Maximum entropy controller synthesis for colocated and noncolocated systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77185/1/AIAA-21277-539.pd

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

Increasing eigenstructure assignment design degree of freedom using lifting

This paper presents the exposition of an output-lifting eigenstructure assignment (EA) design framework, wherein the available EA design degrees of freedom (DoF) is significantly increased, and the desired eigenstructure of a single-rate full state feedback solution can be achieved within an output feedback system. A structural mapping is introduced to release the output-lifting causality constraint. Additionally, the available design DoF can be further enlarged via involving the input-lifting into the output-lifting EA framework. The newly induced design DoF can be utilised to calculate a structurally constrained, causal gain matrix which will maintain the same assignment capability. In this paper, the robustification of the output-lifting EA is also proposed, which allows a trade-off between performance and robustness in the presence of structured model uncertainties to be established. A lateral flight control benchmark in the EA literature and a numerical example are used to demonstrate the effectiveness of the design framework

Launcher attitude control: discrete-time robust design and gain-scheduling

In this paper, a robust multi-objective design for the control of a launcher during atmospheric flight is investigated. This approach is based on the Cross Standard Form formulation which allows to incorporate the various specifications of the launcher problem in a streamlined manner. An important feature of this approach is that a non-conventional LQG/LTR approach, required to satisfy time-domain specifications, can be embedded into a more general standard problem in order to account for frequency-domain robustness constraints. The specific form of this standard problem is also very interesting for gain scheduling

Robust H2/H∞-state estimation for discrete-time systems with error variance constraints

Copyright [1997] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper studies the problem of an H∞-norm and variance-constrained state estimator design for uncertain linear discrete-time systems. The system under consideration is subjected to time-invariant norm-bounded parameter uncertainties in both the state and measurement matrices. The problem addressed is the design of a gain-scheduled linear state estimator such that, for all admissible measurable uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞-norm upper bound constraint, simultaneously. The conditions for the existence of desired estimators are obtained in terms of matrix inequalities, and the explicit expression of these estimators is also derived. A numerical example is provided to demonstrate various aspects of theoretical results

Multistage Output-lifting Eigenstructure Assignment: A Multirate Ball and Plate Example

By exploiting both the left and the right allowable subspaces in consecutive stages, this paper extends a recently-developed output-lifting eigenstructure assignment approach into a multistage eigenstructure assignment scheme. In this scheme, design degrees of freedom, enlarged via output-lifting, are further exploited to improve eigenvector assignment. To mitigate the inherent conflicts between the theoretical development of eigenstructure assignment and inherent physical system characteristics, the paper also clearly demonstrates how to derive an ideal eigenstructure, particularly the desired eigenvectors, to distribute and decouple the natural modes among appropriate states or outputs, based upon an example: a novel multirate Ball and Plate system. The design and simulation results show the efficacy of the scheme

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

Eigenstructure assignment in vibrating systems through active and passive approaches

The dynamic behaviour of a vibrating system depends on its eigenstructure, which consists of the eigenvalues and the eigenvectors. In fact, eigenvalues define natural frequencies, damping and settling time, while eigenvectors define the spatial distribution of vibrations, i.e. the mode shape, and also affect the sensitivity of eigenvalues with respect to the system parameters. Therefore, eigenstructure assignment, which is aimed at modifying the system in such a way that it features the desired set of eigenvalues and eigenvectors, is of fundamental importance in mechanical design. However, similarly to several other inverse problems, eigenstructure assignment is inherently challenging, due to its ill-posed nature. Despite the recent advancements of the state of the art in eigenstructure assignment, in fact, there are still important open issues. The available methods for eigenstructure assignment can be grouped into two classes: passive approaches, which consist in modifying the physical parameters of the system, and active approaches, which consist in employing actuators and sensors to exert suitable control forces as determined by a specified control law. Since both these approaches have advantages and drawbacks, it is important to choose the most appropriate strategy for the application of interest. In the present thesis, in fact, are collected passive, active, and even hybrid methods, in which active and passive techniques are concurrently employed. All the methods proposed in the thesis are aimed at solving open issues that emerged from the literature and which have applicative relevance, as well as theoretical. In contrast to several state-of-the-art methods, in fact, the proposed ones implement strategies that enable to ensure that the computed solutions are meaningful and feasible. Moreover, given that in modern mechanical design large-scale systems are increasingly common, computational issues have become a major concern and thus have been adequately addressed in the thesis. The proposed methods have been developed to be general and broadly applicable. In order to demonstrate the versatility of the methods, in the thesis it is provided an extensive numerical assessment, hence diverse test-cases have been used for validation purposes. In order to evaluate without bias the performances of the proposed methods, it has been chosen to employ well-established benchmarks from the literature. Moreover, selected experimental applications are presented in the thesis, in order to determine the capabilities of the developed methods when critically challenged. Given the focus on these issues, it is expected that the methods here proposed can constitute effective tools to improve the dynamic behaviour of vibrating systems and it is hoped that the present work could contribute to spread the use of eigenstructure assignment in the solution of engineering design problems