Analysis of potential small satellite launch operations at the Denel Overberg test range.

Master Degree. University of KwaZulu-Natal, Durban.One of the primary objectives of the South African First Integrated Rocket Engine (SAFFIRE) programme of UKZN’s Aerospace System Research Group (ASReG) is to develop the capacity for orbital injection missions to Low Earth Orbits (LEOs) from South Africa. The most likely launch site for these missions is the Denel Overberg Test Range (OTR) near Cape Agulhas in the Western Cape. In order to determine the suitability of OTR as a launch site, it is imperative to gain an understanding of the performance, mechanics and structural loads of a vehicle entering orbit. The goal of this dissertation is to analyse the performance of a variety of modern two-stage launch vehicles as they travel along orbital injection trajectories into LEOs from OTR. This study considers solutions for the ascent-to-orbit trajectory for various launch vehicles. The primary method was to utilise trajectory optimisation methods and this was achieved by developing an optimal control solver, which makes use of direct Hermite-Simpson collocation methods, and a sequential quadratic programming solver. In order to improve the robustness and speed of the solver, formulae for the first order analytical derivative information of direct Hermite-Simpson collocation were developed. The optimal control solver was then validated using various linear and nonlinear examples from literature. The optimal control solver was used to analyse the performance of various hypothetical missions conducted by the following established launch vehicles: Rocket Lab’s Electron, SpaceX’s Falcon 1, SpaceX’s Falcon 9, and ASReG’s proposed small satellite launch vehicle, CLV. As a baseline comparison, all vehicles were launched from OTR into various LEOs. The payloads, trajectories, control histories and structural loads of these vehicles for injection were investigated. Finally, the effect of perigee altitude, inclination, and eccentricity of orbits on the extracted results was studied. The payload performance of the launch vehicles considered were relatively similar to that provided by each vehicle’s corresponding payload user guide. On all missions, the altitude of the Electron, Falcon 9 and CLV would constantly increase with range, however the Falcon 1 would tend to rise, dip, and then rise once more on missions to orbits with a perigee altitude of 200 km. Such trajectories are referred to as lofted trajectories and are common among vehicles with a low upper stage thrust to weight ratio (Patton and Hopkins, 2006), such as the Falcon 1. The tangent yaw and pitch of the thrust direction was highly linear for all analysed missions. This result allows for a reasonable control law which can be used to determine trajectory solutions using indirect optimal control methods. This study demonstrates the viability of the Denel Overberg Test Range as a competitive base of operation for space launch missions to LEO

Real-Time Optimization for Estimation and Control: Application to Waste Heat Recovery for Heavy Duty Trucks

This thesis aims at the investigation and development of the control of waste heat recovery systems (WHR) for heavy duty trucks based on the organic Rankine cycle. It is desired to control these systems in real time so that they recover as much energy as possible, but this is no trivial task since their highly nonlinear dynamics are strongly affected by external inputs (disturbances). Additionally, nonlinear operational constraints must be satisfied. To deal with this problem, in this thesis a dynamic model of a WHR that is based on first principles and empirical relationships from thermodynamics and heat transfer is formulated. This model corresponds to a DAE of index 1. In view of the requirements of the employed numerical methods, it includes a spline-based evaluation method for the thermophysical properties needed to evaluate the model. Therewith, the continuous differentiability of the state trajectories with respect to controls and states on its domain of evaluation is achieved. Next, an optimal control problem (OCP) for a fixed time horizon is formulated. From the OCP, a nonlinear model-predictive control (NMPC) scheme is formulated as well. Since NMPC corresponds to a state feedback strategy, a state estimator is also formulated in the form of a moving horizon estimation (MHE) scheme. In this thesis, we make use of efficient numerical methods based on the direct multiple shooting (DMS) method for optimal control, backward differentiation formulae for the solution of initial value problems for DAE, and the corresponding versions of the real-time iteration (RTI) scheme in order to approximately solve the OCP and implement the MHE and NMPC schemes. The simultaneous implementation of NMPC and MHE schemes based on RTI has been already proven to be stable in the control literature. Several numerical instances of the DMS method for the proposed OCP, NMPC and MHE schemes are tested assuming a given real-world operation scenario consisting of truck exhaust gas data recorded during a real trip. These data have been kindly provided by our industry cooperation partner Daimler AG. Additionally, the PI and LQGI control strategies, of wide-spread use in the literature of control of WHR, are also considered for comparison with the proposed scheme. An important result of this thesis is that, considering the highest energy recovery obtained from both strategies as a reference for the given operation scenario, the proposed NMPC scheme is able to reach an additional energy generation of around 3% when the full state vector is assumed to be known, and its computational speed allows it to update the control function in times shorter than the considered sampling time of 100 [ms], which makes it a suitable candidate for real-time implementation. In a more realistic scenario in which the state has to be estimated from noisy measurements, a combination of both aforementioned NMPC and MHE schemes yields an additional energy generation of around 2%. Concretely, this thesis presents novel results and advances in the following areas: • A first principles DAE model of the WHR is presented. The model is derived from the energy and mass conservation considerations and empirical heat transfer relationships; and features a tailored evaluation method of thermophysical properties with which it possesses the property of being at least continuously differentiable with respect to its controls and states on its whole domain of evaluation. • A new real-time optimization control strategy for the WHR is developed. It consists of an NMPC strategy based on efficient simulation, optimization and control tools developed in previous works. The scheme is able to explicitly handle nonlinear constraints on controls and states. In contrast to other NMPC instances for the WHR found in the literature, our scheme's efficient numerical treatment make it real-time feasible even if the full nonlinear WHR dynamics are considered. • To the author's knowledge, this is the first implementation that considers both the NMPC and the MHE approaches used simultaneously in the control of the WHR. The combination of NMPC and MHE produces a closed-loop, model-based implementation that can treat realistic measurements as inputs and calculates the corresponding control functions as outputs

