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

A necessary and sufficient minimality condition for uncertain systems

A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFTs) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well as Kalman-like decomposition structures. A related minimality condition, the converse of the reducibility condition, may then be inferred from these results and the equivalence class of all minimal LFT realizations defined. These results comprise the first stage of a complete generalization of realization theory concepts to uncertain systems. Subsequent results, such as the definition of and rank tests on structured controllability and observability matrices are also given. The minimality results described are applicable to multidimensional system realizations as well as to uncertain systems; connections to formal powers series representations also exist

WTEC panel report on European nuclear instrumentation and controls

Control and instrumentation systems might be called the 'brain' and 'senses' of a nuclear power plant. As such they become the key elements in the integrated operation of these plants. Recent developments in digital equipment have allowed a dramatic change in the design of these instrument and control (I&C) systems. New designs are evolving with cathode ray tube (CRT)-based control rooms, more automation, and better logical information for the human operators. As these new advanced systems are developed, various decisions must be made about the degree of automation and the human-to-machine interface. Different stages of the development of control automation and of advanced digital systems can be found in various countries. The purpose of this technology assessment is to make a comparative evaluation of the control and instrumentation systems that are being used for commercial nuclear power plants in Europe and the United States. This study is limited to pressurized water reactors (PWR's). Part of the evaluation includes comparisons with a previous similar study assessing Japanese technology

An advanced technology space station for the year 2025, study and concepts

A survey was made of potential space station missions that might exist in the 2020 to 2030 time period. Also, a brief study of the current state-of-the-art of the major subsystems was undertaken, and trends in technologies that could impact the subsystems were reviewed. The results of the survey and study were then used to arrive at a conceptual design of a space station for the year 2025. Factors addressed in the conceptual design included requirements for artificial gravity, synergies between subsystems, and the use of robotics. Suggestions are made relative to more in-depth studies concerning the conceptual design and alternative configurations

The Second Conference on Lunar Bases and Space Activities of the 21st Century, volume 2

These 92 papers comprise a peer-reviewed selection of presentations by authors from NASA, the Lunar and Planetary Institute (LPI), industry, and academia at the Second Conference on Lunar Bases and Space Activities of the 21st Century. These papers go into more technical depth than did those published from the first NASA-sponsored symposium on the topic, held in 1984. Session topics included the following: (1) design and operation of transportation systems to, in orbit around, and on the Moon; (2) lunar base site selection; (3) design, architecture, construction, and operation of lunar bases and human habitats; (4) lunar-based scientific research and experimentation in astronomy, exobiology, and lunar geology; (5) recovery and use of lunar resources; (6) environmental and human factors of and life support technology for human presence on the Moon; and (7) program management of human exploration of the Moon and space

Reduced order modelling in nuclear reaction thermal hydraulics

The context of the present thesis is to assess the potential of Reduced Order Models (ROMs) for nuclear reactor thermal hydraulics applications. ROMs constitute advanced modelling techniques aiming at fast high fidelity simulations. For the purposes of this research, two approaches have been selected and are investigated in depth: the Proper Orthogonal Decomposition (POD) with Galerkin projection (POD-Galerkin) and the hybrid method of Proper Orthogonal Decomposition with Interpolation using Radial Basis Functions, PODI - Galerkin, in the context of parametric model order reduction. Additionally, in terms of the POD method, two sampling techniques are presented and compared: the standard and the nested POD. The aforementioned methods are applied to a parametric case of non-isothermal mixing in a T-junction pipe for laminar and turbulent flow regimes. The flow is governed by the 3D, unsteady Navier - Stokes equations coupled with the energy equation. Furthermore, a ROM for modelling buoyancy driven flows with the Boussinesq approximation is discussed. Two cases are considered: a closed flow, where the method is applied to a benchmark case of a differentially heated square cavity, and an open flow, where a case of a "cold-trap" formation in a U-bend pipe is investigated. The suitability of the above techniques is assessed based on a comparison between the reduced order results and those obtained using high fidelity OpenFOAM solvers.Open Acces

Physics-model-based Optimization and Feedback Control of the Current Profile Dynamics in Fusion Tokamak Reactors

