Quasilinear Control PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Quasilinear Control PDF full book. Access full book title Quasilinear Control by ShiNung Ching. Download full books in PDF and EPUB format.
Author: ShiNung Ching
Publisher: Cambridge University Press
ISBN: 1139495321
Category : Mathematics
Languages : en
Pages : 301
Get Book Here
Book Description
This is a textbook and reference for readers interested in quasilinear control (QLC). QLC is a set of methods for performance analysis and design of linear plant or nonlinear instrumentation (LPNI) systems. The approach of QLC is based on the method of stochastic linearization, which reduces the nonlinearities of actuators and sensors to quasilinear gains. Unlike the usual - Jacobian linearization - stochastic linearization is global. Using this approximation, QLC extends most of the linear control theory techniques to LPNI systems. A bisection algorithm for solving these equations is provided. In addition, QLC includes new problems, specific for the LPNI scenario. Examples include Instrumented LQR/LQG, in which the controller is designed simultaneously with the actuator and sensor, and partial and complete performance recovery, in which the degradation of linear performance is either contained by selecting the right instrumentation or completely eliminated by the controller boosting.
Author: ShiNung Ching
Publisher: Cambridge University Press
ISBN: 1139495321
Category : Mathematics
Languages : en
Pages : 301
Get Book Here
Book Description
This is a textbook and reference for readers interested in quasilinear control (QLC). QLC is a set of methods for performance analysis and design of linear plant or nonlinear instrumentation (LPNI) systems. The approach of QLC is based on the method of stochastic linearization, which reduces the nonlinearities of actuators and sensors to quasilinear gains. Unlike the usual - Jacobian linearization - stochastic linearization is global. Using this approximation, QLC extends most of the linear control theory techniques to LPNI systems. A bisection algorithm for solving these equations is provided. In addition, QLC includes new problems, specific for the LPNI scenario. Examples include Instrumented LQR/LQG, in which the controller is designed simultaneously with the actuator and sensor, and partial and complete performance recovery, in which the degradation of linear performance is either contained by selecting the right instrumentation or completely eliminated by the controller boosting.
Author: ShiNung Ching
Publisher: Cambridge University Press
ISBN: 9781107000568
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
Book Description
This is a textbook and reference for readers interested in quasilinear control (QLC). QLC is a set of methods for performance analysis and design of linear plant or nonlinear instrumentation (LPNI) systems. The approach of QLC is based on the method of stochastic linearization, which reduces the nonlinearities of actuators and sensors to quasilinear gains. Unlike the usual - Jacobian linearization - stochastic linearization is global. Using this approximation, QLC extends most of the linear control theory techniques to LPNI systems. A bisection algorithm for solving these equations is provided. In addition, QLC includes new problems, specific for the LPNI scenario. Examples include Instrumented LQR/LQG, in which the controller is designed simultaneously with the actuator and sensor, and partial and complete performance recovery, in which the degradation of linear performance is either contained by selecting the right instrumentation or completely eliminated by the controller boosting.
Author: Jonathan de Halleux
Publisher: Presses univ. de Louvain
ISBN: 9782930344690
Category : Science
Languages : en
Pages : 158
Get Book Here
Book Description
The thesis presents different control design approaches for stabilizing networks of quasi-linear hyperbolic partial differential equations. These equations are usually conservative, which gives them interesting properties to design stabilizing control laws. Two main design approaches are developed: a methodology based on entropies and Lyapunov functions and a methodology based on the Riemann invariants. The stability theorems are illustrated using numerical simulations. Two practical applications of these methodologies are presented. Network of navigation channels are modelled using the Saint-Venant equation (also known as the Shallow Water Equations). The stabilization problem of such system has an industrial importance in order to satisfy the navigation constraints and to optimize the production of electricity in hydroelectric plants, usually located at each hydraulic gate. A second application deals with the regulation of water waves in moving tanks. This problem is also modelled by a modified version of the shallow water equations and appears in a number industrial fields which deal with liquid moving parts.
