Control of the transition of laminar flow to turbulence would result in lower drag and reduced energy consumption in many engineering applications. A spectral state-space model of linearised plane Poiseuille flow with wall transpiration ac¬tuation and wall shear measurements is developed from the Navier-Stokes and continuity equations, and optimal controllers are synthesized and assessed in sim¬ulations of the flow. The polynomial-form collocation model with control by rate of change of wall-normal velocity is shown to be consistent with previous interpo¬lating models with control by wall-normal velocity. Previous methods of applying the Dirichlet and Neumann boundary conditions to Chebyshev series are shown to be not strictly valid. A partly novel method provides the best numerical behaviour after preconditioning. Two test cases representing the earliest stages of the transition are consid¬ered, and linear quadratic regulators (LQR) and estimators (LQE) are synthesized. Finer discretisation is required for convergence of estimators. A novel estimator covariance weighting improves estimator transient convergence. Initial conditions which generate the highest subsequent transient energy are calculated. Non-linear open- and closed-loop simulations, using an independently derived finite-volume Navier-Stokes solver modified to work in terms of perturbations, agree with linear simulations for small perturbations. Although the transpiration considered is zero net mass flow, large amounts of fluid are required locally. At larger perturbations the flow saturates. State feedback controllers continue to stabilise the flow, but estimators may overshoot and occasionally output feedback destabilises the flow. Actuation by simultaneous wall-normal and tangential transpiration is derived. There are indications that control via tangential actuation produces lower highest transient energy, although requiring larger control effort. State feedback controllers are also synthesized which minimise upper bounds on the highest transient energy and control effort. The performance of these controllers is similar to that of the optimal controllers.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In recent years the aviation industry has shown an interest in the airborne refuelling of large transport aircraft to enable increased payload mass at take-off and to extend aircraft range. Due to the large volume of fuel to be transferred, a boom and receptacle refuelling system with a larger fuel transfer rate is employed. The refuelling operation is particularly difficult and strenuous for the pilot of the receiver aircraft, because the position of the receptacle relative to the tanker aircraft must be maintained within a narrow window for a relatively long period of time. The airborne refuelling of a large aircraft is typically much more difficult than that of a fighter aircraft, since the large aircraft is more sluggish, takes much longer to refuel, and has a relatively large distance between its refuelling receptacle and its centre of mass. These difficulties provide the motivation for developing flight control laws for Autonomous In-Flight Refuelling (AIFR) to alleviate the workload on the pilot. The objective of the research is to design a flight control system that can regulate the receptacle of a receiver aircraft to remain within the boom envelope of a tanker aircraft in light and medium turbulence. The flight control system must be robust to uncertainties in the aircraft dynamic model, and must obey actuator deflection and slew rate limits. Literature on AIFR shows a wide range of approaches, including Linear Quadratic Regulator (LQR), μ-synthesis and neural-network based adaptive control, none of which explicitly includes constraints on actuator amplitudes, actuator rates and regulation errors in the design/synthesis. A new approach to designing AIFR flight control laws is proposed, based on Linear Matrix Inequality (LMI) optimisation. The relatively new LMI technique enables optimised regulation of stochastic systems subject to time-varying uncertainties and coloured noise disturbance, while simultaneously constraining transient behaviour and multiple outputs and actuators to operate within their amplitude, saturation and slew rate limits. These constraints are achieved by directly formulating them as inequalities. / AFRIKAANSE OPSOMMING: Die lugvaart industrie toon huidiglik ’n belangstelling in die brandstof oordrag tussen twee groot vervoervliegtuie gedurende vlug, met die doel om die maksimum opstyggewig kapasiteit sowel as die maksimum ononderbroke vlugafstand vermoë van die hervulde vliegtuig te vermeerder. ’n Boom hervulling-stelsel word geïmplementeer om die hoë spoed van brandstof oordrag te voorsien. Die verrigting van vluggebonde hervulling van ’n groot, trae vliegtuig is moeiliker en meer veeleisend as bv. van ’n vegvliegtuig, veral vir die vlieënier van die hervulde vliegtuig, wat sy boom-skakel moet reguleer binne ’n relatiewe klein boom bewegingsruimte vir ’n relatiewe lang tydperk. Die kinematika betrokke speel ook ’n groter rol in ’n groot hervulde vliegtuig a.g.v. die langer afstand tussen die boom-skakel en die massa middelpunt/ draaipunt. Hierdie bied die motivering om ’n beheerstelsel te ontwikkel wat die taak outomaties uitvoer. Die doel van die navorsing is om ’n beheerstelsel te ontwerp wat die boom-skakel van die hervulde vliegtuig outomaties reguleer binne die bewegingsruimte van die boom, gedurende ligte en matige turbulensie. Daar word van die beheerder vereis om robuust te wees teen onsekerhede in die vliegtuig se meganika, sowel as om die beheer oppervlaktes en turbines van die vliegtuig binne hul defleksie-, wringkrag- en sleurtempo-perke te hou. Daar bestaan reeds ’n groot verskeidenheid van benaderings tot die outomatisering van luggebonde hervulling, onder andere LQR, μ-sintese en neurale-netwerk gebaseerde aanpasbare beheer, waarvan geeneen perke op aktueerders en regulasie foute direk in die ontwerp insluit nie. ’n Nuwe benadering word voorgestel wat gebaseer is op Linear Matrix Inequality (LMI) optimering. Die LMI tegniek is relatief nuut in die gebruik van beheerstelsel ontwerp. Dit stel die ontwerper in staat om ’n stogastiese stelsel, onderworpe aan tydvariante-stelsel-variasie en gekleurde ruis versteurings, optimaal te reguleer, terwyl aktueerders en stelsel gedrag direk beperk word.

