Solutions to trajectory optimization problems are carried out by the direct and indirect methods. Under broad heading of these methods, numerous algorithms such as collocation, direct, indirect and multiple shooting methods have been developed and reported in the literature. Each of these algorithms has certain advantages and limitations. For example, direct shooting technique is not suitable when the number of nonlinear programming variables is large. Indirect shooting method requires analytical derivatives of the control and co-states function and a poorly guessed initial condition can result in numerical unstable values of the adjoint variable. Multiple shooting techniques can alleviate some of these difficulties by breaking down the trajectory into several segments that help in reducing the non-linearity effects of early control on later parts of the trajectory. However, multiple shooting methods then have to handle more number of variables and constraints to satisfy the defects at the segment joints. The sie of the nonlinear programming problem in the collocation method is also large and proper locations of grid points are necessary to satisfy all the path constraints. Stochastic methods such as Genetic algorithms, on the other hand, also require large number of function evaluations before convergence. To overcome some of the limitations of the conventional methods, improved solution techniques are developed. Three improved methods are proposed for the solution of trajectory optimization problems. They are • a genetic algorithm employing dominance and diploidy concept. • a collocation method using chebyshev polynomials , and • a hybrid method that combines collocation and direct shooting technique A conventional binary-coded genetic algorithm uses a haploid chromosome, where a single string contains all the variable information in the coded from. A diploid, as the name suggests, uses pair of chromosomes to store the same characteristic feature. The diploid genetic algorithm uses a dominant map for decoding genotype into a stable, consistent phenotype. In dominance, one allele takes precedence over another. Diploidy and dominance helps in retaining the previous best solution discovered and shields them from harmful selection in a changing environment. Hence, diploid and dominance affect a king of long-term memory in the genetic algorithm. They allow alternate solutions to co-exist. One solution is expressed and the other is held in abeyance. In the improved diploid genetic algorithm, dominant and recessive genes are defined based on the fitness evaluation of each string. The genotype of fittest string is declared as the dominant map. The dominant map is dynamic in nature as it is replaced with a better individual in future generations. The concept of diploidy and dominance in the improved method mimics closer to the principles used in human genetics as compared to any such algorithms reported in the literature. It is observed that the improved diploid genetic algorithm is able to locate the optima for a given trajectory optimization problem with 10% lower computational time as compared to the haploid genetic algorithm. A parameter optimization problem arising from an optimal control problem where states and control are approximated by piecewise Chebyshev polynomials is well known. These polynomials are more accurate than the interpolating segments involving equal spaced data. In the collocation method involving Chebyshev polynomials, derivatives of two neighboring polynomials are matched with the dynamics at the nodal points. This leads to a large number of equality constraints in the optimization problem. In the improved method, derivative of the polynomial is also matched with the dynamics at the center of segments. Though is appears the problem size is merely increased, the additional computations improve the accuracy of the polynomial for a larger segment. The implicit integration step size is enhanced and overall size of the problem is brought down to one-fourth of the problem size defined with a conventional collocation method using Chebyshev polynomials. Hybrid method uses both collocation and direct shooting techniques. Advantages of both the methods are combined to give more synergy. Collocation method is used in the starting phase of the hybrid method. The disadvantage of standalone collocation method is that tuning of grid points is required to satisfy the path constraints. Nevertheless, collocation method does give a good guess required for the terminal phase of the hybrid method, which uses a direct shooting approach. Results show nearly 30% reduction in computation time for the hybrid approach as compared to a method in which direct shooting alone is used, for the same initial guess of control. The solutions obtained from the three improved methods are compared with an indirect method. The indirect method requires derivations of the control and adjoint equations, which are difficult and problem specific. Due to sensitivity of the costate variables, it is often difficult to find a solution through the indirect method. Nevertheless, these methods do provide an accurate result, which defines a benchmark for comparing the solutions obtained through the improved methods. Trajectory design and optimization of a RLV(Reusable Launch Vehicle) Demonstrator mission is considered as a test problem for evaluating the performance of the improved methods. The optimization problem is difficult than a conventional launch vehicle trajectory optimization problem because of the following two reasons. • aerodynamic lift forces in the RLV add one more dimension to the already complex launch vehicle optimization problem. • as RLV performs a sub orbital flight, the ascent phase trajectory influences the re-entry trajectory. Both the ascent and re-entry optimization problem of the RLV mission is addressed. It is observed that the hybrid method gives accurate results with least computational effort, as compared with other improved techniques for the trajectory optimization problem of RLV during its ascent flight. Hybrid method is then successfully used during the re-entry phase and in designing the feasible optimal trajectories under the dispersion conditions. Analytical solutions obtained from literature are used to compare the optimized trajectory during the re-entry phase. Trajectory optimization studies are also carried out for the off-nominal performances. Being a thrusting phase, the ascent trajectory is subjected to significant deviations, mainly arising out of solid booster performance dispersions. The performance index during rhe ascent phase is modified in a novel way for handling dispersions. It minimizes the state errors in a least square sense, defined at the burnout conditions ensure possibilities of safe re-entry trajectories. The optimal trajectories under dispersion conditions serve as a benchmark for validating the closed-loop guidance algorithm that is developed for the ascent phase flight. Finally, an on-line trajectory command-reshaping algorithm is developed which meets the flight objectives under the dispersion conditions. The guidance algorithm uses a pre-computed trajectory database along with some real-time measured parameters in generating the optimal steering profiles. The flight objectives are met under the dispersion conditions and the guidance generated steering profiles matches closely with the optimal trajectories.

