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

Direct learning ofLPVcontrollers from data

In many control applications, it is attractive to describe nonlinear (NL) and time-varying (TV) plants by linear parametervarying (LPV) models and design controllers based on such representations to regulate the behaviour of the system. The LPV system class offers the representation of NL and TV phenomena as a linear dynamic relationship between input and output signals, which relationship is dependent on some measurable signals, e.g., operating conditions, often called as scheduling variables. For such models, powerful control synthesis tools are available, but the way how to systematically convert available first principles models to LPV descriptions of the plant, to efficiently identify LPV models for control from data and to understand how modeling errors affect the control performance are still subject of undergoing research. Therefore, it is attractive to synthesize the controller directly from data without the need of modeling the plant and addressing the underlying difficulties. Hence, in this paper, a novel data-driven synthesis scheme is proposed in a stochastic framework to provide a practically applicable solution for synthesizing LPV controllers directly from data. Both the cases of fixed order controller tuning and controller structure learning are discussed and two different design approaches are provided. The effectiveness of the proposed methods is also illustrated by means of an academic example and a real application based simulation case study

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

This paper presents a robust adaptive control solution for linear parameter-varying (LPV) systems with unknown input gain and unmatched nonlinear (state- and time-dependent) uncertainties based on the $\mathcal{L}_1$ adaptive control architecture and peak-to-peak gain (PPG) analysis/minimization from robust control. Specifically, we introduce new tools for stability and performance analysis leveraging the PPG bound of an LPV system that is computable using linear matrix inequality (LMI) techniques. A piecewise-constant estimation law is introduced to estimate the lumped uncertainty with quantifiable error bounds, which can be systematically improved by reducing the estimation sampling time. We also present a new approach to attenuate the unmatched uncertainty based on the PPG minimization that is applicable to a broad class of systems with linear nominal dynamics. In addition, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system as compared to the same signals of a virtual reference system that represents the possibly best achievable performance. Under mild assumptions, we prove that the transient performance bounds can be uniformly reduced by decreasing the estimation sampling time, which is subject only to hardware limitations. The theoretical development is validated by extensive simulations on the short-period dynamics of an F-16 aircraft