Development of a Procedure to Optimize the Geometric and Dynamic Designs of Assistive Upper Limb Exoskeletons

RÉSUMÉ La faiblesse musculaire chez les patients atteints de maladies neuromusculaires peut réduire leur capacité à réaliser des activités quotidiennes primordiales telles que manger ou se laver. Les dispositifs d'assistance disponibles offrent des fonctionnalités limitées et ne permettent pas de restaurer l'autonomie des patients. D'autre part, la fatigue musculaire chez les travailleurs œuvrant dans un environnement éprouvant peut provoquer des blessures et une mauvaise qualité de vie. Bien qu'il existe de nombreux outils pour les aider, l'effort requis peut tout de même être hautement exigeant. Les exosquelettes d’assistance sont bien adaptés pour aider ces deux populations, car ils visent à supporter l'utilisateur en diminuant l'effort nécessaire pour accomplir ses tâches quotidiennes. Le développement de tels dispositifs est une tâche fastidieuse, car les interactions en 3D entre le corps humain et l'exosquelette ainsi que le choix des caractéristiques du système de transmission de puissance, c'est-à-dire les moteurs ou les éléments passifs, sont très complexes et interdépendants. Pour ajouter à cette difficulté, il existe très peu de lignes directrices ou de procédures claires pour soutenir la synthèse géométrique et dynamique d'exosquelettes d’assistance et portable des membres supérieurs. Les paramètres géométriques sont les dimensions de l'exosquelette tandis que les paramètres dynamiques sont les caractéristiques des moteurs et des éléments passifs, tels que des ressorts. L'objectif de ce mémoire de maîtrise est de développer une procédure de synthèse géométrique et dynamique pour soutenir la conception d'un exosquelette de membre supérieur. Tout d'abord, une optimisation géométrique des dimensions de l'exosquelette a permis de maximiser la fermeture de la boucle cinématique et d'éviter les collisions avec les segments du corps tout en réalisant des tâches fonctionnelles spécifiques. Ensuite, grâce à un problème de contrôle optimal, les caractéristiques dynamiques de l'exosquelette ont été obtenues en minimisant les couples articulaires de l'utilisateur pour les mêmes tâches fonctionnelles. Les dimensions optimisées de l'exosquelette ont permis de réussir la fermeture de boucles pour toutes les tâches, soit 10,8 % de plus qu'avec une identification visuelle des dimensions. Quant à eux, les paramètres dynamiques ont pu réduire le couple articulaire de l'utilisateur à moins de 10,6 % des simulations sans exosquelettes pour presque toutes les articulations et les tâches. En conclusion, ces résultats ont montré que la procédure de synthèse était réussie. Cela pourra permettre le développement d'exosquelettes plus légers et plus petits ayant le potentiel d'être commercialisés à court terme. Les perspectives de cette recherche sont de développer une procédure d'optimisation où les paramètres géométriques et dynamiques sont optimisés simultanément et de minimiser les forces musculaires plutôt que les couples articulaires de l'utilisateur pour soutenir des objectifs de design et des objectifs cliniques.----------ABSTRACT Muscular weakness for patients affected by neuromuscular diseases can reduce their ability to realize primordial daily activities such as eating or washing themselves. The available assistance devices offer limited functionalities and do not restore autonomy for the patients. On the other hand, muscular fatigue for workers in tough physical environments can cause injuries and poor quality of life. While there are a lot of tools to help them, the required effort can still be very demanding. Assistive exoskeletons are well suited to help both these populations as they aim to assist the user by lowering the effort necessary to accomplish his everyday tasks. The development of such devices is a tedious task as the 3D human-exoskeleton interactions and the selection of the power transmission system characteristics, i.e. motors or passive elements, are highly complex and interdependent. To add to this complexity, there are very little to no guidelines or clear procedures for supporting the geometric and dynamic synthesis of wearable and assistive upper limb exoskeletons. The geometric parameters are the dimensions of the exoskeleton while the dynamic parameters are the characteristics of motors and passive elements such as springs. The objective of this master thesis was to develop a geometric and dynamic synthesis procedure to support the design of an upper limb exoskeleton. First, a geometric optimization of the exoskeleton dimensions enabled to maximize the kinematic loops closure and to avoid collisions with the body segments while carrying out specific functional tasks. Then, through an optimal control problem, the exoskeleton dynamic characteristics were obtained by minimizing the user joint torques for the same functional tasks. The optimized exoskeleton dimensions could reach loop closure for all tasks, 10.8% more than with a visual identification of the dimensions. The resulting dynamic parameters could reduce the user’s joint torque to less than 10.6% of the human-only simulations for nearly all joints and tasks. To conclude, these results showed that the synthesis procedure was successful. This is important as it can enable the development of lighter and smaller exoskeletons that have the potential to reach commercialization. The future perspectives are to build an optimization framework where the geometric and dynamic parameters are optimized together and to minimize the muscle force instead of the user’s joint torques to support clinical and design purposes