Finite Element Modeling and Experiments of Systems with Viscoelastic Materials for Vibration Attenuation

This chapter addresses the finite element modeling methodologies intended for performance evaluation, analysis, and design of viscoelastic systems. The mathematical models widely used to represent the frequency and temperature dependent behavior of viscoelastic materials are also considered, namely the complex modulus approach, the fractional derivative model, the Golla-Hughes-McTavish (GHM) model, and the anelastic displacement fields (ADFs) model. The straightforward strategies to integrate the viscoelastic effects into finite element matrices of structural systems such as three-layer sandwich plates, intended for the modeling of medium and large-scale engineering structures, are presented. In the same context, emphasis is placed on the condensation methods for the reduction of the order of the finite element matrices to perform frequency-response functions, complex eigenvalue problem, and time domain analyses. Based on the fact that for viscoelastic materials subjected to dynamic loadings superimposed on static preloads, the classical modeling assuming isothermal conditions can lead to poor designs, since the energy dissipated within the volume of the material leads to temperature rises, an experimental investigation of the self-heating phenomenon is also addressed

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Dynamical Analysis and Robust Control Synthesis for Water Treatment Processes

Nowadays, water demand and water scarcity are very urgent issues due to population growth, drought and poor water quality all over the world. Therefore, water treatment plants are playing a vital role for good living condition of human. Water area needs more concentration study to increase water productivity and decrease water cost. This dissertation presents the analysis and control of water treatment plants using robust control techniques. The applied control algorithms include H∞, gain scheduled and observer-based loop-shaping control technique. They are modern control algorithms and very powerful in robust controlling of systems with uncertainties and disturbances. The water treatment plants include a desalination system and a wastewater process. Since fresh water scarcity is getting more serious, the desalination plants are to produce drinking water and wastewater treatment plants give the reusable water. The desalination system is a RO one used to produce drinking water from seawater and brackish water. The nonlinear behaviors of this system is carefully analyzed before the linearization. Due to the uncertainty caused by concentration polarization, the system is linearized using linear state-space parametric uncertainty framework. The system also suffer from many disturbances which water hammer is one of the most influential one. The mixed robust H∞ and μ-synthesis control algorithm is applied to control the RO system coping with large uncertainties, disturbances and noises. The wastewater treatment process is an activated sludge process. This biological process use microorganisms to convert organic and certain inorganic matter from wastewater into cell mass. The process is very complex with many coupled biological and chemical reactions. Due to the large variation in the influent flow, the system is modelized and linearized as a linear parametric varying system using affine parameter-dependent representation. Since the influent flow is quickly variable and easily to be measured, the robust gain scheduled robust controller is applied to deal with the large uncertainty caused by the scheduled parameter. This control algorithm often gives better performances than those of general robust H∞ one. In the wastewater treatment plant, there exist an anaerobic digestion, which is controlled by the observer-based loop-shaping algorithm. The simulations show that all the controllers can effectively deal with large uncertainties, disturbances and noises in water treatment plants. They help improve the system performances and safeties, save energy and reduce product water costs. The studies contribute some potential control approaches for water treatment plants, which is currently a very active research area in the world.Contents ······················································································· iv List of Tables ··············································································· viii List of Figures ··············································································· ix Chapter 1. Introduction ···································································· 1 1.1 Reverse osmosis process ···································································· 2 1.2 Activated sludge process ···································································· 6 1.3 Robust H∞ and gain scheduling control ··················································· 10 Chapter 2. Robust H∞ controller ······················································· 13 2.1 Introduction ·················································································· 13 2.2 Uncertainty modelling ······································································ 13 2.2.1 Unstructured uncertainties ···························································· 14 2.2.2 Parametric uncertainties ······························································· 15 2.2.3 Structured uncertainties ································································ 16 2.2.4 Linear fractional transformation ······················································ 16 2.3 Stability criterion ············································································ 17 2.3.1 Small gain theorem ····································································· 17 2.3.2 Structured singular value (muy) synthesis brief definition ·························· 19 2.4 Robustness analysis and controller design ··············································· 20 2.4.1 Forming generalised plant and N-delta structure ····································· 20 2.4.2 Robustness analysis ···································································· 24 2.5 Reduced controller ·········································································· 26 2.5.1 Truncation ··············································································· 27 2.5.2 Residualization ········································································· 29 2.5.3 Balanced realization···································································· 29 2.5.4 Optimal Hankel norm approximation ················································ 31 Chapter 3. Robust gain scheduling controller ······································· 37 3.1 Introduction ·················································································· 37 3.2 Linear parameter varying (LPV) system ·················································· 39 3.3 Matrix Polytope ·············································································· 40 3.4 Polytope and affine parameter-dependent representation ······························· 41 3.4.1 Polytope representation ································································ 41 3.4.2 Affine parameter-dependent representation ········································· 42 3.5 Quadratic stability of LPV systems and quadratic (robust) H∞ performance ········· 43 3.6 Robust gain scheduling ····································································· 44 3.6.1 LPV system linearization ······························································ 44 3.6.2 Polytope-based gain scheduling ······················································ 45 3.6.3 LFT-based gain scheduling ··························································· 48 Chapter 4. Mixed robust H∞ and μ-synthesis controller applied for a reverse osmosis desalination system ····························································· 52 4.1 RO principles ················································································ 52 4.1.1 Osmosis and reverse osmosis ························································· 52 4.1.2 Dead-end filtration and cross-flow filtration ········································ 53 4.2 Membranes ··················································································· 54 4.2.1 Structure and material ································································· 54 4.2.2 Hollow fine fiber membrane module ················································ 55 4.2.3 Spiral wound membrane module ····················································· 57 4.3 Nonlinear RO modelling and analysis ···················································· 58 4.3.1 RO system introduction ······························································· 58 4.3.2 Modelling ··············································································· 60 4.3.3 Nonlinear analysis ······································································ 62 4.3.4 Concentration polarization ···························································· 64 4.4 Water hammer phenomenon ······························································· 66 4.4.1 Water hammer, column separation and vaporous cavitation ······················ 66 4.4.2 Water hammer analysis and simulation ·············································· 69 4.4.3 Prevention of water hammer effect··················································· 78 4.5 RO linearization ············································································· 79 4.5.1 Nominal linearization ·································································· 79 4.5.2 Uncertainty modeling ·································································· 81 4.5.3 Parametric uncertainty linearization ················································· 83 4.6 Robust H∞ controller design for RO system ·············································· 85 4.6.1 Control of uncertain RO system ······················································ 85 4.6.2 Robustness analysis and H∞ controller design ······································ 86 4.7 Simulation result and discussion··························································· 90 4.8 Conclusion ··················································································· 95 Chapter 5. Robust gain scheduling control of activated sludge process ······· 96 5.1 Introduction about activated sludge process ············································· 96 5.1.1 State variables ·········································································· 98 5.1.2 ASM1 processes ······································································ 100 5.1.3 The control problem of activated sludge process ································· 102 5.2 System modelling ········································································· 104 5.3 Model linearization ········································································ 107 5.4 Robust gain-schedule controller design for activated sludge process ··············· 109 5.5 Simulation result and discussion························································· 115 5.6 Conclusion ················································································· 120 Chapter 6. Observer-based loop-shaping control of anaerobic digestion ···· 121 6.1 Introduction ················································································ 121 6.1.1 Control problem in anaerobic digestion ··········································· 122 6.2 System modelling ········································································· 123 6.3 Controller design ·········································································· 124 6.3.1 H∞ loop-shaping controller ························································· 125 6.3.2 Coprime factor uncertainty ·························································· 126 6.3.3 Control synthesis ····································································· 127 6.4 Simulation result ··········································································· 131 6.5 Conclusion ················································································· 133 Chapter 7. Conclusion ··································································· 134 References ·················································································· 136 Appendices ················································································· 144Docto