Control of the transition of laminar flow to turbulence would result in lower drag and reduced energy consumption in many engineering applications. A spectral state-space model of linearised plane Poiseuille flow with wall transpiration ac¬tuation and wall shear measurements is developed from the Navier-Stokes and continuity equations, and optimal controllers are synthesized and assessed in sim¬ulations of the flow. The polynomial-form collocation model with control by rate of change of wall-normal velocity is shown to be consistent with previous interpo¬lating models with control by wall-normal velocity. Previous methods of applying the Dirichlet and Neumann boundary conditions to Chebyshev series are shown to be not strictly valid. A partly novel method provides the best numerical behaviour after preconditioning. Two test cases representing the earliest stages of the transition are consid¬ered, and linear quadratic regulators (LQR) and estimators (LQE) are synthesized. Finer discretisation is required for convergence of estimators. A novel estimator covariance weighting improves estimator transient convergence. Initial conditions which generate the highest subsequent transient energy are calculated. Non-linear open- and closed-loop simulations, using an independently derived finite-volume Navier-Stokes solver modified to work in terms of perturbations, agree with linear simulations for small perturbations. Although the transpiration considered is zero net mass flow, large amounts of fluid are required locally. At larger perturbations the flow saturates. State feedback controllers continue to stabilise the flow, but estimators may overshoot and occasionally output feedback destabilises the flow. Actuation by simultaneous wall-normal and tangential transpiration is derived. There are indications that control via tangential actuation produces lower highest transient energy, although requiring larger control effort. State feedback controllers are also synthesized which minimise upper bounds on the highest transient energy and control effort. The performance of these controllers is similar to that of the optimal controllers.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23545号 / 情博第775号 / 新制||情||132(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 太田 快人, 教授 山下 信雄, 教授 大塚 敏之 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Dans le contexte des systèmes dynamiques, cette thèse développe des techniques d'estimation d'état ensemblistes pour différentes classes de systèmes. On considère pour cela le cas d'un système standard linéaire invariant dans le temps soumis à des perturbations, des bruits de mesure et des incertitudes inconnus, mais bornés. Dans une première étape, une technique d'estimation d'état ellipsoïdale est étendue, puis appliquée sur un modèle d'octorotor utilisé dans un contexte radar. Une extension de cette approche ellipsoïdale d'estimation d'état est proposée pour des systèmes descripteurs. Dans la deuxième partie, nous proposons une méthode fondée sur la minimisation du P-rayon d'un zonotope, appliquée à un modèle d'octorotor. Cette méthode est ensuite étendue pour traiter les systèmes affines par morceaux. Dans la continuité des approches précédentes, un nouveau filtre de Kalman sous contraintes zonotopiques est proposé dans la dernière partie de cette thèse. En utilisant la forme duale d'un problème d'optimisation, l'algorithme projette l'état sur un zonotope qui forme l'enveloppe de l'ensemble des contraintes auxquelles l'état est soumis. La complexité de l'algorithme est ensuite améliorée en remplaçant le zonotope initial par une forme réduite en limitant son nombre de générateurs. / In the context of dynamical systems, this thesis focuses on the development of robust set-membership state estimation procedures for different classes of systems. We consider the case of standard linear time-invariant systems, subject to unknown but bounded perturbations and measurement noises. The first part of this thesis builds upon previous results on ellipsoidal set-membership approaches. An extended ellipsoidal set-membership state estimation technique is applied to a model of an octorotor used for radar applications. Then, an extension of this ellipsoidal state estimation approach is proposed for descriptor systems. In the second part, we propose a state estimation technique based on the minimization of the P-radius of a zonotope, applied to the same model of the octorotor. This approach is further extended to deal with piecewise affine systems. In the continuity of the previous approaches, a new zonotopic constrained Kalman filter is proposed in the last part of this thesis. By solving a dual form of an optimization problem, the algorithm projects the state on a zonotope forming the envelope of the set of constraints that the state is subject to. Then, the computational complexity of the algorithm is improved by replacing the original possibly large-scale zonotope with a reduced form, by limiting its number of generators.

