Browsing by Subject "Distributed parameter systems"
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Item A root locus methodology for parabolic boundary control systems(Texas Tech University, 1993-05) He, JianqiuRecently, C. I. Byrnes and D. S. Gilliam initiated an interest in the development of a root locus methodology for distributed parameter systems. Along with the author, a fairly complete root locus theory was established for an important class of parabolic distributed parameter control problems with spatial part given by general even order ordinary differential operators with real C°° coefficients on a bounded interval. Due to the technically complicated nature of such problems, this preliminary work was restricted to systems with "separated" boundary conditions with an equal number at highest order at each end of the interval. Moreover, it was also assumed that the actuator and sensor, i.e., the boundary input and output, were collocated. It is important to note that, even in this case, the differential operators as well as the associated boundary conditions almost never correspond to self-adjoint problems. However, with a relative degree assumption that the order of the input exceeds the order of the output, it was shown that the open-loop transfer function exists, is strictly proper and, in fact, is in the Callier-Desoer class. A complete root locus analysis was given for a closed-loop system obtained via a proportional error feedback control law. In this thesis, we extend these results in several directions including the more general class of systems governed by so-called "Birkhoff regular" boundary conditions. We note that separated boundary conditions with an equal number at each end are always Birkhoff regular. More precisely, we introduce the class of Birkhoff regular distributed parameter feedback control systems and investigate the root loci for these systems. This class of problems is considerably more complicated than the separated case and includes the case of non-collocated actuator and sensor pairs. General root locus results are established for these problems. In particular, the quantities that specify and characterize the asymptotic behavior of the closed-loop poles are analyzed in detail and the resulting root loci are described and illustrated in a classified way. Another class of distributed parameter feedback control systems is also considered, in which the boundary operators are "completely separated" but do not necessarily have an equal number of conditions at each endpoint. We note that a system of this type can never be either Birkhoff regular or self-adjoint in the case of unequal numbers of conditions at the endpoints. We are able to show that, nevertheless, the return difference equation for these systems can be written in the same asymptotic form as for Birkhoff regular systems. Thus, many of the results obtained for Birkhoff regular systems are also true in this case. Indeed, the conclusions for these systems are parallel to what was established for systems with separated boundary conditions with an equal number of conditions at each endpoint.Item Control of distributed parameter systems(Texas Tech University, 1986-12) Tubach-Ley, Wilhelmina BarbaraNot availableItem A framework for distributed applications on systems with mobile hosts(2002) Skawratananond, Chakarat; Garg, Vijay K. (Vijay Kumar), 1963-Item A moving boundary problem in a distributed parameter system with application to diode modeling(2001-08) Zhang, Hanzhong; Longoria, Raul G.; Driga, Mircea D.Item System identification and model-based control for a class of distributed parameter systems(Texas Tech University, 2003-05) Zheng, DaguangA large number of processes in the chemical and petroleum industries are distributed in nature. The diversity of distribution patterns and functions make modeling of distributed parameter systems (DPS) a very challenging problem. Employment of first principles about the physics and chemistry will yield mathematical models in the form of systems of linear or nonlinear partial differential equations (PDEs). The analytical and numerical solutions for PDEs are infinite or very high dimension, which are not suitable for implementable control designs. The first objective of this research is to develop a general model reduction methodology to reduce the system of PDEs to a finite dimensional system of ODEs, which can be used to synthesize a model-based control. This methodology is based on the identification of empirical eigenfunctions (EEFs) from data and using the Galerkin method to obtain a model with dominant modes. For a system of first-order hyperbolic PDEs, accelerated EEFs are used to find a reduced-order model. In the case where the physics-based modeling approach cannot be applied with confidence, an input/output model developed based on experimental data may suffice. A novel system identification method to develop the model using a data-driven approach is proposed. The method combines the fundamental principles of singular value decomposition (SVD) and Karhunen-Loeve (KL) expansion in the identification of a finite order model. The application of SVD and KL provides natural decoupling of the inputs and outputs while yielding a model that captures the dominant spatial and temporal behavior of the distributed system. The fundamental theorems to assure the accuracy of this method are provided. Implementable control designs to regulate the DPS are now realizable with a finite order model. Dynamic matrix control (DMC) and Quadratic DMC (QDMC) are selected as control strategies, wherein the merit of the control design is dependent on the fidelity of the identified by SVD-KL method. Sufficient conditions are proposed to tune the QDMC control strategy so that stable closed-loop performance is guaranteed. The regulation of several candidate chemical reactor systems and the hydro-dealkylation process that produces benzene from toluene (HDA) are used to illustrate the potential of this data-driven modeling and model-based control framework for distributed parameter systems.