An Identification Procedure For Linear Multivariable Systems

In the report, the direct method of Lyapunov is employed to outline a procedure for the continuous identification of a multivariable dynamical system from measurements on the inputs and the state variables of the system. The procedure results in the convergence of every parameter of a model to the corresponding one of the system as time t approaches infinity. The overall process is also shown to be asymptotically stable. Computer simulation results are included to illustrate the effectiveness of the suggested scheme. (Author).

In the paper, the direct method of Lyapunov is employed to outline a procedure for the identification of a discrete multivariable system from the measurements on the inputs and the state variables of the system. It is assumed that all the state variables of the plant are accessible and that there is no measurement noise. The procedure results in the convergence of every parameter of a model to the corresponding one of the system as the number of stages k nears infinity. The overall process is also shown to be asymptotically stable. (Author).

The report describes a procedure for adjusting the parameters of a model for the identification of linear and nonlinear discrete multivariable systems when all the state variables are accessible and no observation noise is present. The scheme is shown to be stable when using Lyapunov's direct method.

Subspace Identification for Linear Systems focuses on the theory, implementation and applications of subspace identification algorithms for linear time-invariant finite- dimensional dynamical systems. These algorithms allow for a fast, straightforward and accurate determination of linear multivariable models from measured input-output data. The theory of subspace identification algorithms is presented in detail. Several chapters are devoted to deterministic, stochastic and combined deterministic-stochastic subspace identification algorithms. For each case, the geometric properties are stated in a main 'subspace' Theorem. Relations to existing algorithms and literature are explored, as are the interconnections between different subspace algorithms. The subspace identification theory is linked to the theory of frequency weighted model reduction, which leads to new interpretations and insights. The implementation of subspace identification algorithms is discussed in terms of the robust and computationally efficient RQ and singular value decompositions, which are well-established algorithms from numerical linear algebra. The algorithms are implemented in combination with a whole set of classical identification algorithms, processing and validation tools in Xmath's ISID, a commercially available graphical user interface toolbox. The basic subspace algorithms in the book are also implemented in a set of Matlab files accompanying the book. An application of ISID to an industrial glass tube manufacturing process is presented in detail, illustrating the power and user-friendliness of the subspace identification algorithms and of their implementation in ISID. The identified model allows for an optimal control of the process, leading to a significant enhancement of the production quality. The applicability of subspace identification algorithms in industry is further illustrated with the application of the Matlab files to ten practical problems. Since all necessary data and Matlab files are included, the reader can easily step through these applications, and thus get more insight in the algorithms. Subspace Identification for Linear Systems is an important reference for all researchers in system theory, control theory, signal processing, automization, mechatronics, chemical, electrical, mechanical and aeronautical engineering.

Most systems involved in a chemical process plant are interactive multivariable systems, to control which, the transfer function matrix model is required. This lucid book considers the identification and control of such systems. It discusses open loop and closed loop identification methods, as well as the design of multivariable controllers based on steady state gain matrix. Simple methods for designing controllers based on transfer function matrix model have been reviewed. The design of controllers for non-square systems, and closed loop identification of multivariable unstable systems by the optimization method are also covered. Several simulation examples and exercise problems at the end of each chapter further help the reader consolidate the knowledge gained. This book will be useful to any engineering student, researcher or practitioner who works with interactive, multivariable control systems.

Systems and control theory has experienced significant development in the past few decades. New techniques have emerged which hold enormous potential for industrial applications, and which have therefore also attracted much interest from academic researchers. However, the impact of these developments on the process industries has been limited.The purpose of Multivariable System Identification for Process Control is to bridge the gap between theory and application, and to provide industrial solutions, based on sound scientific theory, to process identification problems. The book is organized in a reader-friendly way, starting with the simplest methods, and then gradually introducing more complex techniques. Thus, the reader is offered clear physical insight without recourse to large amounts of mathematics. Each method is covered in a single chapter or section, and experimental design is explained before any identification algorithms are discussed. The many simulation examples and industrial case studies demonstrate the power and efficiency of process identification, helping to make the theory more applicable. MatlabTM M-files, designed to help the reader to learn identification in a computing environment, are included.

The field's leading text, now completely updated. Modeling dynamical systems — theory, methodology, and applications. Lennart Ljung's System Identification: Theory for the User is a complete, coherent description of the theory, methodology, and practice of System Identification. This completely revised Second Edition introduces subspace methods, methods that utilize frequency domain data, and general non-linear black box methods, including neural networks and neuro-fuzzy modeling. The book contains many new computer-based examples designed for Ljung's market-leading software, System Identification Toolbox for MATLAB. Ljung combines careful mathematics, a practical understanding of real-world applications, and extensive exercises. He introduces both black-box and tailor-made models of linear as well as non-linear systems, and he describes principles, properties, and algorithms for a variety of identification techniques: Nonparametric time-domain and frequency-domain methods. Parameter estimation methods in a general prediction error setting. Frequency domain data and frequency domain interpretations. Asymptotic analysis of parameter estimates. Linear regressions, iterative search methods, and other ways to compute estimates. Recursive (adaptive) estimation techniques. Ljung also presents detailed coverage of the key issues that can make or break system identification projects, such as defining objectives, designing experiments, controlling the bias distribution of transfer-function estimates, and carefully validating the resulting models. The first edition of System Identification has been the field's most widely cited reference for over a decade. This new edition will be the new text of choice for anyone concerned with system identification theory and practice.

This book trains engineering students to identify multivariable transfer function models and design classical controllers for such systems.