The traditional approach to damp inter-area oscillations is through the installation of Power System Stabilizers (PSSs) which provide damping control action through excitation control systems of the generating units. However, study of recent blackouts has shown that the control action provided by a PSS alone is not sufficient for damping oscillations in modern power systems which operate under stressed conditions. An integrated form of control using remote measurements to coordinate the different control elements present in the system is the need of the hour. One way of implementing such a coordinated control is through the development of a Linear Matrix Inequality (LMI)-based polytopic model of the system that guarantees pole placement for a variety of operating conditions. The size of the polytopic formulation is an issue for application of LMIs to large systems. The use of Selective Modal Analysis (SMA) alleviates this problem by reducing the size of the system. The previous attempts have used a model containing all the and modes, with SMA being used to eliminate all the other states. In practical applications the resulting system was still found to be too large to use in a polytopic model. This thesis presents an algorithm to reduce the size of the system to the relevant modes of oscillations. A 16 machine, 68 bus equivalent model of the New England-New York interconnected power system is used as the test case with DC lines and SVCs acting as the control. The algorithm is then applied to a 127-bus equivalent model of the WECC System. The use of ESDs as a form of control is also demonstrated. The results indicate that the proposed control successfully damps the relevant modes of oscillations without negatively damping the other modes. The control is then transferred to a more detailed 4000+ bus model of the WECC system to realize its performance on real-world systems. / Master of Science

<p>Flight Control Systems are often designed in linearization points over a flight envelope and it must be proven to clearance authorities that the system works for different parameter variations and failures all over this envelope. </p><p>In this thesis µ-analysis is tried as a complement for linear analysis in the frequency plane. Using this method stability can be guaranteed for all static parameter combinations modelled and linear criteria such as phase and gain margins and most unstable eigenvalue can be included in the analysis. A way of including bounds on the parameter variations using parameter dependent Lyapunov functions is also tried. </p><p>To perform µ-analysis the system must be described as a Linear Fractional Transformation (LFT). This is a way of reformulating a parameter dependent system description as an interconnection of a nominal linear time invariant system and a structured parameter block. </p><p>A linear and a rational approximation of the system are used to make LFTs. These methods are compared. Four algorithms for calculation of the upper and lower bounds of µ are evaluated. The methods are tried on VEGAS, a SAAB research aircraft model. </p><p>µ-analysis works quite well for linear clearance. The rational approximation LFT gives best results and can be cleared for the criteria mentioned above. A combination of the algorithms is used for best results. When the Lyapunov based method is used the size of the problem grows quite fast and, due to numerical problems, stability can only be guaranteed for a reduced model.</p>

Two micro air vehicles, namely Sapthami and Sapthami-flyer, are developed in this thesis. Their total weight is less than 200grams each. They fit inside a 30cm and 32cm sphere respectively and carry the commercially available Kestrel autopilot hardware. The vehicles have an endurance of around 20-30 minutes. The stall speed of Sapthami is around 7m/s and that of Sapthami-flyer is around 5m/s as found by nonlinear modeling. The low stall speed makes it possible for them to be launched by hand. This enhances their portability as they do not require any launching equipment. The vehicle installed with Kestrel autopilot system is capable of many modes of operations. It is capable of fully autonomous flight with the aid of a variety of sensors like the GPS unit, heading sensor, 2-axis magnetometer, 3-axis accelerometer and 3-axis gyros. The vehicle carrying the Kestrel autopilot hardware is capable of autonomous and semi-autonomous flights after installation and tuning of feedback loops. Sapthami, is a tailless flying wing with an inverse zimmermann profile. A flying wing is a preferred configuration for the MAV as it maximizes the lifting area for a given size constraint. For a maximum size constraint of 30cm and aspect ratio around 1, the vehicle operates at Reynolds number between 100,000 to 250,000, at flight velocity 7 m/s to 15 m/s. The Inverse Zimmerman profile has a higher lift coefficient, CL, in comparison to the other planforms such as rectangular, elliptical and