Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Gain-scheduling multivariable LPV control of an irrigation canal system

The purpose of this paper is to present a multivariable linear parameter varying (LPV) controller with a gain scheduling Smith Predictor (SP) scheme applicable to open-flow canal systems. This LPV controller based on SP is designed taking into account the uncertainty in the estimation of delay and the variation of plant parameters according to the operating point. This new methodology can be applied to a class of delay systems that can be represented by a set of models that can be factorized into a rational multivariable model in series with left/right diagonal (multiple) delays, such as, the case of irrigation canals. A multiple pool canal system is used to test and validate the proposed control approach.Peer ReviewedPostprint (author's final draft

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Design robust controllers for load reduction in wind turbines

This thesis determines a design methodology of robust and multivariable controllers based on the H∞ norm reduction and on LPV (Linear Parameter Varying) techniques for load reduction in wind turbines. In order to do this, a 5 MW offshore wind turbine model based on the ‘Upwind’ European project is developed using GH Bladed, which is a wind turbine modelling specific software package. These controllers work in the above rated control zone, where the non-linearities of the wind turbine appear with more intensity. The main control objective in this zone is to keep the generator working at the nominal values of rotational speed and torque to correctly extract the nominal electric power in high winds. Furthermore, new control objectives are included to mitigate the loads in different components of the wind turbine, which involves the need of a multivariable control design. The family of linear models extracted from the non-linear model is used to design the proposed controllers. In this work, the family of linear models extracted from the GH Bladed is high ordered due to the complexity and accuracy of the wind turbine model. The Robust Control and LPVMAD MATLAB toolboxes are used to make the controller synthesis. LPVMAD is a toolbox developed by the scientific control group directed by Prof. Dr. Carsten Scherer at the Stuttgart University. After an exhaustive analysis of the State of the Art about the wind turbine control systems, a baseline control strategy based on classical control methods is initially designed. Five monovariable, MISO (Multiple Input Single Output) and multivariable robust control strategies, based on the H∞ norm reduction, are presented to improve the benefits of the baseline controller. These controllers fulfill some control objectives to mitigate the loads in the wind turbine: generator speed regulation, drive train mode damping, tower first fore-aft and side-to-side first mode damping and rotor alignment. The designed H∞ controllers generate control signals of generator torque, collective pitch blade angle and individual pitch angles for each blade. On the other hand, two LPV control strategies are designed to improve the generator speed regulation in the above rated zone generating collective pitch angle set-point values. The first LPV controller consists of the interpolation of three H∞ controllers designed in three different operational points. The second LPV controller synthesis is based on a LMI (Linear Matrix Inequalities) solution using the LPVMAD toolbox and a wind turbine LPV model. The wind turbine multivariable LPV modelling process is also explained in this thesis. The designed controllers are validated in GH Bladed and an exhaustive analysis is carried out to calculate the fatigue load reduction on the wind turbine components, as well as to analyze load mitigation in some extreme cases. The controllers are tested in a real time prototype which allows to carry out HIL (Hardware in the Loop) simulations. A GUI interface tool is developed in MATLAB to determine a sequential method making easier the controller design explained in this thesis. Finally, the proposed design methodology of robust and multivariable controllers is applied to a commercial 3 MW wind turbine.Tesi honek aldagai anitzeko kontrolatzaile sendoak diseinatzeko metodologia bat ezartzen du, non kontrolatzaileak H∞ normaren gutxitzean eta LPV (Linear Parameter Varying) kontrol-tekniketan oinarrituta dauden, haize-errotetako karga mekanikoak murrizteko. Horretarako, 'Upwind' europar proiektuan definitutako 5 MWeko itsas haize-errotaren eredua garatu da GH Bladed softwarean. Kontrolatzaile horien diseinua 'above rated' izeneko funtzionamendu-zonalderako da. Zonalde horretan haize-erroten ez-linealtasunak garrantzi handikoak dira eta haize-errotaren funtzionamendua biratze-abiadura eta momentu nominaletan egin nahi da, horrela haize altuetan potentzia nominala lortu ahal izateko. Hauxe helburu nagusia izanda, beste kontrol-helburuak ere kontuan hartzen dira: haize-errotaren osagai desberdinetan karga mekanikoak txikitzea kontrolatzaileen diseinua aldagai anitzeko ikuspuntu batetik eginez. GH Bladed paketean definitutako eredu ez-linealaren linealizaziotik lortzen den eredu linealen familia erabiltzen da kontrolatzaileak diseinatzeko, nahiz eta oso orden handiko ereduak izan modelatze-konplexutasuna dela-eta. Kontrolatzaileak sortzeko MATLAB-eko kontrol sendoaren 'toolbox'-a erabiltzen da eta baita Dr. Carsten Scherer-en lantaldeak garatutako LPVMAD 'toolbox'-a ere. Haize-errotentzako kontrol-sistemen Arte-Egoeraren analisi sakon baten ondoren, hasieran, erreferentzi kontrolatzaile bat diseinatzen da, normalean erabiltzen diren kontrolatzaile klasikoetan oinarrituta. Tesian bost kontrolatzaile sendo, H∞ normaren txikitzean oinarrituak, aurkezten dira, aldagai