system consist of those of related uniform models. We also show that our method relaxes the stability condition of the fully discretized model. Finally we examine the performance of the hierarchical model by numerical simulations.
In this paper, we consider two flexible beams connected by a spring as a simple example of the large space structures. The flexible beams and the spring can be regarded as an element of the structure with the distribu...
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In this paper, we consider two flexible beams connected by a spring as a simple example of the large space structures. The flexible beams and the spring can be regarded as an element of the structure with the distributed flexibility and a connective part with lumped flexibility, respectively. As we introduce Voigt type damping, the original open-loop system is exponential stable. In general the natural damping coefficient is very small, so it is necessary to construct a controller which accomplishes higher convergence rate. We propose a direct sensor output feedback controller for vibration absorption. Using the Energy Multiplier method, exponential stability of the closed-loop system is proven. We also prove that the exponential convergence rate for the closed-loop system, which means the controller performance, is larger than that of the open-loop system with the small natural damping. As we don't need an approximated finite-dimensional model at the controller design phase, the controller based on the original distributedparameter system is robust and simple.
The problem of constructing an "observer" to enable us to implement an approximate optimal control for a distributedparameter system is examined where the state is measured at a few pre-specified points. Th...
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The problem of constructing an "observer" to enable us to implement an approximate optimal control for a distributedparameter system is examined where the state is measured at a few pre-specified points. The observer is formulated as the output of a dynamical system described by a set of ordinary differential equations. Both distributed and boundary control problems are studied and the observer-formulation is set up for both cases. Some reasonable assumptions have been made in order that the approximation introduced by the eigenfunction expansion technique be satisfactory. For the case of the boundary control problem, a simple example is solved to illustrate the method.
This paper addresses the design of a distributed, second-order sliding-mode based, tracking controller for a class of uncertain diffusion-reaction processes. Spatially varying uncertain parameters and mixed boundary c...
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ISBN:
(纸本)9781612848006
This paper addresses the design of a distributed, second-order sliding-mode based, tracking controller for a class of uncertain diffusion-reaction processes. Spatially varying uncertain parameters and mixed boundary conditions, along with the presence of an uncertain distributed disturbance, characterize the considered class of processes. The paper presents a constructive Lyapunov-based stability analysis which leads to simple tuning conditions for the controller parameters, The good performance of the proposed control systems are verified by means of computer simulations.
This paper focuses on the application of sliding mode control theory to distributedparameter chemical process systems. For a class of partial differential equations, the method of characteristics is used to exactly t...
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This paper focuses on the application of sliding mode control theory to distributedparameter chemical process systems. For a class of partial differential equations, the method of characteristics is used to exactly transform the distributedparameter system to a finite set of ordinary differential equations, allowing for the implementation of geometric methods to extend sliding mode concepts. Through simulations the method is shown to be effective in controlling a steam heater.
All of the existing results in adaptive control for parabolic PDEs rely on full state measurement. For the first time, we consider a problem of output feedback stabilization of distributed parameter systems with unkno...
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ISBN:
(纸本)1424401704;9781424401703
All of the existing results in adaptive control for parabolic PDEs rely on full state measurement. For the first time, we consider a problem of output feedback stabilization of distributed parameter systems with unknown reaction, advection, and diffusion parameters. Both sensing and actuation are performed at the boundary and the unknown parameters are allowed to be spatially varying. First we construct a special transformation of the original system into the PDE analog of "observer canonical form," with unknown parameters multiplying the measured output. We then use the so-called swapping method for parameter estimation. Input and output filters are implemented so that a dynamic parameterization of the problem is converted into a static parameterization where a gradient estimation algorithm is used. The control gain is computed through the numerical solution of an ordinary integro-differential equation. The results are illustrated by simulations
<正> In the paper constrained approximate controllability for linear dynamical systems described by abstract differential equations with unbounded control operator is considered. Using methods of spectral analysis f...
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<正> In the paper constrained approximate controllability for linear dynamical systems described by abstract differential equations with unbounded control operator is considered. Using methods of spectral analysis for linear selfadjoint operators and general constrained controllability results necessary and sufficient conditions of the constrained approximate controllability for the piecewise constant controls with values in a given cone are formulated and proved. Moreover, as illustrative examples constrained approximate boundary controllability of one dimensional distributedparameter dynamical systems described by partial differential equations of parabolic type with Dirichlet and Neumann boundary conditions are investigated. The constrained controllability conditions obtained in the paper represent an extension of the unconstrained controllability results.
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