Weight growth has been a significant factor in nearly every space and launch vehicle development program. In order to account for weight growth, program managers allocate a design margin. However, methods of estimating design margin are not well suited for the task of assigning a design margin for a novel concept. In order to address this problem, a hybrid method of estimating margin is developed. This hybrid method utilizes range estimating, a well-developed method for conducting a bottom-up weight analysis, and a new forecasting technique known as executable morphological analysis. Executable morphological analysis extends morphological analysis in order to extract quantitative information from the morphological field. Specifically, the morphological field is extended by adding attributes (probability and mass impact) to each condition. This extended morphological field is populated with alternate baseline options with corresponding probabilities of occurrence and impact. The overall impact of alternate baseline options can then be estimated by running a Monte Carlo analysis over the extended morphological field. This methodology was applied to two sample problems. First, the historical design changes of the Space Shuttle Orbiter were evaluated utilizing original mass estimates. Additionally, the FAST reference flight system F served as the basis for a complete sample problem; both range estimating and executable morphological analysis were performed utilizing the work breakdown structure created during the conceptual design of this vehicle.

During its mission, a launch vehicle is subject to broadband, severe, aeroacoustic and structure-borne excitations of various provenances, which can endanger the survivability of the payload and the vehicles electronic equipment, and consequently the success of the mission. Aerospace structures are generally characterized by the use of exotic composite materials of various configurations and thicknesses, as well as by their extensively complex geometries and connections between different subsystems. It is therefore of crucial importance for the modern aerospace industry, the development of analytical and numerical tools that can accurately predict the vibroacoustic response of large, composite structures of various geometries and subject to a combination of aeroacoustic excitations. Recently, a lot of research has been conducted on the modelling of wave propagation characteristics within composite structures. In this study, the Wave Finite Element Method (WFEM) is used in order to predict the wave dispersion characteristics within orthotropic composite structures of various geometries, namely flat panels, singly curved panels, doubly curved panels and cylindrical shells. These characteristics are initially used for predicting the modal density and the coupling loss factor of the structures connected to the acoustic medium. Subsequently the broad-band Transmission Loss (TL) of the modelled structures within a Statistical Energy Analysis (SEA) wave-context approach is calculated. Mainly due to the extensive geometric complexity of structures, the use of Finite Element(FE) modelling within the aerospace industry is frequently inevitable. The use of such models is limited mainly because of the large computation time demanded even for calculations in the low frequency range. During the last years, a lot of researchers focus on the model reduction of large FE models, in order to make their application feasible. In this study, the Second Order ARnoldi (SOAR) reduction approach is adopted, in order to minimize the computation time for a fully coupled composite structural-acoustic system, while at the same time retaining a satisfactory accuracy of the prediction in a broadband sense. The system is modelled under various aeroacoustic excitations, namely a diffused acoustic field and a Turbulent Boundary Layer (TBL) excitation. Experimental validation of the developed tools is conducted on a set of orthotropic sandwich composite structures. Initially, the wave propagation characteristics of a flat panel are measured and the experimental results are compared to the WFEM predictions. The later are used in order to formulate an Equivalent Single Layer (ESL) approach for the modelling of the spatial response of the panel within a dynamic stiffness matrix approach. The effect of the temperature of the structure as well as of the acoustic medium on the vibroacoustic response of the system is examined and analyzed. Subsequently, a model of the SYLDA structure, also made of an orthotropic sandwich material, is tested mainly in order to investigate the coupling nature between its various subsystems. The developed ESL modelling is used for an efficient calculation of the response of the structure in the lower frequency range, while for higher frequencies a hybrid WFEM/FEM formulation for modelling discontinuous structures is used.