As the demand for energy continues to increase, the need to develop alternative energy sources to complement (and one day replace) conventional fossil fuels is becoming increasingly important. One such energy source is nuclear fusion, which has the potential to provide a clean source of energy and possesses an abundant fuel supply. However, due to the technological difficulty in creating the conditions necessary for controlled fusion to occur, nuclear fusion is not yet commercially viable. The tokamak is a device that utilizes magnetic fields to confine the reactants, which are in the plasma state, and it is one of the most promising devices capable of achieving controlled fusion. The ITER tokamak project is the next phase of tokamak development and will be the first tokamak reactor to explore the burning plasma (one with a significant amount of fusion reactions) operating regime.In order for ITER to meet its demanding goals, extensive research has been conducted to develop advanced tokamak operating scenarios characterized by a high fusion gain, good plasma confinement, magnetohydrodynamic stability, and a significant fraction of noninductively driven plasma current to maximize the plasma performance and potentially enable steady-state operation. As the dynamics of the tokamak plasma magnetic and kinetic states are highly coupled, distributed, nonlinear systems that exhibit many instabilities, it is extremely difficult to robustly achieve advanced operating scenarios. Therefore, active control of the plasma dynamics has significant potential to improve the ability to access advanced operating regimes. One of the key plasma properties investigated in the development of advanced scenarios is the plasma current profile because of its intimate relationship to plasma energy/particle transport and to plasma stability limits that are approached by increasing the plasma pressure. The plasma density and temperature profiles are also important parameters due to their close relationship to the amount of generated fusion power, to the total plasma stored energy, and to the amount of noninductive current drive. In tokamaks, the current and electron temperature profiles are coupled through resistive diffusion, noninductive current drive, and plasma energy/particle transport. As a result, integrated algorithms for current profile and electron temperature profile control will be necessary to maintain plasma stability, optimize plasma performance, and respond to changing power demand in ITER, and eventually a commercial, power producing tokamak reactor.In this work, model-based feedforward and feedback algorithms are developed to control the plasma current profile and thermal state dynamics with the goal of improving the ability to achieve robust tokamak operation. A first-principles-driven (FPD), physics-based approach is employed to develop models of the plasma response to the available actuators, which provides the freedom to handle the trade-off between the physics accuracy and the tractability for control design of the models. A numerical optimization algorithm to synthesize feedforward trajectories for the tokamak actuators that steer the plasma through the tokamak operating space to achieve a predefined target scenario (characterized by a desired current profile and total stored energy), subject to the plasma dynamics (described by the developed physics-based model), actuator constraints, and plasma state constraints, is developed. Additionally, robust feedback control algorithms for current profile, combined current profile + total stored energy, and simultaneous current profile + electron temperature profile control are synthesized for various tokamaks by embedding a FPD model into the control design process.Examples of the performance of the controllers in simulations (DIII-D, ITER, and TCV tokamaks) and DIII-D experiments are presented to illustrate the potential and versatility of the employed control methodology. The DIII-D experimental tests demonstrate the potential physics-model-based profile control has to provide a systematic approach for the development and robust sustainment of advanced scenarios. The ITER simulations demonstrate the ability to drive the current profile to a stationary target while simultaneously modulating the amount of fusion power that is generated. Finally, the TCV simulations demonstrate the ability to drive the current and electron temperature profiles to a self consistent target, as well as to maintain the current profile in a stationary condition while simultaneously modulating the electron temperature profile between equilibrium points

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools

Model reduction in physical domain

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2002.Includes bibliographical references (leaves 107-113).Modeling is an essential part of the analysis and the design of dynamic systems. Contemporary computer algorithms can produce very detailed models for complex systems with little time and effort. However, over complicated models may not be efficient. Therefore, reducing a model to a more manageable size has become an attractive research topic. A very useful type of reduced models is obtained by removing as many physical components as possible from the original model. Such approach is known as model reduction in the physical domain. Many results have been achieved in model reduction in the physical domain during past decades. Nonetheless, the newest developments in engineering practice as well as in theoretical research have brought about further challenges and opportunities. In this thesis, the criteria and the scope of model reduction in the physical domain are reinvestigated. As a result, a criterion based on the Hc norm of certain error model is proposed. Furthermore, the scope of model reduction is also extended. In this thesis, a mathematical framework is constructed for model reduction in physical domain. Specifically, model reduction problem is formulated as an optimization problem with bilinear matrix inequality (BMI) constraints. A branch-and-bound algorithm is developed to solve the BMI problem. The algorithm is proved to converge to global optimum. Several examples are presented to illustrate the use of the proposed model reduction scheme.by Yong Ye.Ph.D

Proceedings of the 6th Annual Summer Conference: NASA/USRA University Advanced Design Program

The NASA/USRA University Advanced Design Program is a unique program that brings together NASA engineers, students, and faculty from United States engineering schools by integrating current and future NASA space/aeronautics engineering design projects into the university curriculum. The Program was conceived in the fall of 1984 as a pilot project to foster engineering design education in the universities and to supplement NASA's in-house efforts in advanced planning for space and aeronautics design. Nine universities and five NASA centers participated in the first year of the pilot project. The study topics cover a broad range of potential space and aeronautics projects that could be undertaken during a 20 to 30 year period beginning with the deployment of the Space Station Freedom scheduled for the mid-1990s. Both manned and unmanned endeavors are embraced, and the systems approach to the design problem is emphasized