bakarrekoak, MISO (Multiple Input Single Output) eta aldagai aniztzekoak, alde batetik erreferentzi kontrol-estrategiaren prestazioak hobetzeko eta beste aldetik haize-errotetan karga mekaniken murrizketak eragiten dituzten helburuak betetzeko: sortzailearen abiadura angeluarra erregulatzea, potentzi trenaren modua moteltzea, dorrearen aurre-atzerako eta alboko lehenengo bibrazio-moduetan haizearen efektuak murriztea eta errotorea lerrokatzea. Kontrolatzaileek sortzaileentzako momentuen kontrol-seinaleak, itxoroskientzat pitch-angelu kolektiboa eta baita itxoroski bakoitzarentzat pitch-angelu independenteak ere sortzen dituzte, inposatutako kontrolhelburuak betetzeko. Horietatik at, beste bi LPV kontrol-estrategia diseinatzen dira 'above rated' funtzionamendu-zonaldean sortzailearen abiadura angeluarraren kontrola hobetzeko pitch-angelu kolektiboaren kontsignen bidez. Lehenengo LPV kontrolatzailea hiru funtzionamendu-puntu desberdinetan diseinaturiko hiru H∞ kontrolatzaileen interpolazioan datza. Bigarren LPV kontrolatzailearen diseinua, ordea, LMI (Linear Matrix Inequalities) sistema baten askatzean datza, LPVMAD 'toolbox'-a eta haize-errotaren LPV eredu bat erabiliz. Haize-errota baten aldagai anitzeko LPV modelatze-prozesua ere zehatz-mehatz azaltzen da tesi honetan. Diseinatutako kontrolatzaileak GH Bladed paketean balioztatu dira analisi sakon baten bidez, non neke-kargen eta mutur-kargen murrizketak haize-errotaren osagai desberdinetan kalkulatzea ahalbideratzen baita. Kontrolatzaileak HIL (Hardware in the Loop) simulazioak egitea errazten duen denbora errealeko prototipo batean ere probatu dira, kontrolatzaileen funtzionamendu egokia ziurtatzen duena. Garatutako kontrolatzaileen diseinua errazteko interfaze grafiko bat gauzatu da MATLAB-en, non tesian aurkeztutako kontrolatzaile bakoitzaren diseinua prozedura sekuentzial baten bidez egin ahal izan den. Azkenean, aldagai anitzeko kontrolatzaile sendoen diseinurako proposaturiko metodologia 3 MWeko haize-errota komertzial batean aplikatu egin da.Esta tesis establece una metodología de diseño de controladores robustos multivariables basados en la reducción de la norma H∞ y en técnicas de control LPV (Linear Parameter Varying) para la reducción de cargas en aerogeneradores. Para ello, se ha desarrollado un modelo de un aerogenerador offshore de 5 MW definido en el proyecto europeo 'Upwind' mediante el software de modelado específico de aerogeneradores GH Bladed. El diseño de estos controladores se centra en la zona de funcionamiento denominada 'above rated', donde se manifiestan con mayor importancia las no-linealidades del aerogenerador y en la que se pretende mantener el funcionamiento del generador en sus valores nominales de velocidad de giro y par para la correcta extracción de potencia nominal a vientos altos. Además de este objetivo principal, se incluyen nuevos objetivos de control que minimicen las cargas en las diferentes partes del aerogenerador haciendo que el diseño de los controladores requiera un punto de vista multivariable. Para el diseño de los controladores se utiliza la familia de modelos lineales extraída de la linealización del modelo no lineal, en este caso definido en GH Bladed, siendo estos modelos de un orden elevado debido a la complejidad del modelado. Para la síntesis de los controladores se utiliza las 'toolbox' de MATLAB de control robusto y la 'toolbox' LPVMAD desarrollada por el grupo de trabajo del Prof. Dr. Carsten Scherer. Tras un profundo análisis del estado del arte sobre los sistemas de control en los aerogeneradores, inicialmente se diseña una estrategia de control referencia basada en los controladores clásicos comúnmente utilizados. En la tesis se presentan cinco controladores robustos monovariables, MISO (Multiple Input Single Output) y multivariables basados en la reducción de la norma H∞ para mejorar las prestaciones de la estrategia de control referencia y que cumplen con diferentes objetivos de control que implican una reducción de cargas en el sistema: regulación de la velocidad angular del generador, amortiguamiento del modo del tren de potencia, reducción del efecto del viento sobre los primeros modos adelante-atrás y lateral de la torre y alineamiento del rotor. Los controladores generan señales de control de par en el generador, ángulo de pitch colectivo en las palas y ángulos independientes de pitch para cada pala con la finalidad de satisfacer los objetivos de control impuestos. Por otro lado, se diseñan dos estrategias de control LPV para mejorar la regulación de velocidad angular del generador en la zona de 'above rated' mediante consignas de ángulo de pitch colectivo. El primer control LPV consiste en la interpolación de tres controladores H∞ diseñados en tres puntos de operación diferentes, mientras que la síntesis del segundo controlador LPV se basa en la solución de un sistema LMI (Linear Matrix Inequalities) mediante la toolbox LPVMAD y utilizando el modelo LPV del aerogenerador. El proceso de modelado LPV multivariable de un aerogenerador también es explicado con detenimiento en esta tesis. Los controladores diseñados son validados en GH Bladed mediante un exhaustivo análisis que permite calcular la reducción de cargas extremas y cargas de fatiga en los diferentes componentes del aerogenerador. Los controladores son probados en un prototipo en tiempo real que permite realizar simulaciones HIL (Hardware in the Loop) que ratifican el correcto funcionamiento de los controladores. Para facilitar el diseño de estos controladores se ha implementado una interfaz gráfica en MATLAB que permite establecer un procedimiento secuencial para el diseño de cada controlador explicado en la tesis. Finalmente, la metodología propuesta para el diseño de controladores robustos multivariables se ha aplicado a un aerogenerador comercial de 3 MW

