State feedback control with time delay

In this thesis we start with an introduction to the theory of vibration control. We broadly classify the control methods into passive and active schemes. We introduce the problem of state feedback control and provide the classical solution in the form of Ackermann formula. We then identify the limitations of the classical approach and present the more elegant solution of partial pole assignment without spillover. We highlight the problem with model uncertainties and describe the method of pole assignment using data from measured receptances. This approach is extended for pole assignment for a linear vibrating system by using state feedback control delayed in time. This approach is significantly advantageous over various conventional state-space approaches which need to use information of , and matrices. Since the method relies solely on measured receptances, it negates the need to know , and matrices. It is shown that for a system with degrees of freedom, we may assign eigenvalues. Assigning eigenvalues in a time delayed system does not necessarily regulate the dynamics of the system or guarantee its stability. We separate the eigenvalues into two groups, primary and secondary, and propose method of a posteriori analysis to ensure that the primary eigenvalues have been assigned. The method is demonstrated by various examples. For state feedback control, the control is achieved by measuring the states of the system and feeding them back into the system after multiplying them with appropriate control gain. This makes it imperative to measure all the states of the system. In practical control applications, all states are not accessible for measurement. We address the problem of inaccessibility of states making it difficult to implement the state feedback control. We introduce the theory of linear state estimation also called observer design. We identify the limitations of this approach and introduce the concept of state reconstruction by delayed action. We develop a method to reconstruct the inaccessible states by introducing delay in the system and using information from accessible states. The results are demonstrated by examples

Stiffness matrix modification with vibration test data by displacement feedback technique

A no spill-over method is developed which uses measured normal modes and natural frequencies to adjust a structural dynamics model in light of displacement feedback technique. By the method, the required displacement feedback gain matrix is determined, and thus the updated stiffness matrix which satisfies the characteristic equation is found in the Frobenius norm sense and the large number of unmeasured high-order modal data of the original model is preserved. The method directly identifies, without iteration, and the solution of this problem is of a compact expression. The numerical example shows that the modal measured data are better incorporated into the updated model

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

Optimal control with structure constraints and its application to the design of passive mechanical systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Page 214 blank.Includes bibliographical references.Structured control (static output feedback, reduced-order control, and decentralized feedback) is one of the most important open problems in control theory and practice. In this thesis, various techniques for synthesis of structured controllers are surveyed and investigated, including H2 optimization, H[infinity] optimization, L1 control, eigenvalue and eigenstructure treatment, and multiobjective control. Unstructured control-full- state feedback and full-order control-is also discussed. Riccati-based synthesis, linear matrix inequalities (LMI), homotopy methods, gradient- and subgradientbased optimization are used. Some new algorithms and extensions are proposed, such as a subgradient-based method to maximize the minimal damping with structured feedback, a multiplier method for structured optimal H2 control with pole regional placement, and the LMI-based H2/H[infinity]/pole suboptimal synthesis with static output feedback. Recent advances in related areas are comprehensively surveyed and future research directions are suggested. In this thesis we cast the parameter optimization of passive mechanical systems as a decentralized control problem in state space, so that we can apply various decentralized control techniques to the parameter design which might be very hard traditionally. More practical constraints for mechanical system design are considered; for example, the parameters are restricted to be nonnegative, symmetric, or within some physically-achievable ranges. Marginally statable systems and hysterically damped systems are also discussed. Numerical examples and experimental results are given to illustrate the successful application of decentralized control techniques to the design of passive mechanical systems, such as multi-degree-of-freedom tuned-mass dampers, passive vehicle suspensions, and others.by Lei Zuo.S.M

Process and systems based methodologies related to control structure selection

This thesis is concerned with an important aspect of process control design, that is, the synthesis of the control structures. A review of the rapidly growing process methodologies' literature is presented and this leads to the identification of wider issues and new problems which are referred to as global instrumentation and forms the main subject of this thesis. The main objective has been the integration of existing process based tools and methodologies with a much more general approach of a systems and control theory character. The problem of Global Process Instrumentation concerns the selection of systems of measurement and actuation variables, found during the synthesis/design and operation of large-scale industrial processes/systems. The role of traditional instrumentation was considered but the emphasis has been on the systems aspects. In fact, instrumentation leads to the shaping of the final system and thus, is crucial in defining the control quality properties and operability characteristics of the final design. The development of these system aspects led to the emergence of an integrated framework for Global Instrumentation. An attempt was also made to abstract some results and formulate generic issues and problems, that would provide a wider scenario for activities in the future. Development of CAD to support the selection of control structures has been a major task undertaken here. The system aspects of Global Instrumentation are demonstrated by studying two specific problems that involve the study of the structural properties of interconnected systems as a function of local selection of sensors and actuators and the problem of well-conditioning badly structured transfer functions. The role of selection of inputs and outputs, on the overall shaping of composite structure properties, at the subsystem level, was examined, and the significance of an assumption related to interconnections, referred to as the completeness assumption, was investigated. Specifically, the significance of the deviations from the completeness, was the subject of the investigation. Matrix Pencil Theory was used to examine the controllability, observability and zero structure related properties of composite systems under partial or total loss of inputs/outputs at the subsystem level. Selecting subsets of the original sets of inputs, outputs to guarantee full rank transfer function, was also an issue that was examined. The above problems were presented as part of an integrated design philosophy that aims to explore the system structure. An integrated approach to the overall problem of control structure selection was formulated and open issues and problems were identified. It was based on the assumption that there exists a progenitor model of the linear type for the process, which, however, may not be well defined. Structural analysis of the system theoretic framework, the interaction measures and the results for evaluation of alternative decentralisation schemes were then used, to specify a step by step approach to the control structure selection. The problem of handling alternative criteria was also considered and basic elements of a system procedure were given. There are many open issues, which were identified and are still open and thus the proposed structural approach should be considered as the first step to the development of an integrated methodology that involves the following major steps: (a) Classification of system model variables and definition of well structured progenitor model. (b) Definition of effective input, output structure based on operability, controllability criteria. (c) Determining the structure of the control scheme by evaluation of alternative decentralised structures. An important part of the integrated methodology for control structure selection is the - so called - interaction analysis. It consists of a number of diagnostics and structural tests that help to restrict the choice of the best scheme. Several of these tests/methodologies were reviewed and some of them were further expanded. The outcomes obtained by these methodologies provided promising results. These results gave the motivation for the construction of a complete CAD package, the "Interaction Analysis Toolbox", written in MATLAB®t. This Toolbox provides many tools and diagnostics that can be applied during the design stages, for the evaluation of the various alternative control structures