Author: Wei-Ping Huang
Publisher:
ISBN:
Category : Time delay systems
Languages : en
Pages : 122
Get Book Here
Book Description
This thesis investigates Quasilinear Control (QLC) of time-delay systems with nonlinear actuators and sensors and analyzes the accuracy of stochastic linearization for these systems. QLC leverages the method of stochastic linearization to replace each nonlinearity with an equivalent gain, which is obtained by solving a transcendental equation. The idea of QLC is to stochastically linearize the system in order to analyze and design controllers using classical linear control theory. In this thesis, the existence of the equivalent gain for a closed-loop time-delay system is discussed. To compute the equivalent gain, two methods are explored. The first method uses an explicit but complex algorithm based on delay Lyapunov equation to study the time-delay, while the second method uses Pade approximant. It is shown that, under a suitable criterion, Pade approximant can be effectively applied for QLC of time-delay systems. Furthermore, the method of Saturated-Root Locus (S-RL) is extended to nonlinear time-delay systems. It turns out that, in a time-delay system, S-RL always terminates prematurely as opposed to a delay-free system, which may or may not terminate prematurely. Statistical experiments are performed to investigate the accuracy of stochastic linearization compared to a system without time-delay. The impact of increasing the time-delay in the approach of stochastic linearization is also investigated. Results show that stochastic linearization effectively linearizes a nonlinear time-delay system, even though delays generally degrade accuracy. Overall, the accuracy remains relatively high over the selected parameters. Finally, this approach is applied to pitch control in a wind turbine system as a practical example of a nonlinear time-delay system, and its performance is analyzed to demonstrate the efficacy of the approach.
Author: Karl-Heinz Hoffmann
Publisher: Springer Science & Business Media
ISBN: 9783764361518
Category : Mathematics
Languages : en
Pages : 344
Get Book Here
Book Description
Well-posedness of Semilinear Heat Equations with Iterated Logarithms.- Uniform Stability of Nonlinear Thermoelastic Plates with Free Boundary Conditions.- Exponential Bases in Sobolev Spaces in Control and Observation Problems.- Sampling and Interpolation of Functions with Multi-Band Spectra and Controllability Problems.- Discretization of the Controllability Grammian in View of Exact Boundary Control: the Case of Thin Plates.- Stability of Holomorphic Semigroup Systems under Nonlinear Boundary Perturbations.- Shape Control in Hyperbolic Problems.- Second Order Optimality Conditions for Some Control Problems of Semilinear Elliptic Equations with Integral State Constraints.- Intrinsic P(2, 1) Thin Shell Models and Naghdi's Models without A Priori Assumption on the Stress Tensor.- On the Approximate Controllability for some Explosive Parabolic Problems.- Fréchet-Differentiability and Sufficient Optimality Conditions for Shape Functionals.- State Constrained Optimal Control for some Quasilinear Parabolic Equations.- Controllability property for the Navier-Stokes equations.- Shape Sensitivity and Large Deformation of the Domain for Norton-Hoff Flows.- On a Distributed Control Law with an Application to the Control of Unsteady Flow around a Cylinder.- Homogenization of a Model Describing Vibration of Nonlinear Thin Plates Excited by Piezopatches.- Stabilization of the Dynamic System of Elasticity by Nonlinear Boundary Feedback.- Griffith Formula and Rice-Cherepanov's Integral for Elliptic Equations with Unilateral Conditions in Nonsmooth Domains.- A Domain Optimization Problem for a Nonlinear Thermoelastic System.- Approximate Controllability for a Hydro-Elastic Model in a Rectangular Domain.- Noncooperative Games with Elliptic Systems.- Incomplete Indefinite Decompositions as Multigrid Smoothers for KKT Systems.- Domain Optimization for the Navier-Stokes Equations by an Embedding Domain Method.- On the Approximation and Optimization of Fourth Order Elliptic Systems.- On the Existence and Approximation of Solutions for the Optimal Control of Nonlinear Hyperbolic Conservation Laws.- Identification of Memory Kernels in Heat Conduction and Viscoelasticity.- Variational Formulation for Incompressible Euler Equation by Weak Shape Evolution.