La conception de lanceurs est un problème d’optimisation multidisciplinaire dont l’objectif est de trouverl’architecture du lanceur qui garantit une performance optimale tout en assurant un niveau de fiabilité requis.En vue de l’obtention de la solution optimale, les phases d’avant-projet sont cruciales pour le processus deconception et se caractérisent par la présence d’incertitudes dues aux phénomènes physiques impliqués etaux méconnaissances existantes sur les modèles employés. Cette thèse s’intéresse aux méthodes d’analyse et d’optimisation multidisciplinaire en présence d’incertitudes afin d’améliorer le processus de conception de lanceurs. Trois sujets complémentaires sont abordés. Tout d’abord, deux nouvelles formulations du problème de conception ont été proposées afin d’améliorer la prise en compte des interactions disciplinaires. Ensuite, deux nouvelles méthodes d’analyse de fiabilité, permettant de tenir compte d’incertitudes de natures variées, ont été proposées, impliquant des techniques d’échantillonnage préférentiel et des modèles de substitution. Enfin, une nouvelle technique de gestion des contraintes pour l’algorithme d’optimisation ”Covariance Matrix Adaptation - Evolutionary Strategy” a été développée, visant à assurer la faisabilité de la solution optimale. Les approches développées ont été comparées aux techniques proposées dans la littérature sur des cas tests d’analyse et de conception de lanceurs. Les résultats montrent que les approches proposées permettent d’améliorer l’efficacité du processus d’optimisation et la fiabilité de la solution obtenue. / Launch vehicle design is a Multidisciplinary Design Optimization problem whose objective is to find the launch vehicle architecture providing the optimal performance while ensuring the required reliability. In order to obtain an optimal solution, the early design phases are essential for the design process and are characterized by the presence of uncertainty due to the involved physical phenomena and the lack of knowledge on the used models. This thesis is focused on methodologies for multidisciplinary analysis and optimization under uncertainty for launch vehicle design. Three complementary topics are tackled. First, two new formulations have been developed in order to ensure adequate interdisciplinary coupling handling. Then, two new reliability techniques have been proposed in order to take into account the various natures of uncertainty, involving surrogate models and efficient sampling methods. Eventually, a new approach of constraint handling for optimization algorithm ”Covariance Matrix Adaptation - Evolutionary Strategy” has been developed to ensure the feasibility of the optimal solution. All the proposed methods have been compared to existing techniques in literature on analysis and design test cases of launch vehicles. The results illustrate that the proposed approaches allow the improvement of the efficiency of the design process and of the reliability of the found solution.

In a process monitoring/control applications tens to thousands of sensors are used for monitoring system parameters. To achieve overall system goals, their reliable performance is critical. Generally a sensor’s output signal is too small or too noisy and may not be compatible with the input requirements of a Data Acquisition System. The sensor is interfaced to Data Acquisition System, through cabling, junction boxes and Interface Electronics like excitation circuitry, multiplexers, signal-conditioning circuitry etc. An interface or signal conditioning circuit does impedance matching, filtering, multiplexing, pre-amplification, amplification and digitization to make the sensor’s output signal compatible with the Data Acquisition System. Conventional Signal Conditioning includes Multiplexers, Anti aliasing filters, Operational Amplifier, Instrumentation Amplifiers, Isolation Amplifiers and Charge Preamplifiers etc. Operational Amplifiers e.g. voltage followers with High input impedance and low output impedance are used for impedance matching between the sensor and processing electronics. Anti aliasing filters remove noise from the sensor’s output signal. Normally the sensor is located away from the processing electronics and data is transmitted through wires/cables. During transmission, interference from external fields’ especially strong Audio Frequency, Radio Frequency and 50Hz power line fields affects the sensor’s output signal. To minimize the effect of external field twisted pair shielded cables are used. Amplifiers with Differential input configuration are used to suppress the effect of interfering signals. Differential input Instrumentation Amplifiers with High input impedance, high CMRR; are most widely employed. Isolation Amplifiers isolate the input and output circuits by an extremely high impedance. Galvanic, optical isolations are most common. The conditioned data is transmitted to Data Acquisition System (DAS) and at the DAS the signal is multiplexed, filtered and digitized using Analog to Digital Converters (ADCs), followed by Digital Filtering and processing. For Control applications, the processed data is converted back to analog form using Digital to Analog Converters (DACs) for interfacing to external world. The transmission distance varies from tens of centimeters to few meters. Depending upon the distance twisted pair cables, IR transmission