Control oriented modelling of an integrated attitude and vibration suppression architecture for large space structures

This thesis is divided into two parts. The main focus of the research, namely active vibration control for large flexible spacecraft, is exposed in Part I and, in parallel, the topic of machine learning techniques for modern space applications is described in Part II. In particular, this thesis aims at proposing an end-to-end general architecture for an integrated attitude-vibration control system, starting from the design of structural models to the synthesis of the control laws. To this purpose, large space structures based on realistic missions are investigated as study cases, in accordance with the tendency of increasing the size of the scientific instruments to improve their sensitivity, being the drawback an increase of its overall flexibility. An active control method is therefore investigated to guarantee satisfactory pointing and maximum deformation by avoiding classical stiffening methods. Therefore, the instrument is designed to be supported by an active deployable frame hosting an optimal minimum set of collocated smart actuators and sensors. Different spatial configurations for the placement of the distributed network of active devices are investigated, both at closed-loop and open-loop levels. Concerning closed-loop techniques, a method to optimally place the poles of the system via a Direct Velocity Feedback (DVF) controller is proposed to identify simultaneously the location and number of active devices for vibration control with an in-cascade optimization technique. Then, two general and computationally efficient open-loop placement techniques, namely Gramian and Modal Strain Energy (MSE)-based methods, are adopted as opposed to heuristic algorithms, which imply high computational costs and are generally not suitable for high-dimensional systems, to propose a placement architecture for generically shaped tridimensional space structures. Then, an integrated robust control architecture for the spacecraft is presented as composed of both an attitude control scheme and a vibration control system. To conclude the study, attitude manoeuvres are performed to excite main flexible modes and prove the efficacy of both attitude and vibration control architectures. Moreover, Part II is dedicated to address the problem of improving autonomy and self-awareness of modern spacecraft, by using machine-learning based techniques to carry out Failure Identification for large space structures and improving the pointing performance of spacecraft (both flexible satellite with sloshing models and small rigid platforms) when performing repetitive Earth Observation manoeuvres

Proceedings of the Workshop on Computational Aspects in the Control of Flexible Systems, part 2

The Control/Structures Integration Program, a survey of available software for control of flexible structures, computational efficiency and capability, modeling and parameter estimation, and control synthesis and optimization software are discussed