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

From Fixed-Order Gain-Scheduling to Fixed-Structure LPV Controller Design

This thesis focuses on the development of some fixed-order controller design methods in the gain-scheduling/Linear Parameter Varying (LPV) framework. Gain-scheduled controllers designed using frequency-domain Single Input Single Output (SISO) models are considered first, followed by LPV controller design in the SISO transfer function setting and, finally, by Multiple Input Multiple Output (MIMO) LPV controller design in the state-space setting. In addition to the guarantee of closed-loop stability, each of the methods optimizes some classical performance measure, such as the $\mathscr{H}_\infty$ or $\mathscr{H}_2$ performance metrics. In the LPV state-space setting, the practical assumption of bounded scheduling parameter variations is taken into account in order to allow a higher performance level to be achieved. The fixed-order gain-scheduled controller design method is based on frequency-domain models dependent on the scheduling parameters. Based on the linearly parameterized gain-scheduled controllers and desired open-loop transfer functions, the $\mathscr{H}_\infty$ performance of the weighted closed-loop transfer functions is presented in the Nyquist diagram as a set of convex constraints. No a posteriori interpolation is needed, so the stability and performance level are guaranteed for all values of scheduling parameters considered in the design. Controllers designed with this method are successfully applied to the international benchmark in adaptive regulation. These low-order controllers ensure good rejection of the multisinusoidal disturbance with time-varying frequencies on the active suspension testbed. One issue related to the gain-scheduled controller design using the frequency response model is the computational burden due to the constraint sampling in the frequency domain. The other is a guarantee of stability and performance for all the values of scheduling parameters, not just those treated in design. To overcome these issues, a method for the design of fixed-order LPV controllers with the transfer function representation is proposed. The LPV controller parameterization considered in this approach leads to design variables in both the numerator and denominator of the controller. Stability and $\mathscr{H}_\infty$ performance conditions for all fixed values of scheduling parameters are presented in terms of Linear Matrix Inequalities (LMIs). With a problem of rejection of a multisinusoidal disturbance with time-varying frequencies in mind, LPV controller is designed for an LTI plant with a transfer function model. The extension of these methods from SISO to MIMO systems is far from trivial. The state-space setting is used for this reason, as there the transition from SISO to MIMO systems is natural. A method for fixed-order output-feedback LPV controller design for continuous-time state-space LPV plants with affine dependence on scheduling parameters is proposed. Bounds on the scheduling parameters and their variation rates are exploited in design through the use of affine Parameter Dependent Lyapunov Functions (PDLFs). The exponential decay rate, induced $\mathscr{L}_2$-norm and $\mathscr{H}_2$ performance constraints are expressed through a set of LMIs. The proposed method is applied to the 2DOF gyroscope experimental setup. In practice control is performed using digital computers, so some effort needs to be put into the LPV controller discretization. If the discrete-time LPV model of the system is available [...