and Optical transmission is employed. During transmission, the data is prone to interferences from EMI, EMC, Noise and Signal to Noise ratio (SNR) degradation with distance. This affects the reliability of the system and increases the overall system cost. To eliminate the effects due to the environmental disturbances during transmission and to maintain signal integrity, it is preferred to have a unique and compact solution for each sensor where signal conditioning (excitation, filtering, amplification, compensation and digitization) is carried out and digital data can be transmitted to Data Acquisition System. Here each sensor has its own signal conditioning module. Directly interfacing sensors with micro controller yields simple and compact design solutions. Direct Sensor interface Technology (DSiT) is one of the state of the art technologies for sensor interfaces where an unconditioned, uncompensated, raw output signals from sensors are interfaced directly to a single-chip solution. The sensors’ output are multiplexed using Multiplexer; Amplified using Programmable Gain Amplifier (PGA), digitized using ADC, filtered using Digital Filters and transmitted using Digital Interfaces (SPI, I2C, UART) in a single chip. DSiT scheme incorporates all the elements necessary in an instrumentation system creating a balanced combination of features, to create truly intelligent sensor systems. The sensors are interfaced directly to a single DSiT chip, without any additional circuitry and the direct digital data transmission is achieved with the help of Digital Interfaces SPI, UART, SMBus/I2C. As this involves onchip signal conditioning and digital data transmission, expenditure on additional signal conditioning circuitry, analog interfaces for analog data transmission, separate Analog to Digital Converter for each sensor is reduced. This reduces the overall system cost and as the count of discrete components is reduced the system reliability is improved. In addition, as the data is transmitted digitally the effects of noise, S/N degradation and electromagnetic interferences are eliminated. The accuracy level achieved is sufficiently good for monitoring and control applications. In Launch Vehicles/Satellites number of sensors are used for performance evaluation, monitoring and control purposes. Harnessing, signal conditioning of the sensors’ output and onboard processing of the sensor data is carried out individually for each sensor. Implementation of the DSiT system will reduce the total weight of the launch vehicles and satellites, resulting in reduced overall system cost, increased reliability and reduced onboard processing overhead. In addition, the reduction in weight allows incorporation of larger payloads/ more propellant loading in payloads which increases the life of the Satellites. As it is compact, it can be readily used for facility parameter measurements during the ground testing of liquid engines and stages at LPSC/ISRO. Implementation of DSiT for facility parameter measurements will reduce the cabling cost and improve the reliability of the chain.

In the present thesis, the objective was to find the maximum amount of payload mass that can be put into a 500 km polar orbit by a 1400 kg air-launched multi-stage rocket launched from a fighter jet platform. To fulfill the objective an algorithm incorporating several modules was developed. The modules performed calculations based on theoretical models and literature values to arrive at optimal design variables. From the design the maximum payload mass was able to be derived and it was concluded that a three-stage launch vehicle was able to deliver a 22.0 kg payload to the desired orbit. / I den här avhandlingen var syftet att hitta den maximala mängden nyttolastmassa som kan transporteras av en 1400 kg flerstegsraket uppskjuten från luften till en 500 km polär bana. För att uppfylla målet utvecklades en algoritm med flera moduler. Modulerna utförde beräkningar baserade på teoretiska modeller och litteraturvärden för att komma fram till optimala designvariabler. Från konstruktionen kunde den maximala nyttolastmassan härledas och det konstaterades att en trestegsraket kunde leverera en nyttolast på 22.0 kg till den önskade omloppsbanan.

In the present thesis, the objective was to find the maximum amount of payload mass that can be put into a 500 km polar orbit by a 1400 kg air-launched multi-stage rocket launched from a fighter jet platform. To fulfill the objective an algorithm incorporating several modules was developed. The modules performed calculations based on theoretical models and literature values to arrive at optimal design variables. From the design the maximum payload mass was able to be derived and it was concluded that a three-stage launch vehicle was able to deliver a 22.0 kg payload to the desired orbit. / I den här avhandlingen var syftet att hitta den maximala mängden nyttolastmassa som kan transporteras av en 1400 kg flerstegsraket uppskjuten från luften till en 500 km polär bana. För att uppfylla målet utvecklades en algoritm med flera moduler. Modulerna utförde beräkningar baserade på teoretiska modeller och litteraturvärden för att komma fram till optimala designvariabler. Från konstruktionen kunde den maximala nyttolastmassan härledas och det konstaterades att en trestegsraket kunde leverera en nyttolast på 22.0 kg till den önskade omloppsbanan.

