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

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

Performance Guarantee of a Class of Continuous LPV System with Restricted-Model-Based Control

This paper considers the problem of the robust stabilisation of a class of continuous Linear Parameter Varying (LPV) systems under specifications. In order to guarantee the stabilisation of the plant with very large parameter uncertainties or variations, an output derivative estimation controller is considered. The design of such controller that guarantee desired  induced gain performance is examined. Furthermore, a simple procedure for achieving the  norm performance is proved for any all-poles single-input/single-output second order plant. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. Finally, the effectiveness of the proposed method is verified via a numerical example

Robust quasi-LPV model reference FTC of a quadrotor UAV subject to actuator faults

A solution for fault tolerant control (FTC) of a quadrotor unmanned aerial vehicle (UAV) is proposed. It relies on model reference-based control, where a reference model generates the desired trajectory. Depending on the type of reference model used for generating the reference trajectory, and on the assumptions about the availability and uncertainty of fault estimation, different error models are obtained. These error models are suitable for passive FTC, active FTC and hybrid FTC, the latter being able to merge the benefits of active and passive FTC while reducing their respective drawbacks. The controller is generated using results from the robust linear parameter varying (LPV) polytopic framework, where the vector of varying parameters is used to schedule between uncertain linear time invariant (LTI) systems. The design procedure relies on solving a set of linear matrix inequalities (LMIs) in order to achieve regional pole placement and H8 norm bounding constraints. Simulation results are used to compare the different FTC strategies.Peer ReviewedPostprint (published version

Energy efficient wireless sensor network protocols for monitoring and prognostics of large scale systems

In this work, energy-efficient protocols for wireless sensor networks (WSN) with applications to prognostics are investigated. Both analytical methods and verification are shown for the proposed methods via either hardware experiments or simulation. This work is presented in five papers. Energy-efficiency methods for WSN include distributed algorithms for i) optimal routing, ii) adaptive scheduling, iii) adaptive transmission power and data-rate control --Abstract, page iv

Design and Implementation of Adaptive PID and Adaptive Fuzzy Controllers for a Level Process Station

This proposed work proposes the design and real-time implementation of an adaptive fuzzy logic controller (FLC) and a proportional-integral-derivative (PID) controller for adaptive gain scheduling that can be configured for any complex industrial nonlinear application. Initially, the open-loop test of the single-input single-output (SISO) system, with nonlinearities and disturbances, is conducted to represent the mathematical model of the process around a set of equilibrium points. The adaptive controllers are then developed and deployed by using the national instruments reconfigurable input/output data acquisition device (NI RIO), NI myRIO-1900, and the control parameters are adapted in real-time corresponding to the changes in the process variable. The resulting servo and regulatory performance of the controllers are compared in MATLAB® software. The adaptive fuzzy controller is deduced to be the better controller as it can generate the desired output with quicker settling times, fewer oscillations, and negligible overshoot