Zimmermann, for aspect ratio 1 to 1.25 and tested at Reynolds number of 100,000. The configuration of Sapthami is clean as there is no fuselage and all the components like autopilot hardware and battery are housed inside the wing. A thick reflex Martin Hepperle (MH) airfoil MH18 is chosen which gives sufficient space to place the components. This airfoil is specially used for tailless configurations due to its negative camber at the trailing edge. This negative camber helps in reducing the negative pitching moment of the wing, since no separate horizontal tail is available on a tailless aircraft to compensate for it. The vehicle is fabricated using the blue foam, having a density of 30kg/m3 . The wing is fabricated by CNC machining after which slots are cut manually to embed the electronics. The vehicle is found to have stable flying characteristics. Limited flight trials are done for Sapthami. It takes large time to fabricate the vehicle due to limited availability of CNC machining facility. Therefore, a new tailless, wing-fuselage configuration, which can be fabricated with balsa wood, is designed. Sapthami-flyer is the second vehicle designed in this thesis. Its wing span is slightly more than Sapthami. Since it is a wing-fuselage configuration, therefore there is no need for a thick airfoil. Mark drela’s AG airfoils are found to have better lift than MH airfoils for the inverse Zimmerman profile. The thickness of the airfoils is reduced to 1% so that the wing can be made by a 1.5mm thick balsa sheet to reduce weight. The inverse Zimmermann profile wing with the AG09 airfoil is found to have best lift-to-drag ratio when compared to AG36, MH45 and MH18. The analysis is done using commercially available AVL software. AG09 with 1% thickness is used in the final configuration. This configuration has better short period damping than Sapthami. It also has slower modes of operation than Sapthami. The operating modes of most of the MAVs, including Sapthami and Sapthami-flyer, are lowly damped but fast. This makes it difficult for the pilot to fly the vehicle. To improve the flying qualities of the vehicle artificial stabilization is required. The feedback is implemented on the Kestrel autopilot hardware. It allows only PID based feedback structures to be implemented, hence gives no choice to the designer to implement higher order control. The digital integrator and differentiator implementation for feedback are non-ideal. This further reduces the effectiveness of control. The problem is dealt with by incorporating the additional dynamics introduced by these implementation while formulating the control problem. Further the modeling of the micro air vehicle is done by using vortex lattice simulation based softwares. The fidelity of the obtained dynamics is low. Therefore, there is high uncertainty in the plant model. The controller also needs to reject the wind gust disturbances which are of the order of the flight speed of the vehicle. All the above stated requirements from the control design can be best addressed by a robust control design. Sapthami-flyer uses aileron and elevator for control. There is no rudder in the configuration in order to reduce weight. In the longitudinal dynamics, pitch rate and pitch error feedback to elevator are used to increase the short period and phugoid damping respectively. In the lateral dynamics, a combination of roll rate, yaw rate and roll error feedback is given to aileron to improve the dutch roll damping and stabilize the spiral mode. The feedback loops for both longitudinal and lateral dynamics are multi-output single input design problems, therefore simultaneous tuning of loops is beneficial. The PID control is designed by first converting the actual plant to a static output feedback equivalent plant. The dynamics introduced by non-ideal differentiator and integrator implementation on the autopilot hardware are incorporated in the open loop static output feedback formulation. The robust pole placement for the SOF plant is done by using the modified iterative matrix inequality algorithm developed in this thesis. It is capable of multi-loop, multi-objective feedback design for SOF plants. The algorithm finds the optimal solution by simultaneously putting constraints on the H2 performance, pole placement, gain and phase margin of the closed loop system. The pole placement is done to minimize the real part of largest eigenvalue. A single controller is designed at a suit-able operating point and constraints are put on the gain and phase margin of the closed loop plant at other operating points. The designed controller is tested in flight on board Sapthami-flyer. The vehicle is also capable of tracking commanded pitch and roll attitude with the help of pitch error, roller or feedbacks. This is shown in the flight when the pilot leaves the RC stick and the vehicle tracks the desired attitude. The vehicle has shown improved flying characteristics in the closed loop mode.