The Fifth NASA/DOD Controls-Structures Interaction Technology Conference, part 1

This publication is a compilation of the papers presented at the Fifth NASA/DoD Controls-Structures Interaction (CSI) Technology Conference held in Lake Tahoe, Nevada, March 3-5, 1992. The conference, which was jointly sponsored by the NASA Office of Aeronautics and Space Technology and the Department of Defense, was organized by the NASA Langley Research Center. The purpose of this conference was to report to industry, academia, and government agencies on the current status of controls-structures interaction technology. The agenda covered ground testing, integrated design, analysis, flight experiments and concepts

Active Metastructures for Light-Weight Vibration Suppression

The primary objective of this work is to examine the effectiveness of metastructures for vibration suppression from a weight standpoint. Metastructures, a metamaterial inspired concept, are structures with distributed vibration absorbers. In automotive and aerospace industries, it is critical to have low levels of vibrations while also using lightweight materials. Previous work has shown that metastructures are effective at mitigating vibrations but does not consider the effects of mass. This work considers mass by comparing a metastructure to a baseline structure of equal mass with no absorbers. The metastructures are characterized by the number of vibration absorbers, the mass ratio, and the natural frequencies of the vibration absorbers. The metastructure and baseline structure are modeled using a lumped mass model and a distributed mass model. The lumped mass model allows for mass and stiffness parameters to be varied independently without the need to consider geometry constraints. The distributed mass model is a more realistic representation of a physical structure and uses relevant material properties. The steady-state and transient time responses of the structure are obtained. The results of these models examine how the performance of the structure varies with respect to the number of vibration absorbers and the mass ratio. Additionally, the stiffness and mass distributions of the vibration absorbers are considered. When the ratio of stiffness over mass varies linearly, the absorbers create broad-band suppression. Overall, these results show it is possible to obtain a favorable vibration response without adding additional mass to the structure. The distributed vibration absorbers are realized through geometry modifications on the centimeter scale. To obtain the complex geometry needed for these structures, the metastructures are typically manufactured using 3D printers, specifically the Objet Connex 3D printer. To better understand the damping properties of the materials used by the Objet Connex, the viscoelastic properties are characterized. These properties are characterized by measuring the frequency and temperature dependent complex modulus values using a dynamic mechanical analysis (DMA) machine. The material properties are incorporated into the Golla-Hughes-McTavish (GHM) model to capture the damping effect. Using the time-temperature equivalence, the material properties are transformed to various temperatures, allowing the response of the structures to be modeled at various temperatures. A 3D printed metastructure is experimentally tested and compared to the GHM model. These results show the GHM model can accurately predict the natural frequencies of the vibration absorbers. Lastly, the concept of adding active vibration control to a metastructure to get additional vibration suppression is explored. This is done by attaching piezoelectric materials to the metastructure and utilizing the positive position feedback (PPF) control law to further reduce vibrations. Two active vibration absorber designs are explored; the first uses a stack actuator to control the position of a single absorber and the second design bonds PZT patches in a bimorph cantilevered configuration to the beam of one absorber. This work shows that the active vibration absorber design utilizing a stack actuator is not practical, but the PZT bimorph configuration is capable of further reducing vibrations. Due to the metastructure design, each mode corresponds to the oscillation of a single absorber. When a single vibration absorber is active, the controller can control the corresponding mode. Overall, this shows that integrating active vibration control into a metastructure design can provide additional performance improvements.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144044/1/reichl_1.pd

Optimization methods for deadbeat control design: a state space approach

This thesis addresses the synthesis problem of state deadbeat regulator using state space techniques. Deadbeat control is a linear control strategy in discrete time systems and consists of driving the system from any arbitrary initial state to a desired final state infinite number of time steps. Having described the framework for development of the thesis which is in the form of a lower linear-fractional transformation (LFT), the conditions for internal stability based on the notion of coprime factorization over the set of proper and stable transfer matrices, namely RH, is discussed. This leads to the derivation of the class of all stabilizing linear controllers, which are parameterized affinely in terms of a stable but otherwise free parameter Q, usually known as the Q-parameterization. In this work, the classical Q- parameterization is generalized to deliver a parameterization for the family of deadbeat regulators. Time response characteristics of the deadbeat system are investigated. In particular, the deadbeat regulator design problem in which the system must satisfy time domain specifications and minimize a quadratic (LQG-type) performance criterion is examined. It is shown that the attained parameterization for deadbeat controllers leads to the formulation of the synthesis problem in a quadratic programming framework with Q regarded as the design variable. The equivalent formulation of this objective as a quadratic integral in the frequency domain provides the means for shaping the frequency response characteristics of the system. Using the LMI characterization of the standard H problem, a new scheme for shaping the system frequency response characteristics by minimizing the infinity norm of an appropriate closed-loop transfer function is introduced. As shown, the derived parameterization of deadbeat compensators simplifies considerably the formulation and solution of this problem. The last part of the work described in this thesis is devoted to addressing the synthesis problem of deadbeat regulators in a robust way, when the plant is subject to structured norm-bounded parametric uncertainties. A novel approach which is expressed as an LMI feasibility condition has been proposed and analysed