Modelling and control of wind turbines with aeroelastically tailoring blades

The increased size of wind turbines (WTs) improves power generation efficiency but also imposes larger loading effects on the turbine system. A wind turbine with an aeroelastic tailoring blade (ATB) is proposed to alleviate the loading effect in wind turbine blades. A turbine with ATB is designed to respond to the incoming wind forces by deforming the shape of the blade and then reforming to its initial formation. The blade is manufactured with composite materials, incorporated with pre-twist angle and bend twist coupling (BTC) characteristics. Wind turbines with ATB are a new development that needs a better understanding of their operational performance and their potential when properly controlled. This PhD project aims to investigate the modelling and control of industrial-scale ATB WTs and assess the control performance with systematic studies. The thesis work includes two connected parts, model development, and control system design. A set of models has been developed for system analysis and controller design. To start with, a baseline model is revisited that covers key modelling elements of a 5MW standard HAWT wind turbine. This model is indexed as Model 0 in this thesis, it is the basis for other ATB WTs. To characterise ATB features, firstly the static BTC distribution is added to the turbine aerodynamics to account for the blade’s pre-bend-twist design. This static ATB model is integrated to the baseline model giving the full nonlinear turbine model, called Model 1, which will be used for the gain-scheduling baseline controller. Next, the ATB dynamics is approximated by a spring damper model to describe the blade structural dynamic response to wind speed variations. The developed turbine model combining the static ATB and dynamic ATB is called Model 2, based on which a linearised and discretised state-space model is developed for adaptive model predictive control (MPC). Additionally, a composite ATB model is established, in which the power coefficient values are generated from physical laboratory experiments for a composite materials blade. This model is referred to as Model 3, will also be used for adaptive MPC. Two controllers are investigated for the above-rated ATB WT operational control. The first controller is the gain scheduling baseline controller developed by the Wind Energy and Control Centre, initially for full envelope WT control of a standard machine without ATB. This baseline controller is redeveloped for the ATB WT using Model 1. The second controller is the adaptive MPC proposed and developed in this thesis work, which includes a general predictive controller enhanced by the use of a Kalman filter and online model update. This adaptive MPC is applied to Model 2 and Model 3 to examine the control performance. Several tools are used to support model development and controller design. Model 0 (including the baseline controller) is a nonlinear full-envelope model developed in Simulink (Chapter 3). Model 1 is developed by introducing the pre-twist angle and BTC in GL Bladed software, the generated power coefficients are then imported to the Simulink model. The simulation of Model 1 and the adapted baseline controller is made in Simulink (Chapter 3). Model 2 is developed by combining the data generated for static ATB in Model 1 and the dynamic ATB model. The full model for baseline control (Chapter 4) and the simplified state-space model for adaptive MPC (Chapter 5) are implemented in Matlab and Simulink. Model 3 is used for adaptive MPC, also realised in Matlab and Simulink (Chapter 6). Based on the comprehensive investigation, it is concluded that the ATB WT models developed in this work are suitable for controller design. Both the adapted gain scheduling baseline controller and the proposed adaptive MPC can be applied to achieve satisfactory control performance, that is, to mitigate fatigue load without compromising the power generation of the turbine system. With adaptive MPC, the system demonstrates improvement in reducing pitch activity, tower acceleration and blade root bending moment.The increased size of wind turbines (WTs) improves power generation efficiency but also imposes larger loading effects on the turbine system. A wind turbine with an aeroelastic tailoring blade (ATB) is proposed to alleviate the loading effect in wind turbine blades. A turbine with ATB is designed to respond to the incoming wind forces by deforming the shape of the blade and then reforming to its initial formation. The blade is manufactured with composite materials, incorporated with pre-twist angle and bend twist coupling (BTC) characteristics. Wind turbines with ATB are a new development that needs a better understanding of their operational performance and their potential when properly controlled. This PhD project aims to investigate the modelling and control of industrial-scale ATB WTs and assess the control performance with systematic studies. The thesis work includes two connected parts, model development, and control system design. A set of models has been developed for system analysis and controller design. To start with, a baseline model is revisited that covers key modelling elements of a 5MW standard HAWT wind turbine. This model is indexed as Model 0 in this thesis, it is the basis for other ATB WTs. To characterise ATB features, firstly the static BTC distribution is added to the turbine aerodynamics to account for the blade’s pre-bend-twist design. This static ATB model is integrated to the baseline model giving the full nonlinear turbine model, called Model 1, which will be used for the gain-scheduling baseline controller. Next, the ATB dynamics is approximated by a spring damper model to describe the blade structural dynamic response to wind speed variations. The developed turbine model combining the static ATB and dynamic ATB is called Model 2, based on which a linearised and discretised state-space model is developed for adaptive model predictive control (MPC). Additionally, a composite ATB model is established, in which the power coefficient values are generated from physical laboratory experiments for a composite materials blade. This model is referred to as Model 3, will also be used for adaptive MPC. Two controllers are investigated for the above-rated ATB WT operational control. The first controller is the gain scheduling baseline controller developed by the Wind Energy and Control Centre, initially for full envelope WT control of a standard machine without ATB. This baseline controller is redeveloped for the ATB WT using Model 1. The second controller is the adaptive MPC proposed and developed in this thesis work, which includes a general predictive controller enhanced by the use of a Kalman filter and online model update. This adaptive MPC is applied to Model 2 and Model 3 to examine the control performance. Several tools are used to support model development and controller design. Model 0 (including the baseline controller) is a nonlinear full-envelope model developed in Simulink (Chapter 3). Model 1 is developed by introducing the pre-twist angle and BTC in GL Bladed software, the generated power coefficients are then imported to the Simulink model. The simulation of Model 1 and the adapted baseline controller is made in Simulink (Chapter 3). Model 2 is developed by combining the data generated for static ATB in Model 1 and the dynamic ATB model. The full model for baseline control (Chapter 4) and the simplified state-space model for adaptive MPC (Chapter 5) are implemented in Matlab and Simulink. Model 3 is used for adaptive MPC, also realised in Matlab and Simulink (Chapter 6). Based on the comprehensive investigation, it is concluded that the ATB WT models developed in this work are suitable for controller design. Both the adapted gain scheduling baseline controller and the proposed adaptive MPC can be applied to achieve satisfactory control performance, that is, to mitigate fatigue load without compromising the power generation of the turbine system. With adaptive MPC, the system demonstrates improvement in reducing pitch activity, tower acceleration and blade root bending moment

A non-linear approach to modelling and control of electrically stimulated skeletal muscle

This thesis is concerned with the development and analysis of a non-linear approach to modelling and control of the contraction of electrically stimulated skeletal muscle. For muscle which has lost nervous control, artificial electrical stimulation can be used as a technique aimed at providing muscular contraction and producing a functionally useful movement. This is generally referred to as Functional Electrical Stimulation (FES) and is used in different application areas such as the rehabilitation of paralysed patient and in cardiac assistance where skeletal muscle can be used to support a failing heart. For both these FES applications a model of the muscle is essential to develop algorithms for the controlled stimulation. For the identification of muscle models, real data are available from experiments with rabbit muscle. Data for contraction with constant muscle length were collected from two muscle with very different characteristics. An empirical modelling approach is developed which is suitable for both muscles. The approach is based on a decomposition of the operating space into smaller sub-regions which are then described by local models of simple, possibly linear structure. The local models are blended together by a scheduler, and the resulting non-linear model is called a Local Model Network (LMN). It is shown how a priori knowledge about the system can be used directly when identifying Local Model Networks. Aspects of the structure selection are discussed and algorithms for the identification of the model parameters are presented. Tools of the analysis of Local Model Networks have been developed and are used to validate the models. The problem of designing a controller based on the LMN structure is discussed. The structure of Local Controller Networks is introduced. These can be derived directly from Local Model Networks. Design techniques for input-output and for state feedback controllers, based on pole placement, are presented. Aspects of the generation of optimal stimulation patterns (which are defined as stimulation patterns which deliver the smallest number of pulses to obtain a desired contraction) are discussed, and various techniques to generate them are presented. In particular, it is shown how a control structure can be used to generate optimal stimulation patterns. A Local Controller Network is used as the controller with a design based on a non-linear LMN model of muscle. Experimental data from a non-linear heat transfer process have been collected and are used to demonstrate the basic modelling and control principles throughout the first part of the thesis