Author: Sarnaduti Brahma
Publisher:
ISBN:
Category : Nonlinear control theory
Languages : en
Pages : 300
Get Book Here
Book Description
Quasilinear Control (QLC) is a theory with a set of tools used for the analysis and design of controllers for nonlinear feedback systems driven by stochastic inputs. It is based on the concept of Stochastic Linearization (SL), which is a method of linearizing a nonlinear function that, unlike traditional Jacobian linearization, uses statistical properties of the input to the nonlinearity to linearize it. Until now in the literature of QLC, SL was applied only to feedback systems with single-variable nonlinearities that appear only in actuators and/or sensors. In this dissertation, my recent contributions to the literature of QLC are summarized. First, the QLC theory is extended to feedback systems with isolated multivariate nonlinearities that can appear anywhere in the loop and applied to optimal controller design problems, including systems with state-multiplicative noise. Second, the numerical properties of SL, particularly, the accuracy, robustness, and computation of SL, are investigated. Upper bounds are provided for the open-loop relative accuracy and, consequently, the closed-loop accuracy of SL. A comparison of the computational costs of several common numerical algorithms in solving the SL equations is provided, and a coordinate transformation proposed to improve most of their success rates. A numerical investigation is carried out to determine the relative sensitivities of SL coefficients to system parameters. Finally, QLC is applied to the optimal primary frequency control of power systems with generator saturation, and control of virtual batteries in distribution feeders. The expected impacts of this work are far-reaching. On the technical front, this work provides: i) a new set of theoretical and algorithmic tools that can improve and simplify control of complex systems affected by noise, ii) information to control engineers on accuracy guarantees, choice of solvers, and relative sensitivities of SL coefficients to system parameters to guide the analysis and design of nonlinear stochastic systems in the context of QLC, iii) a new computationally efficient method of addressing saturation in generators or virtual batteries in modern electric power systems, resulting in efficient utilization of resources in providing grid services. On the societal front, this work: i) enables technologies that rely on computationally-efficient algorithms for automation of complex systems, e.g., control of soil temperature for agriculture, which depends on multiple factors like soil moisture and net radiation, ii) allows effective coordination of controllable smart devices in people's homes, so as not to hamper their quality of service, and iii) provides a stepping stone towards key societal challenges like combating climate change by facilitating reliable operation of the grid with significant renewable penetration.
Author: Aleksandr L?vovich Fradkov
Publisher: World Scientific
ISBN: 9789810230692
Category : Science
Languages : en
Pages : 410
Get Book Here
Book Description
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.
Author: K.-H. Hoffmann
Publisher: Birkhäuser
ISBN: 3034876270
Category : Science
Languages : en
Pages : 227
Get Book Here
Book Description
This volume contains the contributions of participants of the conference "Optimal Control of Partial Differential Equations" which, under the chairmanship of the editors, took place at the Mathematisches Forschungsinstitut Oberwolfach from May 18 to May 24, 1986. The great variety of topics covered by the contributions strongly indicates that also in the future it will be impossible to develop a unifying control theory of partial differential equations. On the other hand, there is a strong tendency to treat prob lems which are directly connected to practical applications. So this volume contains real-world applications like optimal cooling laws for the production of rolled steel or concrete solutions for the problem of optimal shape design in mechanics and hydrody namics. Another main topic is the construction of numerical methods. This includes applications of the finite element method as well as of Quasi-Newton-methods to con strained and unconstrained control problems. Also, very complex problems arising in the theory of free boundary value problems are treated. ]~inally, some contribu tions show how practical problems stimulate the further development of the theory; in particular, this is the case for fields like suboptimal control, necessary optimality conditions and sensitivity analysis. As usual, the lectures and stimulating discussions took place in the pleasant at mosphere of the Mathematisches Forschungsinstitut Oberwolfach. Special thanks of the participants are returned to the Director as well as to the staff of the institute.
Author: Georges Bastin
Publisher: Birkhäuser
ISBN: 3319320629
Category : Mathematics
Languages : en
Pages : 317
Get Book Here
Book Description
This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.
Author: Reiner Onken
Publisher: Springer Science & Business Media
ISBN: 364203134X
Category : Computers
Languages : en
Pages : 390
Get Book Here
Book Description
Why this book? Simply because it is due. Cognitive automation and its system-ergonomic introduction into work systems have been advanced in the meantime to such a degree that already applications for operational work systems are slowly becoming reality. This book shall contribute to give system designers some more guidelines about designing work systems and associated cognitive machines effectively, in particular those related to guidance and control of manned and unmanned vehicles. The issue is that the findings on cognition have to become sufficient commonsense for all from the various disciplines involved in system design, and that guidelines are given how to make use of it in an appropriate and systematic manner. These guidelines are to account for both the needs of the human operator in the work process and the use of computational potentials to make the work system a really most effective one. In other words, this book is meant to provide guidelines for the organisational and technical design of work systems. Therefore, this book is an interdisciplinary one. Findings in individual disciplines are not the main issue. It is rather the combination of these findings for the sake of the performance of work systems which makes this book a useful one for designers who are interested in this modern approach and its implementation.