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A satellite launch vehicle not subjected to any perturbations, external or internal, could be guided along a trajectory by following a stored, pre-computed steering program. In practice, perturbations do occur, and in order to take account of them and to achieve an accurate injection, a closed loop guidance system is required. Guidance algorithm is developed by solving the optimal control problem. Closed form solution is difficult because the necessary conditions are in the form of Two Point Boundary Value Problems (TBVP) or Multi Point Boundary Value Problems (MPBVP). Development of non-iterative guidance algorithm is taken as a prime objective of this thesis to ensure reliable on-board implementation. If non-iterative algorithms are required, the usual practice is to approximate the system equations to derive closed form solutions. In the present work, approximations cannot be used because the algorithm has to cater to a wide variety of vehicles and missions. Present development adopts an alternate approach by splitting the reconfigurable algorithm development in to smaller sub-problems such that each sub-problem has closed form solution. The splitting is done in such a way that the solution of the sub-problems can be used as building blocks to construct the final solution. By adding or removing the building blocks, the algorithm can be configured to suit specific requirements. Chapter 1 discusses the motivation and objectives of the thesis and gives a literature survey. In chapter 2, Classical Flat Earth (CFE) guidance algorithm is discussed. The assumptions and the nature of solution are closely analyzed because CFE guidance is used as the baseline for further developments. New contribution in chapter 2 is the extension of CFE guidance for a generalized propulsion system in which liquid and solid engines are present. In chapter 3, CFE guidance is applied for a mission with large pitch steering angles. The result shows loss of optimality and performance. An algorithm based on regular perturbation is developed to compensate for the small angle approximation. The new contribution in chapter 3 is the development of Regular Perturbation based FE (RPFE) guidance as an extension of CFE guidance. RPFE guidance can be configured as CFE guidance and FEGP. Algorithms presented up to chapter 3 are developed to inject a satellite in to orbits with unspecified inertial orientation. Communication satellite missions demand injection in to an orbit with a specific inertial orientation defined by argument of perigee. This problem is formulated using Calculus of Variations in chapter 4. A non-iterative closed form solution (Predicted target Flat Earth or PFE guidance) is derived for this problem. In chapter 5, PFE guidance is extended to a multi-stage vehicle with a constraint on the impact point of spent lower stage. Since the problem is not analytically solvable, the original problem is split in to three sub-problems and solved. Chapter 6 has two parts. First part gives theoretical analysis of the sub-optimal strategies with special emphasis to guidance. Behavior of predicted terminal error and control commands in presence of plant approximations are theoretically analyzed for a class of optimal control problems and the results are presented as six theorems. Chapter 7 presents the conclusions and future works.

A framework is proposed that combines separately developed multidisciplinary optimization, multi-objective optimization, and joint probability assessment methods together but in a decoupled way, to solve joint probabilistic constraint, multi-objective, multidisciplinary optimization problems that are representative of realistic conceptual design problems of design alternative generation and selection. The intent here is to find the Weak Pareto Frontier (WPF) solutions that include additional compromised solutions besides the ones identified by a conventional Pareto frontier. This framework starts with constructing fast and accurate surrogate models of different disciplinary analyses. A new hybrid method is formed that consists of the second order Response Surface Methodology (RSM) and the Support Vector Regression (SVR) method. The three parameters needed by SVR to be pre-specified are automatically selected using a modified information criterion based on model fitting error, predicting error, and model complexity information. The model predicting error is estimated inexpensively with a new method called Random Cross Validation. This modified information criterion is also used to select the best surrogate model for a given problem out of the RSM, SVR, and the hybrid methods. A new neighborhood search method based on Monte Carlo simulation is proposed to find valid designs that satisfy the deterministic constraints and are consistent for the coupling variables featured in a multidisciplinary design problem, and at the same time decouple the three loops required by the multidisciplinary, multi-objective, and probabilistic features. Two schemes have been developed. One scheme finds the WPF by finding a large enough number of valid design solutions such that some WPF solutions are included in those valid solutions. Another scheme finds the WPF by directly finding the WPF of each consistent design zone. Then the probabilities of the PCs are estimated, and the WPF and corresponding design solutions are found. Various examples demonstrate the feasibility of this framework.