Flight Control Systems are often designed in linearization points over a flight envelope and it must be proven to clearance authorities that the system works for different parameter variations and failures all over this envelope. In this thesis µ-analysis is tried as a complement for linear analysis in the frequency plane. Using this method stability can be guaranteed for all static parameter combinations modelled and linear criteria such as phase and gain margins and most unstable eigenvalue can be included in the analysis. A way of including bounds on the parameter variations using parameter dependent Lyapunov functions is also tried. To perform µ-analysis the system must be described as a Linear Fractional Transformation (LFT). This is a way of reformulating a parameter dependent system description as an interconnection of a nominal linear time invariant system and a structured parameter block. A linear and a rational approximation of the system are used to make LFTs. These methods are compared. Four algorithms for calculation of the upper and lower bounds of µ are evaluated. The methods are tried on VEGAS, a SAAB research aircraft model. µ-analysis works quite well for linear clearance. The rational approximation LFT gives best results and can be cleared for the criteria mentioned above. A combination of the algorithms is used for best results. When the Lyapunov based method is used the size of the problem grows quite fast and, due to numerical problems, stability can only be guaranteed for a reduced model.

Cette thèse porte sur la conception d’une classe particulière d’estimateurs d'état, les observateurs intervalles. L’objectif est d’estimer de manière garantie, les bornes supérieure et inférieure de l’ensemble admissible de l'état d’un système, à chaque instant de temps. L’approche considérée repose sur la connaissance a priori du domaine d’appartenance, supposé borné, des incertitudes du système (incertitudes de modélisation, perturbations, bruits, etc). Une classe d'observateurs intervalles à entrées inconnues est proposée pour la classe des systèmes Linéaires à Paramètres Variants (LPV). La synthèse des paramètres de l’observateur repose sur la résolution d’un problème d’optimisation sous contraintes de type inégalités matricielles linéaires (LMI) permettant de garantir simultanément les conditions d’existence de l’observateur ainsi qu’un niveau de performance, soit dans un contexte énergie, soit dans un contexte amplitude ou soit dans un contexte mixte énergie/amplitude. Plus particulièrement, la performance de l'observateur repose sur une technique de découplage pour annuler les effets des entrées inconnues et une technique d’optimisation destinée à minimiser, au sens de critères de type gain L2et/ou gain L∞, les effets des perturbations sur la largeur totale de l’enveloppe de l'état du système LPV. La méthodologie de synthèse proposée est illustrée sur un exemple académique. Enfin, la méthodologie est appliquée au cas de la phase d’atterrissage du véhicule spatial HL20, sous des conditions de simulations réalistes. / This thesis addresses the design of a class of estimator, named interval obser-ver, which evaluates in a guaranteed way, a set for the state of the system at each instant of time. The proposed approach is based on a priori knowledge of bounded sets for the system uncertainties (modeling uncertainties, disturbances, noise, etc.). A methodology to design an interval observer is proposed for the class of Linear Parameter Varying (LPV) Systems. The feasibility of the latter is based on the resolution of linear Matrix Inequalities (LMI) constraints allowing to simultaneously get the existence conditions of the intervalobserver and a certain level of a priori given performance for the state estimation of the system. Specifically, the performance of the estimates is based on a decoupling technique to avoid the effects of unknown inputs and an optimization technique to minimize, in the L2 and/or L∞ gain sense, the effects of disturbances on the estimated interval length for the state of the LPV system. The design methodology is illustrated on academic examples.Finally, the methodology is applied on the landing phase of the HL20 shuttle.